/*-------------------------------------------------------------------------
 *
 * nbtinsert.c
 *	  Item insertion in Lehman and Yao btrees for Postgres.
 *
 * Portions Copyright (c) 1996-2019, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *	  src/backend/access/nbtree/nbtinsert.c
 *
 *-------------------------------------------------------------------------
 */

#include "postgres.h"

#include "access/nbtree.h"
#include "access/nbtxlog.h"
#include "access/tableam.h"
#include "access/transam.h"
#include "access/xloginsert.h"
#include "miscadmin.h"
#include "storage/lmgr.h"
#include "storage/predicate.h"
#include "storage/smgr.h"

/* Minimum tree height for application of fastpath optimization */
#define BTREE_FASTPATH_MIN_LEVEL	2


static Buffer _bt_newroot(Relation rel, Buffer lbuf, Buffer rbuf);

static TransactionId _bt_check_unique(Relation rel, BTInsertState insertstate,
				 Relation heapRel,
				 IndexUniqueCheck checkUnique, bool *is_unique,
				 uint32 *speculativeToken);
static OffsetNumber _bt_findinsertloc(Relation rel,
				  BTInsertState insertstate,
				  bool checkingunique,
				  BTStack stack,
				  Relation heapRel);
static void _bt_stepright(Relation rel, BTInsertState insertstate, BTStack stack);
static void _bt_insertonpg(Relation rel, BTScanInsert itup_key,
			   Buffer buf,
			   Buffer cbuf,
			   BTStack stack,
			   IndexTuple itup,
			   OffsetNumber newitemoff,
			   bool split_only_page);
static Buffer _bt_split(Relation rel, BTScanInsert itup_key, Buffer buf,
		  Buffer cbuf, OffsetNumber firstright, OffsetNumber newitemoff,
		  Size newitemsz, IndexTuple newitem, bool newitemonleft);
static void _bt_insert_parent(Relation rel, Buffer buf, Buffer rbuf,
				  BTStack stack, bool is_root, bool is_only);
static bool _bt_pgaddtup(Page page, Size itemsize, IndexTuple itup,
			 OffsetNumber itup_off);
static bool _bt_isequal(TupleDesc itupdesc, BTScanInsert itup_key,
			Page page, OffsetNumber offnum);
static void _bt_vacuum_one_page(Relation rel, Buffer buffer, Relation heapRel);

/*
 *	_bt_doinsert() -- Handle insertion of a single index tuple in the tree.
 *
 *		This routine is called by the public interface routine, btinsert.
 *		By here, itup is filled in, including the TID.
 *
 *		If checkUnique is UNIQUE_CHECK_NO or UNIQUE_CHECK_PARTIAL, this
 *		will allow duplicates.  Otherwise (UNIQUE_CHECK_YES or
 *		UNIQUE_CHECK_EXISTING) it will throw error for a duplicate.
 *		For UNIQUE_CHECK_EXISTING we merely run the duplicate check, and
 *		don't actually insert.
 *
 *		The result value is only significant for UNIQUE_CHECK_PARTIAL:
 *		it must be true if the entry is known unique, else false.
 *		(In the current implementation we'll also return true after a
 *		successful UNIQUE_CHECK_YES or UNIQUE_CHECK_EXISTING call, but
 *		that's just a coding artifact.)
 */
bool
_bt_doinsert(Relation rel, IndexTuple itup,
			 IndexUniqueCheck checkUnique, Relation heapRel)
{
	bool		is_unique = false;
	BTInsertStateData insertstate;
	BTScanInsert itup_key;
	BTStack		stack = NULL;
	Buffer		buf;
	bool		fastpath;
	bool		checkingunique = (checkUnique != UNIQUE_CHECK_NO);

	/* we need an insertion scan key to do our search, so build one */
	itup_key = _bt_mkscankey(rel, itup);
	/* No scantid until uniqueness established in checkingunique case */
	if (checkingunique && itup_key->heapkeyspace)
		itup_key->scantid = NULL;

	/*
	 * Fill in the BTInsertState working area, to track the current page and
	 * position within the page to insert on
	 */
	insertstate.itup = itup;
	/* PageAddItem will MAXALIGN(), but be consistent */
	insertstate.itemsz = MAXALIGN(IndexTupleSize(itup));
	insertstate.itup_key = itup_key;
	insertstate.bounds_valid = false;
	insertstate.buf = InvalidBuffer;

	/*
	 * It's very common to have an index on an auto-incremented or
	 * monotonically increasing value. In such cases, every insertion happens
	 * towards the end of the index. We try to optimize that case by caching
	 * the right-most leaf of the index. If our cached block is still the
	 * rightmost leaf, has enough free space to accommodate a new entry and
	 * the insertion key is strictly greater than the first key in this page,
	 * then we can safely conclude that the new key will be inserted in the
	 * cached block. So we simply search within the cached block and insert
	 * the key at the appropriate location. We call it a fastpath.
	 *
	 * Testing has revealed, though, that the fastpath can result in increased
	 * contention on the exclusive-lock on the rightmost leaf page. So we
	 * conditionally check if the lock is available. If it's not available
	 * then we simply abandon the fastpath and take the regular path. This
	 * makes sense because unavailability of the lock also signals that some
	 * other backend might be concurrently inserting into the page, thus
	 * reducing our chances to finding an insertion place in this page.
	 */
top:
	fastpath = false;
	if (RelationGetTargetBlock(rel) != InvalidBlockNumber)
	{
		Page		page;
		BTPageOpaque lpageop;

		/*
		 * Conditionally acquire exclusive lock on the buffer before doing any
		 * checks. If we don't get the lock, we simply follow slowpath. If we
		 * do get the lock, this ensures that the index state cannot change,
		 * as far as the rightmost part of the index is concerned.
		 */
		buf = ReadBuffer(rel, RelationGetTargetBlock(rel));

		if (ConditionalLockBuffer(buf))
		{
			_bt_checkpage(rel, buf);

			page = BufferGetPage(buf);

			lpageop = (BTPageOpaque) PageGetSpecialPointer(page);

			/*
			 * Check if the page is still the rightmost leaf page, has enough
			 * free space to accommodate the new tuple, and the insertion scan
			 * key is strictly greater than the first key on the page.
			 */
			if (P_ISLEAF(lpageop) && P_RIGHTMOST(lpageop) &&
				!P_IGNORE(lpageop) &&
				(PageGetFreeSpace(page) > insertstate.itemsz) &&
				PageGetMaxOffsetNumber(page) >= P_FIRSTDATAKEY(lpageop) &&
				_bt_compare(rel, itup_key, page, P_FIRSTDATAKEY(lpageop)) > 0)
			{
				/*
				 * The right-most block should never have an incomplete split.
				 * But be paranoid and check for it anyway.
				 */
				Assert(!P_INCOMPLETE_SPLIT(lpageop));
				fastpath = true;
			}
			else
			{
				_bt_relbuf(rel, buf);

				/*
				 * Something did not work out. Just forget about the cached
				 * block and follow the normal path. It might be set again if
				 * the conditions are favourable.
				 */
				RelationSetTargetBlock(rel, InvalidBlockNumber);
			}
		}
		else
		{
			ReleaseBuffer(buf);

			/*
			 * If someone's holding a lock, it's likely to change anyway, so
			 * don't try again until we get an updated rightmost leaf.
			 */
			RelationSetTargetBlock(rel, InvalidBlockNumber);
		}
	}

	if (!fastpath)
	{
		/*
		 * Find the first page containing this key.  Buffer returned by
		 * _bt_search() is locked in exclusive mode.
		 */
		stack = _bt_search(rel, itup_key, &buf, BT_WRITE, NULL);
	}

	insertstate.buf = buf;
	buf = InvalidBuffer;		/* insertstate.buf now owns the buffer */

	/*
	 * If we're not allowing duplicates, make sure the key isn't already in
	 * the index.
	 *
	 * NOTE: obviously, _bt_check_unique can only detect keys that are already
	 * in the index; so it cannot defend against concurrent insertions of the
	 * same key.  We protect against that by means of holding a write lock on
	 * the first page the value could be on, regardless of the value of its
	 * implicit heap TID tiebreaker attribute.  Any other would-be inserter of
	 * the same key must acquire a write lock on the same page, so only one
	 * would-be inserter can be making the check at one time.  Furthermore,
	 * once we are past the check we hold write locks continuously until we
	 * have performed our insertion, so no later inserter can fail to see our
	 * insertion.  (This requires some care in _bt_findinsertloc.)
	 *
	 * If we must wait for another xact, we release the lock while waiting,
	 * and then must start over completely.
	 *
	 * For a partial uniqueness check, we don't wait for the other xact. Just
	 * let the tuple in and return false for possibly non-unique, or true for
	 * definitely unique.
	 */
	if (checkingunique)
	{
		TransactionId xwait;
		uint32		speculativeToken;

		xwait = _bt_check_unique(rel, &insertstate, heapRel, checkUnique,
								 &is_unique, &speculativeToken);

		if (TransactionIdIsValid(xwait))
		{
			/* Have to wait for the other guy ... */
			_bt_relbuf(rel, insertstate.buf);
			insertstate.buf = InvalidBuffer;

			/*
			 * If it's a speculative insertion, wait for it to finish (ie. to
			 * go ahead with the insertion, or kill the tuple).  Otherwise
			 * wait for the transaction to finish as usual.
			 */
			if (speculativeToken)
				SpeculativeInsertionWait(xwait, speculativeToken);
			else
				XactLockTableWait(xwait, rel, &itup->t_tid, XLTW_InsertIndex);

			/* start over... */
			if (stack)
				_bt_freestack(stack);
			goto top;
		}

		/* Uniqueness is established -- restore heap tid as scantid */
		if (itup_key->heapkeyspace)
			itup_key->scantid = &itup->t_tid;
	}

	if (checkUnique != UNIQUE_CHECK_EXISTING)
	{
		OffsetNumber newitemoff;

		/*
		 * The only conflict predicate locking cares about for indexes is when
		 * an index tuple insert conflicts with an existing lock.  We don't
		 * know the actual page we're going to insert to yet because scantid
		 * was not filled in initially, but it's okay to use the "first valid"
		 * page instead.  This reasoning also applies to INCLUDE indexes,
		 * whose extra attributes are not considered part of the key space.
		 */
		CheckForSerializableConflictIn(rel, NULL, insertstate.buf);

