nbtinsert.c

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/*-------------------------------------------------------------------------
 *
 * 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 newitemoff, Size newitemsz,
                        IndexTuple newitem);
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 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);

    if (checkingunique)
    {
        if (!itup_key->anynullkeys)
        {
            /* No (heapkeyspace) scantid until uniqueness established */
            itup_key->scantid = NULL;
        }
        else
        {
            /*
             * Scan key for new tuple contains NULL key values.  Bypass
             * checkingunique steps.  They are unnecessary because core code
             * considers NULL unequal to every value, including NULL.
             *
             * This optimization avoids O(N^2) behavior within the
             * _bt_findinsertloc() heapkeyspace path when a unique index has a
             * large