		/*
		 * Do the insertion.  Note that insertstate contains cached binary
		 * search bounds established within _bt_check_unique when insertion is
		 * checkingunique.
		 */
		newitemoff = _bt_findinsertloc(rel, &insertstate, checkingunique,
									   stack, heapRel);
		_bt_insertonpg(rel, itup_key, insertstate.buf, InvalidBuffer, stack,
					   itup, newitemoff, false);
	}
	else
	{
		/* just release the buffer */
		_bt_relbuf(rel, insertstate.buf);
	}

	/* be tidy */
	if (stack)
		_bt_freestack(stack);
	pfree(itup_key);

	return is_unique;
}

/*
 *	_bt_check_unique() -- Check for violation of unique index constraint
 *
 * Returns InvalidTransactionId if there is no conflict, else an xact ID
 * we must wait for to see if it commits a conflicting tuple.   If an actual
 * conflict is detected, no return --- just ereport().  If an xact ID is
 * returned, and the conflicting tuple still has a speculative insertion in
 * progress, *speculativeToken is set to non-zero, and the caller can wait for
 * the verdict on the insertion using SpeculativeInsertionWait().
 *
 * However, if checkUnique == UNIQUE_CHECK_PARTIAL, we always return
 * InvalidTransactionId because we don't want to wait.  In this case we
 * set *is_unique to false if there is a potential conflict, and the
 * core code must redo the uniqueness check later.
 *
 * As a side-effect, sets state in insertstate that can later be used by
 * _bt_findinsertloc() to reuse most of the binary search work we do
 * here.
 */
static TransactionId
_bt_check_unique(Relation rel, BTInsertState insertstate, Relation heapRel,
				 IndexUniqueCheck checkUnique, bool *is_unique,
				 uint32 *speculativeToken)
{
	TupleDesc	itupdesc = RelationGetDescr(rel);
	IndexTuple	itup = insertstate->itup;
	BTScanInsert itup_key = insertstate->itup_key;
	SnapshotData SnapshotDirty;
	OffsetNumber offset;
	OffsetNumber maxoff;
	Page		page;
	BTPageOpaque opaque;
	Buffer		nbuf = InvalidBuffer;
	bool		found = false;

	/* Assume unique until we find a duplicate */
	*is_unique = true;

	InitDirtySnapshot(SnapshotDirty);

	page = BufferGetPage(insertstate->buf);
	opaque = (BTPageOpaque) PageGetSpecialPointer(page);
	maxoff = PageGetMaxOffsetNumber(page);

	/*
	 * Find the first tuple with the same key.
	 *
	 * This also saves the binary search bounds in insertstate.  We use them
	 * in the fastpath below, but also in the _bt_findinsertloc() call later.
	 */
	offset = _bt_binsrch_insert(rel, insertstate);

	/*
	 * Scan over all equal tuples, looking for live conflicts.
	 */
	Assert(!insertstate->bounds_valid || insertstate->low == offset);
	Assert(itup_key->scantid == NULL);
	for (;;)
	{
		ItemId		curitemid;
		IndexTuple	curitup;
		BlockNumber nblkno;

		/*
		 * make sure the offset points to an actual item before trying to
		 * examine it...
		 */
		if (offset <= maxoff)
		{
			/*
			 * Fastpath: In most cases, we can use cached search bounds to
			 * limit our consideration to items that are definitely
			 * duplicates.  This fastpath doesn't apply when the original page
			 * is empty, or when initial offset is past the end of the
			 * original page, which may indicate that we need to examine a
			 * second or subsequent page.
			 *
			 * Note that this optimization avoids calling _bt_isequal()
			 * entirely when there are no duplicates, as long as the offset
			 * where the key will go is not at the end of the page.
			 */
			if (nbuf == InvalidBuffer && offset == insertstate->stricthigh)
			{
				Assert(insertstate->bounds_valid);
				Assert(insertstate->low >= P_FIRSTDATAKEY(opaque));
				Assert(insertstate->low <= insertstate->stricthigh);
				Assert(!_bt_isequal(itupdesc, itup_key, page, offset));
				break;
			}

			curitemid = PageGetItemId(page, offset);

			/*
			 * We can skip items that are marked killed.
			 *
			 * In the presence of heavy update activity an index may contain
			 * many killed items with the same key; running _bt_isequal() on
			 * each killed item gets expensive.  Just advance over killed
			 * items as quickly as we can.  We only apply _bt_isequal() when
			 * we get to a non-killed item.  Even those comparisons could be
			 * avoided (in the common case where there is only one page to
			 * visit) by reusing bounds, but just skipping dead items is fast
			 * enough.
			 */
			if (!ItemIdIsDead(curitemid))
			{
				ItemPointerData htid;
				bool		all_dead;

				/*
				 * _bt_compare returns 0 for (1,NULL) and (1,NULL) - this's
				 * how we handling NULLs - and so we must not use _bt_compare
				 * in real comparison, but only for ordering/finding items on
				 * pages. - vadim 03/24/97
				 */
				if (!_bt_isequal(itupdesc, itup_key, page, offset))
					break;		/* we're past all the equal tuples */

				/* okay, we gotta fetch the heap tuple ... */
				curitup = (IndexTuple) PageGetItem(page, curitemid);
				htid = curitup->t_tid;

				/*
				 * If we are doing a recheck, we expect to find the tuple we
				 * are rechecking.  It's not a duplicate, but we have to keep
				 * scanning.
				 */
				if (checkUnique == UNIQUE_CHECK_EXISTING &&
					ItemPointerCompare(&htid, &itup->t_tid) == 0)
				{
					found = true;
				}

				/*
				 * Check if there's any table tuples for this index entry
				 * satisfying SnapshotDirty. This is necessary because for AMs
				 * with optimizations like heap's HOT, we have just a single
				 * index entry for the entire chain.
				 */
				else if (table_index_fetch_tuple_check(heapRel, &htid,
													   &SnapshotDirty,
													   &all_dead))
				{
					TransactionId xwait;

					/*
					 * It is a duplicate. If we are only doing a partial
					 * check, then don't bother checking if the tuple is being
					 * updated in another transaction. Just return the fact
					 * that it is a potential conflict and leave the full
					 * check till later.
					 */
					if (checkUnique == UNIQUE_CHECK_PARTIAL)
					{
						if (nbuf != InvalidBuffer)
							_bt_relbuf(rel, nbuf);
						*is_unique = false;
						return InvalidTransactionId;
					}

					/*
					 * If this tuple is being updated by other transaction
					 * then we have to wait for its commit/abort.
					 */
					xwait = (TransactionIdIsValid(SnapshotDirty.xmin)) ?
						SnapshotDirty.xmin : SnapshotDirty.xmax;

					if (TransactionIdIsValid(xwait))
					{
						if (nbuf != InvalidBuffer)
							_bt_relbuf(rel, nbuf);
						/* Tell _bt_doinsert to wait... */
						*speculativeToken = SnapshotDirty.speculativeToken;
						return xwait;
					}

					/*
					 * Otherwise we have a definite conflict.  But before
					 * complaining, look to see if the tuple we want to insert
					 * is itself now committed dead --- if so, don't complain.
					 * This is a waste of time in normal scenarios but we must
					 * do it to support CREATE INDEX CONCURRENTLY.
					 *
					 * We must follow HOT-chains here because during
					 * concurrent index build, we insert the root TID though
					 * the actual tuple may be somewhere in the HOT-chain.
					 * While following the chain we might not stop at the
					 * exact tuple which triggered the insert, but that's OK
					 * because if we find a live tuple anywhere in this chain,
					 * we have a unique key conflict.  The other live tuple is
					 * not part of this chain because it had a different index
					 * entry.
					 */
					htid = itup->t_tid;
					if (table_index_fetch_tuple_check(heapRel, &htid,
													  SnapshotSelf, NULL))
					{
						/* Normal case --- it's still live */
					}
					else
					{
						/*
						 * It's been deleted, so no error, and no need to
						 * continue searching
						 */
						break;
					}

					/*
					 * Check for a conflict-in as we would if we were going to
					 * write to this page.  We aren't actually going to write,
					 * but we want a chance to report SSI conflicts that would
					 * otherwise be masked by this unique constraint
					 * violation.
					 */
					CheckForSerializableConflictIn(rel, NULL, insertstate->buf);

					/*
					 * This is a definite conflict.  Break the tuple down into
					 * datums and report the error.  But first, make sure we
					 * release the buffer locks we're holding ---
					 * BuildIndexValueDescription could make catalog accesses,
					 * which in the worst case might touch this same index and
					 * cause deadlocks.
					 */
					if (nbuf != InvalidBuffer)
						_bt_relbuf(rel, nbuf);
					_bt_relbuf(rel, insertstate->buf);
					insertstate->buf = InvalidBuffer;

					{
						Datum		values[INDEX_MAX_KEYS];
						bool		isnull[INDEX_MAX_KEYS];
						char	   *key_desc;

						index_deform_tuple(itup, RelationGetDescr(rel),
										   values, isnull);

						key_desc = BuildIndexValueDescription(rel, values,
															  isnull);

						ereport(ERROR,
								(errcode(ERRCODE_UNIQUE_VIOLATION),
								 errmsg("duplicate key value violates unique constraint \"%s\"",
										RelationGetRelationName(rel)),
								 key_desc ? errdetail("Key %s already exists.",
													  key_desc) : 0,
								 errtableconstraint(heapRel,
													RelationGetRelationName(rel))));
					}
				}
				else if (all_dead)
				{
					/*
					 * The conflicting tuple (or whole HOT chain) is dead to
					 * everyone, so we may as well mark the index entry
					 * killed.
					 */
					ItemIdMarkDead(curitemid);
					opaque->btpo_flags |= BTP_HAS_GARBAGE;

					/*
					 * Mark buffer with a dirty hint, since state is not
					 * crucial. Be sure to mark the proper buffer dirty.
					 */
					if (nbuf != InvalidBuffer)
						MarkBufferDirtyHint(nbuf, true);
					else
						MarkBufferDirtyHint(insertstate->buf, true);
				}
			}
		}

		/*
		 * Advance to next tuple to continue checking.
		 */
		if (offset < maxoff)
			offset = OffsetNumberNext(offset);
		else
		{
			int			highkeycmp;

			/* If scankey == hikey we gotta check the next page too */
			if (P_RIGHTMOST(opaque))
				break;
			highkeycmp = _bt_compare(rel, itup_key, page, P_HIKEY);
			Assert(highkeycmp <= 0);
			if (highkeycmp != 0)
				break;
			/* Advance to next non-dead page --- there must be one */
			for (;;)
			{
				nblkno = opaque->btpo_next;
				nbuf = _bt_relandgetbuf(rel, nbuf, nblkno, BT_READ);
				page = BufferGetPage(nbuf);
				opaque = (BTPageOpaque) PageGetSpecialPointer(page);
				if (!P_IGNORE(opaque))
					break;
				if (P_RIGHTMOST(opaque))
					elog(ERROR, "fell off the end of index \"%s\"",
						 RelationGetRelationName(rel));
			}
			maxoff = PageGetMaxOffsetNumber(page);
			offset = P_FIRSTDATAKEY(opaque);
		}
	}

	/*
	 * If we are doing a recheck then we should have found the tuple we are
	 * checking.  Otherwise there's something very wrong --- probably, the
	 * index is on a non-immutable expression.
	 */
	if (checkUnique == UNIQUE_CHECK_EXISTING && !found)
		ereport(ERROR,
				(errcode(ERRCODE_INTERNAL_ERROR),
				 errmsg("failed to re-find tuple within index \"%s\"",
						RelationGetRelationName(rel)),
				 errhint("This may be because of a non-immutable index expression."),
				 errtableconstraint(heapRel,
									RelationGetRelationName(rel))));

	if (nbuf != InvalidBuffer)
		_bt_relbuf(rel, nbuf);

	return InvalidTransactionId;
}


/*
 *	_bt_findinsertloc() -- Finds an insert location for a tuple
 *
 *		On entry, insertstate buffer contains the page the new tuple belongs
 *		on.  It is exclusive-locked and pinned by the caller.
 *
 *		If 'checkingunique' is true, the buffer on entry is the first page
 *		that contains duplicates of the new key.  If there are duplicates on
 *		multiple pages, the correct insertion position might be some page to
 *		the right, rather than the first page.  In that case, this function
 *		moves right to the correct target page.
 *
 *		(In a !heapkeyspace index, there can be multiple pages with the same
 *		high key, where the new tuple could legitimately be placed on.  In
 *		that case, the caller passes the first page containing duplicates,
 *		just like when checkinunique=true.  If that page doesn't have enough
 *		room for the new tuple, this function moves right, trying to find a
 *		legal page that does.)
 *
 *		On exit, insertstate buffer contains the chosen insertion page, and
 *		the offset within that page is returned.  If _bt_findinsertloc needed
 *		to move right, the lock and pin on the original page are released, and
 *		the new buffer is exclusively locked and pinned instead.
 *
 *		If insertstate contains cached binary search bounds, we will take
 *		advantage of them.  This avoids repeating comparisons that we made in
 *		_bt_check_unique() already.
 *
 *		If there is not enough room on the page for the new tuple, we try to
 *		make room by removing any LP_DEAD tuples.
 */
static OffsetNumber
_bt_findinsertloc(Relation rel,
				  BTInsertState insertstate,
				  bool checkingunique,
				  BTStack stack,
				  Relation heapRel)
{
	BTScanInsert itup_key = insertstate->itup_key;
	Page		page = BufferGetPage(insertstate->buf);
	BTPageOpaque lpageop;

	lpageop = (BTPageOpaque) PageGetSpecialPointer(page);

	/* Check 1/3 of a page restriction */
	if (unlikely(insertstate->itemsz > BTMaxItemSize(page)))
		_bt_check_third_page(rel, heapRel, itup_key->heapkeyspace, page,
							 insertstate->itup);

	Assert(P_ISLEAF(lpageop) && !P_INCOMPLETE_SPLIT(lpageop));
	Assert(!insertstate->bounds_valid || checkingunique);
	Assert(!itup_key->heapkeyspace || itup_key->scantid != NULL);
	Assert(itup_key->heapkeyspace || itup_key->scantid == NULL);

	if (itup_key->heapkeyspace)
	{
		/*
		 * If we're inserting into a unique index, we may have to walk right
		 * through leaf pages to find the one leaf page that we must insert on
		 * to.
		 *
		 * This is needed for checkingunique callers because a scantid was not
		 * used when we called _bt_search().  scantid can only be set after
		 * _bt_check_unique() has checked for duplicates.  The buffer
		 * initially stored in insertstate->buf has the page where the first
		 * duplicate key might be found, which isn't always the page that new
		 * tuple belongs on.  The heap TID attribute for new tuple (scantid)
		 * could force us to insert on a sibling page, though that should be
		 * very rare in practice.
		 */
		if (checkingunique)
		{
			for (;;)
			{
				/*
				 * Does the new tuple belong on this page?
				 *
				 * The earlier _bt_check_unique() call may well have
				 * established a strict upper bound on the offset for the new
				 * item.  If it's not the last item of the page (i.e. if there
				 * is at least one tuple on the page that goes after the tuple
				 * we're inserting) then we know that the tuple belongs on
				 * this page.  We can skip the high key check.
				 */
				if (insertstate->bounds_valid &&
					insertstate->low <= insertstate->stricthigh &&
					insertstate->stricthigh <= PageGetMaxOffsetNumber(page))
					break;

				/* Test '<=', not '!=', since scantid is set now */
				if (P_RIGHTMOST(lpageop) ||
					_bt_compare(rel, itup_key, page, P_HIKEY) <= 0)
					break;

				_bt_stepright(rel, insertstate, stack);
				/* Update local state after stepping right */
				page = BufferGetPage(insertstate->buf);
				lpageop = (BTPageOpaque) PageGetSpecialPointer(page);
			}
		}

		/*
		 * If the target page is full, see if we can obtain enough space by
		 * erasing LP_DEAD items
		 */
		if (PageGetFreeSpace(page) < insertstate->itemsz &&
			P_HAS_GARBAGE(lpageop))
		{
			_bt_vacuum_one_page(rel, insertstate->buf, heapRel);
			insertstate->bounds_valid = false;
		}
	}
	else
	{
		/*----------
		 * This is a !heapkeyspace (version 2 or 3) index.  The current page
		 * is the first page that we could insert the new tuple to, but there
		 * may be other pages to the right that we could opt to use instead.
		 *
		 * If the new key is equal to one or more existing keys, we can
		 * legitimately place it anywhere in the series of equal keys.  In
		 * fact, if the new key is equal to the page's "high key" we can place
		 * it on the next page.  If it is equal to the high key, and there's
		 * not room to insert the new tuple on the current page without
		 * splitting, then we move right hoping to find more free space and
		 * avoid a split.
		 *
		 * Keep scanning right until we
		 *		(a) find a page with enough free space,
		 *		(b) reach the last page where the tuple can legally go, or
		 *		(c) get tired of searching.
		 * (c) is not flippant; it is important because if there are many
		 * pages' worth of equal keys, it's better to split one of the early
		 * pages than to scan all the way to the end of the run of equal keys
		 * on every insert.  We implement "get tired" as a random choice,
		 * since stopping after scanning a fixed number of pages wouldn't work
		 * well (we'd never reach the right-hand side of previously split
		 * pages).  The probability of moving right is set at 0.99, which may
		 * seem too high to change the behavior much, but it does an excellent
		 * job of preventing O(N^2) behavior with many equal keys.
		 *----------
		 */
		while (PageGetFreeSpace(page) < insertstate->itemsz)
		{
			/*
			 * Before considering moving right, see if we can obtain enough
			 * space by erasing LP_DEAD items
			 */
			if (P_HAS_GARBAGE(lpageop))
			{
				_bt_vacuum_one_page(rel, insertstate->buf, heapRel);
				insertstate->bounds_valid = false;

				if (PageGetFreeSpace(page) >= insertstate->itemsz)
					break;		/* OK, now we have enough space */
			}

			/*
			 * Nope, so check conditions (b) and (c) enumerated above
			 *
			 * The earlier _bt_check_unique() call may well have established a
			 * strict upper bound on the offset for the new item.  If it's not
			 * the last item of the page (i.e. if there is at least one tuple
			 * on the page that's greater than the tuple we're inserting to)
			 * then we know that the tuple belongs on this page.  We can skip
			 * the high key check.
			 */
			if (insertstate->bounds_valid &&
				insertstate->low <= insertstate->stricthigh &&
				insertstate->stricthigh <= PageGetMaxOffsetNumber(page))
				break;

			if (P_RIGHTMOST(lpageop) ||
				_bt_compare(rel, itup_key, page, P_HIKEY) != 0 ||
				random() <= (MAX_RANDOM_VALUE / 100))
				break;

			_bt_stepright(rel, insertstate, stack);
			/* Update local state after stepping right */
			page = BufferGetPage(insertstate->buf);
			lpageop = (BTPageOpaque) PageGetSpecialPointer(page);
		}
	}

	/*
	 * We should now be on the correct page.  Find the offset within the page
	 * for the new tuple. (Possibly reusing earlier search bounds.)
	 */
	Assert(P_RIGHTMOST(lpageop) ||
		   _bt_compare(rel, itup_key, page, P_HIKEY) <= 0);

	return _bt_binsrch_insert(rel, insertstate);
}

/*
 * Step right to next non-dead page, during insertion.
 *
 * This is a bit more complicated than moving right in a search.  We must
 * write-lock the target page before releasing write lock on current page;
 * else someone else's _bt_check_unique scan could fail to see our insertion.
 * Write locks on intermediate dead pages won't do because we don't know when
 * they will get de-linked from the tree.
 *
 * This is more aggressive than it needs to be for non-unique !heapkeyspace
 * indexes.
 */
static void
_bt_stepright(Relation rel, BTInsertState insertstate, BTStack stack)
{
	Page		page;
	BTPageOpaque lpageop;
	Buffer		rbuf;
	BlockNumber rblkno;

	page = BufferGetPage(insertstate->buf);
	lpageop = (BTPageOpaque) PageGetSpecialPointer(page);

	rbuf = InvalidBuffer;
	rblkno = lpageop->btpo_next;
	for (;;)
	{
		rbuf = _bt_relandgetbuf(rel, rbuf, rblkno, BT_WRITE);
		page = BufferGetPage(rbuf);
		lpageop = (BTPageOpaque) PageGetSpecialPointer(page);

		/*
		 * If this page was incompletely split, finish the split now.  We do
		 * this while holding a lock on the left sibling, which is not good
		 * because finishing the split could be a fairly lengthy operation.
		 * But this should happen very seldom.
		 */
		if (P_INCOMPLETE_SPLIT(lpageop))
		{
			_bt_finish_split(rel, rbuf, stack);
			rbuf = InvalidBuffer;
			continue;
		}

		if (!P_IGNORE(lpageop))
			break;
		if (P_RIGHTMOST(lpageop))
			elog(ERROR, "fell off the end of index \"%s\"",
				 RelationGetRelationName(rel));

		rblkno = lpageop->btpo_next;
	}
	/* rbuf locked; unlock buf, update state for caller */
	_bt_relbuf(rel, insertstate->buf);
	insertstate->buf = rbuf;
	insertstate->bounds_valid = false;
}

/*----------
 *	_bt_insertonpg() -- Insert a tuple on a particular page in the index.
 *
 *		This recursive procedure does the following things:
 *
 *			+  if necessary, splits the target page, using 'itup_key' for
 *			   suffix truncation on leaf pages (caller passes NULL for
 *			   non-leaf pages).
 *			+  inserts the tuple.
 *			+  if the page was split, pops the parent stack, and finds the
 *			   right place to insert the new child pointer (by walking
 *			   right using information stored in the parent stack).
 *			+  invokes itself with the appropriate tuple for the right
 *			   child page on the parent.
 *			+  updates the metapage if a true root or fast root is split.
 *
 *		On entry, we must have the correct buffer in which to do the
 *		insertion, and the buffer must be pinned and write-locked.  On return,
 *		we will have dropped both the pin and the lock on the buffer.
 *
 *		This routine only performs retail tuple insertions.  'itup' should
 *		always be either a non-highkey leaf item, or a downlink (new high
 *		key items are created indirectly, when a page is split).  When
 *		inserting to a non-leaf page, 'cbuf' is the left-sibling of the page
 *		we're inserting the downlink for.  This function will clear the
 *		INCOMPLETE_SPLIT flag on it, and release the buffer.
 *
 *		The locking interactions in this code are critical.  You should
 *		grok Lehman and Yao's paper before making any changes.
 *----------
 */
static void
_bt_insertonpg(Relation rel,
			   BTScanInsert itup_key,
			   Buffer buf,
			   Buffer cbuf,
			   BTStack stack,
			   IndexTuple itup,
			   OffsetNumber newitemoff,
			   bool split_only_page)
{
	Page		page;
	BTPageOpaque lpageop;
	OffsetNumber firstright = InvalidOffsetNumber;
	Size		itemsz;

	page = BufferGetPage(buf);
	lpageop = (BTPageOpaque) PageGetSpecialPointer(page);

	/* child buffer must be given iff inserting on an internal page */
	Assert(P_ISLEAF(lpageop) == !BufferIsValid(cbuf));
	/* tuple must have appropriate number of attributes */
	Assert(!P_ISLEAF(lpageop) ||
		   BTreeTupleGetNAtts(itup, rel) ==
		   IndexRelationGetNumberOfAttributes(rel));
	Assert(P_ISLEAF(lpageop) ||
		   BTreeTupleGetNAtts(itup, rel) <=
		   IndexRelationGetNumberOfKeyAttributes(rel));

	/* The caller should've finished any incomplete splits already. */
	if (P_INCOMPLETE_SPLIT(lpageop))
		elog(ERROR, "cannot insert to incompletely split page %u",
			 BufferGetBlockNumber(buf));

	itemsz = IndexTupleSize(itup);
	itemsz = MAXALIGN(itemsz);	/* be safe, PageAddItem will do this but we
								 * need to be consistent */

	/*
	 * Do we need to split the page to fit the item on it?
	 *
	 * Note: PageGetFreeSpace() subtracts sizeof(ItemIdData) from its result,
	 * so this comparison is correct even though we appear to be accounting
	 * only for the item and not for its line pointer.
	 */
	if (PageGetFreeSpace(page) < itemsz)
	{
		bool		is_root = P_ISROOT(lpageop);
		bool		is_only = P_LEFTMOST(lpageop) && P_RIGHTMOST(lpageop);
		bool		newitemonleft;
		Buffer		rbuf;

		/*
		 * If we're here then a pagesplit is needed. We should never reach
		 * here if we're using the fastpath since we should have checked for
		 * all the required conditions, including the fact that this page has
		 * enough freespace. Note that this routine can in theory deal with
		 * the situation where a NULL stack pointer is passed (that's what
		 * would happen if the fastpath is taken). But that path is much
		 * slower, defeating the very purpose of the optimization.  The
		 * following assertion should protect us from any future code changes
		 * that invalidate those assumptions.
		 *
		 * Note that whenever we fail to take the fastpath, we clear the
		 * cached block. Checking for a valid cached block at this point is
		 * enough to decide whether we're in a fastpath or not.
		 */
		Assert(!(P_ISLEAF(lpageop) &&
				 BlockNumberIsValid(RelationGetTargetBlock(rel))));

		/* Choose the split point */
		firstright = _bt_findsplitloc(rel, page,
									  newitemoff, itemsz, itup,
									  &newitemonleft);

		/* split the buffer into left and right halves */
		rbuf = _bt_split(rel, itup_key, buf, cbuf, firstright, newitemoff,
						 itemsz, itup, newitemonleft);
		PredicateLockPageSplit(rel,
							   BufferGetBlockNumber(buf),
							   BufferGetBlockNumber(rbuf));

		/*----------
		 * By here,
		 *
		 *		+  our target page has been split;
		 *		+  the original tuple has been inserted;
		 *		+  we have write locks on both the old (left half)
		 *		   and new (right half) buffers, after the split; and
		 *		+  we know the key we want to insert into the parent
		 *		   (it's the "high key" on the left child page).
		 *
		 * We're ready to do the parent insertion.  We need to hold onto the
		 * locks for the child pages until we locate the parent, but we can
		 * at least release the lock on the right child before doing the
		 * actual insertion.  The lock on the left child will be released
		 * last of all by parent insertion, where it is the 'cbuf' of parent
		 * page.
		 *----------
		 */
		_bt_insert_parent(rel, buf, rbuf, stack, is_root, is_only);
	}
	else
	{
		Buffer		metabuf = InvalidBuffer;
		Page		metapg = NULL;
		BTMetaPageData *metad = NULL;
		OffsetNumber itup_off;
		BlockNumber itup_blkno;
		BlockNumber cachedBlock = InvalidBlockNumber;

		itup_off = newitemoff;
		itup_blkno = BufferGetBlockNumber(buf);

		/*
		 * If we are doing this insert because we split a page that was the
		 * only one on its tree level, but was not the root, it may have been
		 * the "fast root".  We need to ensure that the fast root link points
		 * at or above the current page.  We can safely acquire a lock on the
		 * metapage here --- see comments for _bt_newroot().
		 */
		if (split_only_page)
		{
			Assert(!P_ISLEAF(lpageop));

			metabuf = _bt_getbuf(rel, BTREE_METAPAGE, BT_WRITE);
			metapg = BufferGetPage(metabuf);
			metad = BTPageGetMeta(metapg);

			if (metad->btm_fastlevel >= lpageop->btpo.level)
			{
				/* no update wanted */
				_bt_relbuf(rel, metabuf);
				metabuf = InvalidBuffer;
			}
		}

		/*
		 * Every internal page should have exactly one negative infinity item
		 * at all times.  Only _bt_split() and _bt_newroot() should add items
		 * that become negative infinity items through truncation, since
		 * they're the only routines that allocate new internal pages.  Do not
		 * allow a retail insertion of a new item at the negative infinity
		 * offset.
		 */
		if (!P_ISLEAF(lpageop) && newitemoff == P_FIRSTDATAKEY(lpageop))
			elog(ERROR, "cannot insert second negative infinity item in block %u of index \"%s\"",
				 itup_blkno, RelationGetRelationName(rel));

		/* Do the update.  No ereport(ERROR) until changes are logged */
		START_CRIT_SECTION();

		if (!_bt_pgaddtup(page, itemsz, itup, newitemoff))
			elog(PANIC, "failed to add new item to block %u in index \"%s\"",
				 itup_blkno, RelationGetRelationName(rel));

		MarkBufferDirty(buf);

		if (BufferIsValid(metabuf))
		{
			/* upgrade meta-page if needed */
			if (metad->btm_version < BTREE_NOVAC_VERSION)
				_bt_upgrademetapage(metapg);
			metad->btm_fastroot = itup_blkno;
			metad->btm_fastlevel = lpageop->btpo.level;
			MarkBufferDirty(metabuf);
		}

		/* clear INCOMPLETE_SPLIT flag on child if inserting a downlink */
		if (BufferIsValid(cbuf))
		{
			Page		cpage = BufferGetPage(cbuf);
			BTPageOpaque cpageop = (BTPageOpaque) PageGetSpecialPointer(cpage);

			Assert(P_INCOMPLETE_SPLIT(cpageop));
			cpageop->btpo_flags &= ~BTP_INCOMPLETE_SPLIT;
			MarkBufferDirty(cbuf);
		}

		/*
		 * Cache the block information if we just inserted into the rightmost
		 * leaf page of the index and it's not the root page.  For very small
		 * index where root is also the leaf, there is no point trying for any
		 * optimization.
		 */
		if (P_RIGHTMOST(lpageop) && P_ISLEAF(lpageop) && !P_ISROOT(lpageop))
			cachedBlock = BufferGetBlockNumber(buf);

		/* XLOG stuff */
		if (RelationNeedsWAL(rel))
		{
			xl_btree_insert xlrec;
			xl_btree_metadata xlmeta;
			uint8		xlinfo;
			XLogRecPtr	recptr;

			xlrec.offnum = itup_off;

			XLogBeginInsert();
			XLogRegisterData((char *) &xlrec, SizeOfBtreeInsert);

			if (P_ISLEAF(lpageop))
				xlinfo = XLOG_BTREE_INSERT_LEAF;
			else
			{
				/*
				 * Register the left child whose INCOMPLETE_SPLIT flag was
				 * cleared.
				 */
				XLogRegisterBuffer(1, cbuf, REGBUF_STANDARD);

				xlinfo = XLOG_BTREE_INSERT_UPPER;
			}

			if (BufferIsValid(metabuf))
			{
				Assert(metad->btm_version >= BTREE_NOVAC_VERSION);
				xlmeta.version = metad->btm_version;
				xlmeta.root = metad->btm_root;
				xlmeta.level = metad->btm_level;
				xlmeta.fastroot = metad->btm_fastroot;
				xlmeta.fastlevel = metad->btm_fastlevel;
				xlmeta.oldest_btpo_xact = metad->btm_oldest_btpo_xact;
				xlmeta.last_cleanup_num_heap_tuples =
					metad->btm_last_cleanup_num_heap_tuples;

				XLogRegisterBuffer(2, metabuf, REGBUF_WILL_INIT | REGBUF_STANDARD);
				XLogRegisterBufData(2, (char *) &xlmeta, sizeof(xl_btree_metadata));

				xlinfo = XLOG_BTREE_INSERT_META;
			}

			XLogRegisterBuffer(0, buf, REGBUF_STANDARD);
			XLogRegisterBufData(0, (char *) itup, IndexTupleSize(itup));

			recptr = XLogInsert(RM_BTREE_ID, xlinfo);

			if (BufferIsValid(metabuf))
			{
				PageSetLSN(metapg, recptr);
			}
			if (BufferIsValid(cbuf))
			{
				PageSetLSN(BufferGetPage(cbuf), recptr);
			}

			PageSetLSN(page, recptr);
		}

		END_CRIT_SECTION();

		/* release buffers */
		if (BufferIsValid(metabuf))
			_bt_relbuf(rel, metabuf);
		if (BufferIsValid(cbuf))
			_bt_relbuf(rel, cbuf);
		_bt_relbuf(rel, buf);

		/*
		 * If we decided to cache the insertion target block, then set it now.
		 * But before that, check for the height of the tree and don't go for
		 * the optimization for small indexes. We defer that check to this
		 * point to ensure that we don't call _bt_getrootheight while holding
		 * lock on any other block.
		 *
		 * We do this after dropping locks on all buffers. So the information
		 * about whether the insertion block is still the rightmost block or
		 * not may have changed in between. But we will deal with that during
		 * next insert operation. No special care is required while setting
		 * it.
		 */
		if (BlockNumberIsValid(cachedBlock) &&
			_bt_getrootheight(rel) >= BTREE_FASTPATH_MIN_LEVEL)
			RelationSetTargetBlock(rel, cachedBlock);
	}
}

/*
 *	_bt_split() -- split a page in the btree.
 *
 *		On entry, buf is the page to split, and is pinned and write-locked.
 *		firstright is the item index of the first item to be moved to the
 *		new right page.  newitemoff etc. tell us about the new item that
 *		must be inserted along with the data from the old page.
 *
 *		itup_key is used for suffix truncation on leaf pages (internal
 *		page callers pass NULL).  When splitting a non-leaf page, 'cbuf'
 *		is the left-sibling of the page we're inserting the downlink for.
 *		This function will clear the INCOMPLETE_SPLIT flag on it, and
 *		release the buffer.
 *
 *		Returns the new right sibling of buf, pinned and write-locked.
 *		The pin and lock on buf are maintained.
 */
static Buffer
_bt_split(Relation rel, BTScanInsert itup_key, Buffer buf, Buffer cbuf,
		  OffsetNumber firstright, OffsetNumber newitemoff, Size newitemsz,
		  IndexTuple newitem, bool newitemonleft)
{
	Buffer		rbuf;
	Page		origpage;
	Page		leftpage,
				rightpage;
	BlockNumber origpagenumber,
				rightpagenumber;
	BTPageOpaque ropaque,
				lopaque,
				oopaque;
	Buffer		sbuf = InvalidBuffer;
	Page		spage = NULL;
	BTPageOpaque sopaque = NULL;
	Size		itemsz;
	ItemId		itemid;
	IndexTuple	item;
	OffsetNumber leftoff,
				rightoff;
	OffsetNumber maxoff;
	OffsetNumber i;
	bool		isleaf;
	IndexTuple	lefthikey;
	int			indnatts = IndexRelationGetNumberOfAttributes(rel);
	int			indnkeyatts = IndexRelationGetNumberOfKeyAttributes(rel);

	/* Acquire a new page to split into */
	rbuf = _bt_getbuf(rel, P_NEW, BT_WRITE);

	/*
	 * origpage is the original page to be split.  leftpage is a temporary
	 * buffer that receives the left-sibling data, which will be copied back
	 * into origpage on success.  rightpage is the new page that receives the
	 * right-sibling data.  If we fail before reaching the critical section,
	 * origpage hasn't been modified and leftpage is only workspace. In
	 * principle we shouldn't need to worry about rightpage either, because it
	 * hasn't been linked into the btree page structure; but to avoid leaving
	 * possibly-confusing junk behind, we are careful to rewrite rightpage as
	 * zeroes before throwing any error.
	 */
	origpage = BufferGetPage(buf);
	leftpage = PageGetTempPage(origpage);
	rightpage = BufferGetPage(rbuf);

	origpagenumber = BufferGetBlockNumber(buf);
	rightpagenumber = BufferGetBlockNumber(rbuf);

	_bt_pageinit(leftpage, BufferGetPageSize(buf));
	/* rightpage was already initialized by _bt_getbuf */

	/*
	 * Copy the original page's LSN into leftpage, which will become the
	 * updated version of the page.  We need this because XLogInsert will
	 * examine the LSN and possibly dump it in a page image.
	 */
	PageSetLSN(leftpage, PageGetLSN(origpage));

	/* init btree private data */
	oopaque = (BTPageOpaque) PageGetSpecialPointer(origpage);
	lopaque = (BTPageOpaque) PageGetSpecialPointer(leftpage);
	ropaque = (BTPageOpaque) PageGetSpecialPointer(rightpage);

	isleaf = P_ISLEAF(oopaque);

	/* if we're splitting this page, it won't be the root when we're done */
	/* also, clear the SPLIT_END and HAS_GARBAGE flags in both pages */
	lopaque->btpo_flags = oopaque->btpo_flags;
	lopaque->btpo_flags &= ~(BTP_ROOT | BTP_SPLIT_END | BTP_HAS_GARBAGE);
	ropaque->btpo_flags = lopaque->btpo_flags;
	/* set flag in left page indicating that the right page has no downlink */
	lopaque->btpo_flags |= BTP_INCOMPLETE_SPLIT;
	lopaque->btpo_prev = oopaque->btpo_prev;
	lopaque->btpo_next = rightpagenumber;
	ropaque->btpo_prev = origpagenumber;
	ropaque->btpo_next = oopaque->btpo_next;
	lopaque->btpo.level = ropaque->btpo.level = oopaque->btpo.level;
	/* Since we already have write-lock on both pages, ok to read cycleid */
	lopaque->btpo_cycleid = _bt_vacuum_cycleid(rel);
	ropaque->btpo_cycleid = lopaque->btpo_cycleid;

	/*
	 * If the page we're splitting is not the rightmost page at its level in
	 * the tree, then the first entry on the page is the high key for the
	 * page.  We need to copy that to the right half.  Otherwise (meaning the
	 * rightmost page case), all the items on the right half will be user
	 * data.
	 */
	rightoff = P_HIKEY;

	if (!P_RIGHTMOST(oopaque))
	{
		itemid = PageGetItemId(origpage, P_HIKEY);
		itemsz = ItemIdGetLength(itemid);
		item = (IndexTuple) PageGetItem(origpage, itemid);
		Assert(BTreeTupleGetNAtts(item, rel) > 0);
		Assert(BTreeTupleGetNAtts(item, rel) <= indnkeyatts);
		if (PageAddItem(rightpage, (Item) item, itemsz, rightoff,
						false, false) == InvalidOffsetNumber)
		{
			memset(rightpage, 0, BufferGetPageSize(rbuf));
			elog(ERROR, "failed to add hikey to the right sibling"
				 " while splitting block %u of index \"%s\"",
				 origpagenumber, RelationGetRelationName(rel));
		}
		rightoff = OffsetNumberNext(rightoff);
	}

	/*
	 * The "high key" for the new left page will be the first key that's going
	 * to go into the new right page, or possibly a truncated version if this
	 * is a leaf page split.  This might be either the existing data item at
	 * position firstright, or the incoming tuple.
	 *
	 * The high key for the left page is formed using the first item on the
	 * right page, which may seem to be contrary to Lehman & Yao's approach of
	 * using the left page's last item as its new high key when splitting on
	 * the leaf level.  It isn't, though: suffix truncation will leave the
	 * left page's high key fully equal to the last item on the left page when
	 * two tuples with equal key values (excluding heap TID) enclose the split
	 * point.  It isn't actually necessary for a new leaf high key to be equal
	 * to the last item on the left for the L&Y "subtree" invariant to hold.
	 * It's sufficient to make sure that the new leaf high key is strictly
	 * less than the first item on the right leaf page, and greater than or
	 * equal to (not necessarily equal to) the last item on the left leaf
	 * page.
	 *
	 * In other words, when suffix truncation isn't possible, L&Y's exact
	 * approach to leaf splits is taken.  (Actually, even that is slightly
	 * inaccurate.  A tuple with all the keys from firstright but the heap TID
	 * from lastleft will be used as the new high key, since the last left
	 * tuple could be physically larger despite being opclass-equal in respect
	 * of all attributes prior to the heap TID attribute.)
	 */
	leftoff = P_HIKEY;
	if (!newitemonleft && newitemoff == firstright)
	{
		/* incoming tuple will become first on right page */
		itemsz = newitemsz;
		item = newitem;
	}
	else
	{
		/* existing item at firstright will become first on right page */
		itemid = PageGetItemId(origpage, firstright);
		itemsz = ItemIdGetLength(itemid);
		item = (IndexTuple) PageGetItem(origpage, itemid);
	}

	/*
	 * Truncate unneeded key and non-key attributes of the high key item
	 * before inserting it on the left page.  This can only happen at the leaf
	 * level, since in general all pivot tuple values originate from leaf
	 * level high keys.  A pivot tuple in a grandparent page must guide a
	 * search not only to the correct parent page, but also to the correct
	 * leaf page.
	 */
	if (isleaf && (itup_key->heapkeyspace || indnatts != indnkeyatts))
	{
		IndexTuple	lastleft;

		/*
		 * Determine which tuple will become the last on the left page.  This
		 * is needed to decide how many attributes from the first item on the
		 * right page must remain in new high key for left page.
		 */
		if (newitemonleft && newitemoff == firstright)
		{
			/* incoming tuple will become last on left page */
			lastleft = newitem;
		}
		else
		{
			OffsetNumber lastleftoff;

			/* item just before firstright will become last on left page */
			lastleftoff = OffsetNumberPrev(firstright);
			Assert(lastleftoff >= P_FIRSTDATAKEY(oopaque));
			itemid = PageGetItemId(origpage, lastleftoff);
			lastleft = (IndexTuple) PageGetItem(origpage, itemid);
		}

		Assert(lastleft != item);
		lefthikey = _bt_truncate(rel, lastleft, item, itup_key);
		itemsz = IndexTupleSize(lefthikey);
		itemsz = MAXALIGN(itemsz);
	}
	else
		lefthikey = item;

	Assert(BTreeTupleGetNAtts(lefthikey, rel) > 0);
	Assert(BTreeTupleGetNAtts(lefthikey, rel) <= indnkeyatts);
	if (PageAddItem(leftpage, (Item) lefthikey, itemsz, leftoff,
					false, false) == InvalidOffsetNumber)
	{
		memset(rightpage, 0, BufferGetPageSize(rbuf));
		elog(ERROR, "failed to add hikey to the left sibling"
			 " while splitting block %u of index \"%s\"",
			 origpagenumber, RelationGetRelationName(rel));
	}
	leftoff = OffsetNumberNext(leftoff);
	/* be tidy */
	if (lefthikey != item)
		pfree(lefthikey);

	/*
	 * Now transfer all the data items to the appropriate page.
	 *
	 * Note: we *must* insert at least the right page's items in item-number
	 * order, for the benefit of _bt_restore_page().
	 */
	maxoff = PageGetMaxOffsetNumber(origpage);

	for (i = P_FIRSTDATAKEY(oopaque); i <= maxoff; i = OffsetNumberNext(i))
	{
		itemid = PageGetItemId(origpage, i);
		itemsz = ItemIdGetLength(itemid);
		item = (IndexTuple) PageGetItem(origpage, itemid);

		/* does new item belong before this one? */
		if (i == newitemoff)
		{
			if (newitemonleft)
			{
				if (!_bt_pgaddtup(leftpage, newitemsz, newitem, leftoff))
				{
					memset(rightpage, 0, BufferGetPageSize(rbuf));
					elog(ERROR, "failed to add new item to the left sibling"
						 " while splitting block %u of index \"%s\"",
						 origpagenumber, RelationGetRelationName(rel));
				}
				leftoff = OffsetNumberNext(leftoff);
			}
			else
			{
				if (!_bt_pgaddtup(rightpage, newitemsz, newitem, rightoff))
				{
					memset(rightpage, 0, BufferGetPageSize(rbuf));
					elog(ERROR, "failed to add new item to the right sibling"
						 " while splitting block %u of index \"%s\"",
						 origpagenumber, RelationGetRelationName(rel));
				}
				rightoff = OffsetNumberNext(rightoff);
			}
		}

		/* decide which page to put it on */
		if (i < firstright)
		{
			if (!_bt_pgaddtup(leftpage, itemsz, item, leftoff))
			{
				memset(rightpage, 0, BufferGetPageSize(rbuf));
				elog(ERROR, "failed to add old item to the left sibling"
					 " while splitting block %u of index \"%s\"",
					 origpagenumber, RelationGetRelationName(rel));
			}
			leftoff = OffsetNumberNext(leftoff);
		}
		else
		{
			if (!_bt_pgaddtup(rightpage, itemsz, item, rightoff))
			{
				memset(rightpage, 0, BufferGetPageSize(rbuf));
				elog(ERROR, "failed to add old item to the right sibling"
					 " while splitting block %u of index \"%s\"",
					 origpagenumber, RelationGetRelationName(rel));
			}
			rightoff = OffsetNumberNext(rightoff);
		}
	}

	/* cope with possibility that newitem goes at the end */
	if (i <= newitemoff)
	{
		/*
		 * Can't have newitemonleft here; that would imply we were told to put
		 * *everything* on the left page, which cannot fit (if it could, we'd
		 * not be splitting the page).
		 */
		Assert(!newitemonleft);
		if (!_bt_pgaddtup(rightpage, newitemsz, newitem, rightoff))
		{
			memset(rightpage, 0, BufferGetPageSize(rbuf));
			elog(ERROR, "failed to add new item to the right sibling"
				 " while splitting block %u of index \"%s\"",
				 origpagenumber, RelationGetRelationName(rel));
		}
		rightoff = OffsetNumberNext(rightoff);
	}

	/*
	 * We have to grab the right sibling (if any) and fix the prev pointer
	 * there. We are guaranteed that this is deadlock-free since no other
	 * writer will be holding a lock on that page and trying to move left, and
	 * all readers release locks on a page before trying to fetch its
	 * neighbors.
	 */

	if (!P_RIGHTMOST(oopaque))
	{
		sbuf = _bt_getbuf(rel, oopaque->btpo_next, BT_WRITE);
		spage = BufferGetPage(sbuf);
		sopaque = (BTPageOpaque) PageGetSpecialPointer(spage);
		if (sopaque->btpo_prev != origpagenumber)
		{
			memset(rightpage, 0, BufferGetPageSize(rbuf));
			elog(ERROR, "right sibling's left-link doesn't match: "
				 "block %u links to %u instead of expected %u in index \"%s\"",
				 oopaque->btpo_next, sopaque->btpo_prev, origpagenumber,
				 RelationGetRelationName(rel));
		}

		/*
		 * Check to see if we can set the SPLIT_END flag in the right-hand
		 * split page; this can save some I/O for vacuum since it need not
		 * proceed to the right sibling.  We can set the flag if the right
		 * sibling has a different cycleid: that means it could not be part of
		 * a group of pages that were all split off from the same ancestor
		 * page.  If you're confused, imagine that page A splits to A B and
		 * then again, yielding A C B, while vacuum is in progress.  Tuples
		 * originally in A could now be in either B or C, hence vacuum must
		 * examine both pages.  But if D, our right sibling, has a different
		 * cycleid then it could not contain any tuples that were in A when
		 * the vacuum started.
		 */
		if (sopaque->btpo_cycleid != ropaque->btpo_cycleid)
			ropaque->btpo_flags |= BTP_SPLIT_END;
	}

	/*
	 * Right sibling is locked, new siblings are prepared, but original page
	 * is not updated yet.
	 *
	 * NO EREPORT(ERROR) till right sibling is updated.  We can get away with
	 * not starting the critical section till here because we haven't been
	 * scribbling on the original page yet; see comments above.
	 */
	START_CRIT_SECTION();

	/*
	 * By here, the original data page has been split into two new halves, and
	 * these are correct.  The algorithm requires that the left page never
	 * move during a split, so we copy the new left page back on top of the
	 * original.  Note that this is not a waste of time, since we also require
	 * (in the page management code) that the center of a page always be
	 * clean, and the most efficient way to guarantee this is just to compact
	 * the data by reinserting it into a new left page.  (XXX the latter
	 * comment is probably obsolete; but in any case it's good to not scribble
	 * on the original page until we enter the critical section.)
	 *
	 * We need to do this before writing the WAL record, so that XLogInsert
	 * can WAL log an image of the page if necessary.
	 */
	PageRestoreTempPage(leftpage, origpage);
	/* leftpage, lopaque must not be used below here */

	MarkBufferDirty(buf);
	MarkBufferDirty(rbuf);

	if (!P_RIGHTMOST(ropaque))
	{
		sopaque->btpo_prev = rightpagenumber;
		MarkBufferDirty(sbuf);
	}

	/*
	 * Clear INCOMPLETE_SPLIT flag on child if inserting the new item finishes
	 * a split.
	 */
	if (!isleaf)
	{
		Page		cpage = BufferGetPage(cbuf);
		BTPageOpaque cpageop = (BTPageOpaque) PageGetSpecialPointer(cpage);

		cpageop->btpo_flags &= ~BTP_INCOMPLETE_SPLIT;
		MarkBufferDirty(cbuf);
	}

	/* XLOG stuff */
	if (RelationNeedsWAL(rel))
	{
		xl_btree_split xlrec;
		uint8		xlinfo;
		XLogRecPtr	recptr;

		xlrec.level = ropaque->btpo.level;
		xlrec.firstright = firstright;
		xlrec.newitemoff = newitemoff;

		XLogBeginInsert();
		XLogRegisterData((char *) &xlrec, SizeOfBtreeSplit);

		XLogRegisterBuffer(0, buf, REGBUF_STANDARD);
		XLogRegisterBuffer(1, rbuf, REGBUF_WILL_INIT);
		/* Log the right sibling, because we've changed its prev-pointer. */
		if (!P_RIGHTMOST(ropaque))
			XLogRegisterBuffer(2, sbuf, REGBUF_STANDARD);
		if (BufferIsValid(cbuf))
			XLogRegisterBuffer(3, cbuf, REGBUF_STANDARD);

		/*
		 * Log the new item, if it was inserted on the left page. (If it was
		 * put on the right page, we don't need to explicitly WAL log it
		 * because it's included with all the other items on the right page.)
		 * Show the new item as belonging to the left page buffer, so that it
		 * is not stored if XLogInsert decides it needs a full-page image of
		 * the left page.  We store the offset anyway, though, to support
		 * archive compression of these records.
		 */
		if (newitemonleft)
			XLogRegisterBufData(0, (char *) newitem, MAXALIGN(newitemsz));

		/* Log the left page's new high key */
		itemid = PageGetItemId(origpage, P_HIKEY);
		item = (IndexTuple) PageGetItem(origpage, itemid);
		XLogRegisterBufData(0, (char *) item, MAXALIGN(IndexTupleSize(item)));

		/*
		 * Log the contents of the right page in the format understood by
		 * _bt_restore_page().  The whole right page will be recreated.
		 *
		 * Direct access to page is not good but faster - we should implement
		 * some new func in page API.  Note we only store the tuples
		 * themselves, knowing that they were inserted in item-number order
		 * and so the item pointers can be reconstructed.  See comments for
		 * _bt_restore_page().
		 */
		XLogRegisterBufData(1,
							(char *) rightpage + ((PageHeader) rightpage)->pd_upper,
							((PageHeader) rightpage)->pd_special - ((PageHeader) rightpage)->pd_upper);

		xlinfo = newitemonleft ? XLOG_BTREE_SPLIT_L : XLOG_BTREE_SPLIT_R;
		recptr = XLogInsert(RM_BTREE_ID, xlinfo);

		PageSetLSN(origpage, recptr);
		PageSetLSN(rightpage, recptr);
		if (!P_RIGHTMOST(ropaque))
		{
			PageSetLSN(spage, recptr);
		}
		if (!isleaf)
		{
			PageSetLSN(BufferGetPage(cbuf), recptr);
		}
	}

	END_CRIT_SECTION();

	/* release the old right sibling */
	if (!P_RIGHTMOST(ropaque))
		_bt_relbuf(rel, sbuf);

	/* release the child */
	if (!isleaf)
		_bt_relbuf(rel, cbuf);

	/* split's done */
	return rbuf;
}

/*
 * _bt_insert_parent() -- Insert downlink into parent after a page split.
 *
 * On entry, buf and rbuf are the left and right split pages, which we
 * still hold write locks on per the L&Y algorithm.  We release the
 * write locks once we have write lock on the parent page.  (Any sooner,
 * and it'd be possible for some other process to try to split or delete
 * one of these pages, and get confused because it cannot find the downlink.)
 *
 * stack - stack showing how we got here.  Will be NULL when splitting true
 *			root, or during concurrent root split, where we can be inefficient
 * is_root - we split the true root
 * is_only - we split a page alone on its level (might have been fast root)
 */
static void
_bt_insert_parent(Relation rel,
				  Buffer buf,
				  Buffer rbuf,
				  BTStack stack,
				  bool is_root,
				  bool is_only)
{
	/*
	 * Here we have to do something Lehman and Yao don't talk about: deal with
	 * a root split and construction of a new root.  If our stack is empty
	 * then we have just split a node on what had been the root level when we
	 * descended the tree.  If it was still the root then we perform a
	 * new-root construction.  If it *wasn't* the root anymore, search to find
	 * the next higher level that someone constructed meanwhile, and find the
	 * right place to insert as for the normal case.
	 *
	 * If we have to search for the parent level, we do so by re-descending
	 * from the root.  This is not super-efficient, but it's rare enough not
	 * to matter.
	 */
	if (is_root)
	{
		Buffer		rootbuf;

		Assert(stack == NULL);
		Assert(is_only);
		/* create a new root node and update the metapage */
		rootbuf = _bt_newroot(rel, buf, rbuf);
		/* release the split buffers */
		_bt_relbuf(rel, rootbuf);
		_bt_relbuf(rel, rbuf);
		_bt_relbuf(rel, buf);
	}
	else
	{
		BlockNumber bknum = BufferGetBlockNumber(buf);
		BlockNumber rbknum = BufferGetBlockNumber(rbuf);
		Page		page = BufferGetPage(buf);
		IndexTuple	new_item;
		BTStackData fakestack;
		IndexTuple	ritem;
		Buffer		pbuf;

		if (stack == NULL)
		{
			BTPageOpaque lpageop;

			elog(DEBUG2, "concurrent ROOT page split");
			lpageop = (BTPageOpaque) PageGetSpecialPointer(page);
			/* Find the leftmost page at the next level up */
			pbuf = _bt_get_endpoint(rel, lpageop->btpo.level + 1, false,
									NULL);
			/* Set up a phony stack entry pointing there */
			stack = &fakestack;
			stack->bts_blkno = BufferGetBlockNumber(pbuf);
			stack->bts_offset = InvalidOffsetNumber;
			stack->bts_btentry = InvalidBlockNumber;
			stack->bts_parent = NULL;
			_bt_relbuf(rel, pbuf);
		}

		/* get high key from left, a strict lower bound for new right page */
		ritem = (IndexTuple) PageGetItem(page,
										 PageGetItemId(page, P_HIKEY));

		/* form an index tuple that points at the new right page */
		new_item = CopyIndexTuple(ritem);
		BTreeInnerTupleSetDownLink(new_item, rbknum);

		/*
		 * Find the parent buffer and get the parent page.
		 *
		 * Oops - if we were moved right then we need to change stack item! We
		 * want to find parent pointing to where we are, right ?	- vadim
		 * 05/27/97
		 */
		stack->bts_btentry = bknum;
		pbuf = _bt_getstackbuf(rel, stack);

		/*
		 * Now we can unlock the right child. The left child will be unlocked
		 * by _bt_insertonpg().
		 */
		_bt_relbuf(rel, rbuf);

		/* Check for error only after writing children */
		if (pbuf == InvalidBuffer)
			elog(ERROR, "failed to re-find parent key in index \"%s\" for split pages %u/%u",
				 RelationGetRelationName(rel), bknum, rbknum);

		/* Recursively update the parent */
		_bt_insertonpg(rel, NULL, pbuf, buf, stack->bts_parent,
					   new_item, stack->bts_offset + 1,
					   is_only);

		/* be tidy */
		pfree(new_item);
	}
}

/*
 * _bt_finish_split() -- Finish an incomplete split
 *
 * A crash or other failure can leave a split incomplete.  The insertion
 * routines won't allow to insert on a page that is incompletely split.
 * Before inserting on such a page, call _bt_finish_split().
 *
 * On entry, 'lbuf' must be locked in write-mode.  On exit, it is unlocked
 * and unpinned.
 */
void
_bt_finish_split(Relation rel, Buffer lbuf, BTStack stack)
{
	Page		lpage = BufferGetPage(lbuf);
	BTPageOpaque lpageop = (BTPageOpaque) PageGetSpecialPointer(lpage);
	Buffer		rbuf;
	Page		rpage;
	BTPageOpaque rpageop;
	bool		was_root;
	bool		was_only;

	Assert(P_INCOMPLETE_SPLIT(lpageop));

	/* Lock right sibling, the one missing the downlink */
	rbuf = _bt_getbuf(rel, lpageop->btpo_next, BT_WRITE);
	rpage = BufferGetPage(rbuf);
	rpageop = (BTPageOpaque) PageGetSpecialPointer(rpage);

	/* Could this be a root split? */
	if (!stack)
	{
		Buffer		metabuf;
		Page		metapg;
		BTMetaPageData *metad;

		/* acquire lock on the metapage */
		metabuf = _bt_getbuf(rel, BTREE_METAPAGE, BT_WRITE);
		metapg = BufferGetPage(metabuf);
		metad = BTPageGetMeta(metapg);

		was_root = (metad->btm_root == BufferGetBlockNumber(lbuf));

		_bt_relbuf(rel, metabuf);
	}
	else
		was_root = false;

	/* Was this the only page on the level before split? */
	was_only = (P_LEFTMOST(lpageop) && P_RIGHTMOST(rpageop));

	elog(DEBUG1, "finishing incomplete split of %u/%u",
		 BufferGetBlockNumber(lbuf), BufferGetBlockNumber(rbuf));

	_bt_insert_parent(rel, lbuf, rbuf, stack, was_root, was_only);
}

/*
 *	_bt_getstackbuf() -- Walk back up the tree one step, and find the item
 *						 we last looked at in the parent.
 *
 *		This is possible because we save the downlink from the parent item,
 *		which is enough to uniquely identify it.  Insertions into the parent
 *		level could cause the item to move right; deletions could cause it
 *		to move left, but not left of the page we previously found it in.
 *
 *		Adjusts bts_blkno & bts_offset if changed.
 *
 *		Returns write-locked buffer, or InvalidBuffer if item not found
 *		(should not happen).
 */
Buffer
_bt_getstackbuf(Relation rel, BTStack stack)
{
	BlockNumber blkno;
	OffsetNumber start;

	blkno = stack->bts_blkno;
	start = stack->bts_offset;

	for (;;)
	{
		Buffer		buf;
		Page		page;
		BTPageOpaque opaque;

		buf = _bt_getbuf(rel, blkno, BT_WRITE);
		page = BufferGetPage(buf);
		opaque = (BTPageOpaque) PageGetSpecialPointer(page);

		if (P_INCOMPLETE_SPLIT(opaque))
		{
			_bt_finish_split(rel, buf, stack->bts_parent);
			continue;
		}

		if (!P_IGNORE(opaque))
		{
			OffsetNumber offnum,
						minoff,
						maxoff;
			ItemId		itemid;
			IndexTuple	item;

			minoff = P_FIRSTDATAKEY(opaque);
			maxoff = PageGetMaxOffsetNumber(page);

			/*
			 * start = InvalidOffsetNumber means "search the whole page". We
			 * need this test anyway due to possibility that page has a high
			 * key now when it didn't before.
			 */
			if (start < minoff)
				start = minoff;

			/*
			 * Need this check too, to guard against possibility that page
			 * split since we visited it originally.
			 */
			if (start > maxoff)
				start = OffsetNumberNext(maxoff);

			/*
			 * These loops will check every item on the page --- but in an
			 * order that's attuned to the probability of where it actually
			 * is.  Scan to the right first, then to the left.
			 */
			for (offnum = start;
				 offnum <= maxoff;
				 offnum = OffsetNumberNext(offnum))
			{
				itemid = PageGetItemId(page, offnum);
				item = (IndexTuple) PageGetItem(page, itemid);

				if (BTreeInnerTupleGetDownLink(item) == stack->bts_btentry)
				{
					/* Return accurate pointer to where link is now */
					stack->bts_blkno = blkno;
					stack->bts_offset = offnum;
					return buf;
				}
			}

			for (offnum = OffsetNumberPrev(start);
				 offnum >= minoff;
				 offnum = OffsetNumberPrev(offnum))
			{
				itemid = PageGetItemId(page, offnum);
				item = (IndexTuple) PageGetItem(page, itemid);

				if (BTreeInnerTupleGetDownLink(item) == stack->bts_btentry)
				{
					/* Return accurate pointer to where link is now */
					stack->bts_blkno = blkno;
					stack->bts_offset = offnum;
					return buf;
				}
			}
		}

		/*
		 * The item we're looking for moved right at least one page.
		 */
		if (P_RIGHTMOST(opaque))
		{
			_bt_relbuf(rel, buf);
			return InvalidBuffer;
		}
		blkno = opaque->btpo_next;
		start = InvalidOffsetNumber;
		_bt_relbuf(rel, buf);
	}
}

/*
 *	_bt_newroot() -- Create a new root page for the index.
 *
 *		We've just split the old root page and need to create a new one.
 *		In order to do this, we add a new root page to the file, then lock
 *		the metadata page and update it.  This is guaranteed to be deadlock-
 *		free, because all readers release their locks on the metadata page
 *		before trying to lock the root, and all writers lock the root before
 *		trying to lock the metadata page.  We have a write lock on the old
 *		root page, so we have not introduced any cycles into the waits-for
 *		graph.
 *
 *		On entry, lbuf (the old root) and rbuf (its new peer) are write-
 *		locked. On exit, a new root page exists with entries for the
 *		two new children, metapage is updated and unlocked/unpinned.
 *		The new root buffer is returned to caller which has to unlock/unpin
 *		lbuf, rbuf & rootbuf.
 */
static Buffer
_bt_newroot(Relation rel, Buffer lbuf, Buffer rbuf)
{
	Buffer		rootbuf;
	Page		lpage,
				rootpage;
	BlockNumber lbkno,
				rbkno;
	BlockNumber rootblknum;
	BTPageOpaque rootopaque;
	BTPageOpaque lopaque;
	ItemId		itemid;
	IndexTuple	item;
	IndexTuple	left_item;
	Size		left_item_sz;
	IndexTuple	right_item;
	Size		right_item_sz;
	Buffer		metabuf;
	Page		metapg;
	BTMetaPageData *metad;

	lbkno = BufferGetBlockNumber(lbuf);
	rbkno = BufferGetBlockNumber(rbuf);
	lpage = BufferGetPage(lbuf);
	lopaque = (BTPageOpaque) PageGetSpecialPointer(lpage);

	/* get a new root page */
	rootbuf = _bt_getbuf(rel, P_NEW, BT_WRITE);
	rootpage = BufferGetPage(rootbuf);
	rootblknum = BufferGetBlockNumber(rootbuf);

	/* acquire lock on the metapage */
	metabuf = _bt_getbuf(rel, BTREE_METAPAGE, BT_WRITE);
	metapg = BufferGetPage(metabuf);
	metad = BTPageGetMeta(metapg);

	/*
	 * Create downlink item for left page (old root).  Since this will be the
	 * first item in a non-leaf page, it implicitly has minus-infinity key
	 * value, so we need not store any actual key in it.
	 */
	left_item_sz = sizeof(IndexTupleData);
	left_item = (IndexTuple) palloc(left_item_sz);
	left_item->t_info = left_item_sz;
	BTreeInnerTupleSetDownLink(left_item, lbkno);
	BTreeTupleSetNAtts(left_item, 0);

	/*
	 * Create downlink item for right page.  The key for it is obtained from
	 * the "high key" position in the left page.
	 */
	itemid = PageGetItemId(lpage, P_HIKEY);
	right_item_sz = ItemIdGetLength(itemid);
	item = (IndexTuple) PageGetItem(lpage, itemid);
	right_item = CopyIndexTuple(item);
	BTreeInnerTupleSetDownLink(right_item, rbkno);

	/* NO EREPORT(ERROR) from here till newroot op is logged */
	START_CRIT_SECTION();

	/* upgrade metapage if needed */
	if (metad->btm_version < BTREE_NOVAC_VERSION)
		_bt_upgrademetapage(metapg);

	/* set btree special data */
	rootopaque = (BTPageOpaque) PageGetSpecialPointer(rootpage);
	rootopaque->btpo_prev = rootopaque->btpo_next = P_NONE;
	rootopaque->btpo_flags = BTP_ROOT;
	rootopaque->btpo.level =
		((BTPageOpaque) PageGetSpecialPointer(lpage))->btpo.level + 1;
	rootopaque->btpo_cycleid = 0;

	/* update metapage data */
	metad->btm_root = rootblknum;
	metad->btm_level = rootopaque->btpo.level;
	metad->btm_fastroot = rootblknum;
	metad->btm_fastlevel = rootopaque->btpo.level;

	/*
	 * Insert the left page pointer into the new root page.  The root page is
	 * the rightmost page on its level so there is no "high key" in it; the
	 * two items will go into positions P_HIKEY and P_FIRSTKEY.
	 *
	 * Note: we *must* insert the two items in item-number order, for the
	 * benefit of _bt_restore_page().
	 */
	Assert(BTreeTupleGetNAtts(left_item, rel) == 0);
	if (PageAddItem(rootpage, (Item) left_item, left_item_sz, P_HIKEY,
					false, false) == InvalidOffsetNumber)
		elog(PANIC, "failed to add leftkey to new root page"
			 " while splitting block %u of index \"%s\"",
			 BufferGetBlockNumber(lbuf), RelationGetRelationName(rel));

	/*
	 * insert the right page pointer into the new root page.
	 */
	Assert(BTreeTupleGetNAtts(right_item, rel) > 0);
	Assert(BTreeTupleGetNAtts(right_item, rel) <=
		   IndexRelationGetNumberOfKeyAttributes(rel));
	if (PageAddItem(rootpage, (Item) right_item, right_item_sz, P_FIRSTKEY,
					false, false) == InvalidOffsetNumber)
		elog(PANIC, "failed to add rightkey to new root page"
			 " while splitting block %u of index \"%s\"",
			 BufferGetBlockNumber(lbuf), RelationGetRelationName(rel));

	/* Clear the incomplete-split flag in the left child */
	Assert(P_INCOMPLETE_SPLIT(lopaque));
	lopaque->btpo_flags &= ~BTP_INCOMPLETE_SPLIT;
	MarkBufferDirty(lbuf);

	MarkBufferDirty(rootbuf);
	MarkBufferDirty(metabuf);

	/* XLOG stuff */
	if (RelationNeedsWAL(rel))
	{
		xl_btree_newroot xlrec;
		XLogRecPtr	recptr;
		xl_btree_metadata md;

		xlrec.rootblk = rootblknum;
		xlrec.level = metad->btm_level;

		XLogBeginInsert();
		XLogRegisterData((char *) &xlrec, SizeOfBtreeNewroot);

		XLogRegisterBuffer(0, rootbuf, REGBUF_WILL_INIT);
		XLogRegisterBuffer(1, lbuf, REGBUF_STANDARD);
		XLogRegisterBuffer(2, metabuf, REGBUF_WILL_INIT | REGBUF_STANDARD);

		Assert(metad->btm_version >= BTREE_NOVAC_VERSION);
		md.version = metad->btm_version;
		md.root = rootblknum;
		md.level = metad->btm_level;
		md.fastroot = rootblknum;
		md.fastlevel = metad->btm_level;
		md.oldest_btpo_xact = metad->btm_oldest_btpo_xact;
		md.last_cleanup_num_heap_tuples = metad->btm_last_cleanup_num_heap_tuples;

		XLogRegisterBufData(2, (char *) &md, sizeof(xl_btree_metadata));

		/*
		 * Direct access to page is not good but faster - we should implement
		 * some new func in page API.
		 */
		XLogRegisterBufData(0,
							(char *) rootpage + ((PageHeader) rootpage)->pd_upper,
							((PageHeader) rootpage)->pd_special -
							((PageHeader) rootpage)->pd_upper);

		recptr = XLogInsert(RM_BTREE_ID, XLOG_BTREE_NEWROOT);

		PageSetLSN(lpage, recptr);
		PageSetLSN(rootpage, recptr);
		PageSetLSN(metapg, recptr);
	}

	END_CRIT_SECTION();

	/* done with metapage */
	_bt_relbuf(rel, metabuf);

	pfree(left_item);
	pfree(right_item);

	return rootbuf;
}

/*
 *	_bt_pgaddtup() -- add a tuple to a particular page in the index.
 *
 *		This routine adds the tuple to the page as requested.  It does
 *		not affect pin/lock status, but you'd better have a write lock
 *		and pin on the target buffer!  Don't forget to write and release
 *		the buffer afterwards, either.
 *
 *		The main difference between this routine and a bare PageAddItem call
 *		is that this code knows that the leftmost index tuple on a non-leaf
 *		btree page doesn't need to have a key.  Therefore, it strips such
 *		tuples down to just the tuple header.  CAUTION: this works ONLY if
 *		we insert the tuples in order, so that the given itup_off does
 *		represent the final position of the tuple!
 */
static bool
_bt_pgaddtup(Page page,
			 Size itemsize,
			 IndexTuple itup,
			 OffsetNumber itup_off)
{
	BTPageOpaque opaque = (BTPageOpaque) PageGetSpecialPointer(page);
	IndexTupleData trunctuple;

	if (!P_ISLEAF(opaque) && itup_off == P_FIRSTDATAKEY(opaque))
	{
		trunctuple = *itup;
		trunctuple.t_info = sizeof(IndexTupleData);
		/* Deliberately zero INDEX_ALT_TID_MASK bits */
		BTreeTupleSetNAtts(&trunctuple, 0);
		itup = &trunctuple;
		itemsize = sizeof(IndexTupleData);
	}

	if (PageAddItem(page, (Item) itup, itemsize, itup_off,
					false, false) == InvalidOffsetNumber)
		return false;

	return true;
}

/*
 * _bt_isequal - used in _bt_doinsert in check for duplicates.
 *
 * This is very similar to _bt_compare, except for NULL and negative infinity
 * handling.  Rule is simple: NOT_NULL not equal NULL, NULL not equal NULL too.
 */
static bool
_bt_isequal(TupleDesc itupdesc, BTScanInsert itup_key, Page page,
			OffsetNumber offnum)
{
	IndexTuple	itup;
	ScanKey		scankey;
	int			i;

	/* Better be comparing to a non-pivot item */
	Assert(P_ISLEAF((BTPageOpaque) PageGetSpecialPointer(page)));
	Assert(offnum >= P_FIRSTDATAKEY((BTPageOpaque) PageGetSpecialPointer(page)));
	Assert(itup_key->scantid == NULL);

	scankey = itup_key->scankeys;
	itup = (IndexTuple) PageGetItem(page, PageGetItemId(page, offnum));

	for (i = 1; i <= itup_key->keysz; i++)
	{
		AttrNumber	attno;
		Datum		datum;
		bool		isNull;
		int32		result;

		attno = scankey->sk_attno;
		Assert(attno == i);
		datum = index_getattr(itup, attno, itupdesc, &isNull);

		/* NULLs are never equal to anything */
		if (isNull || (scankey->sk_flags & SK_ISNULL))
			return false;

		result = DatumGetInt32(FunctionCall2Coll(&scankey->sk_func,
												 scankey->sk_collation,
												 datum,
												 scankey->sk_argument));

		if (result != 0)
			return false;

		scankey++;
	}

	/* if we get here, the keys are equal */
	return true;
}

/*
 * _bt_vacuum_one_page - vacuum just one index page.
 *
 * Try to remove LP_DEAD items from the given page.  The passed buffer
 * must be exclusive-locked, but unlike a real VACUUM, we don't need a
 * super-exclusive "cleanup" lock (see nbtree/README).
 */
static void
_bt_vacuum_one_page(Relation rel, Buffer buffer, Relation heapRel)
{
	OffsetNumber deletable[MaxOffsetNumber];
	int			ndeletable = 0;
	OffsetNumber offnum,
				minoff,
				maxoff;
	Page		page = BufferGetPage(buffer);
	BTPageOpaque opaque = (BTPageOpaque) PageGetSpecialPointer(page);

	Assert(P_ISLEAF(opaque));

	/*
	 * Scan over all items to see which ones need to be deleted according to
	 * LP_DEAD flags.
	 */
	minoff = P_FIRSTDATAKEY(opaque);
	maxoff = PageGetMaxOffsetNumber(page);
	for (offnum = minoff;
		 offnum <= maxoff;
		 offnum = OffsetNumberNext(offnum))
	{
		ItemId		itemId = PageGetItemId(page, offnum);

		if (ItemIdIsDead(itemId))
			deletable[ndeletable++] = offnum;
	}

	if (ndeletable > 0)
		_bt_delitems_delete(rel, buffer, deletable, ndeletable, heapRel);

	/*
	 * Note: if we didn't find any LP_DEAD items, then the page's
	 * BTP_HAS_GARBAGE hint bit is falsely set.  We do not bother expending a
	 * separate write to clear it, however.  We will clear it when we split
	 * the page.
	 */
}
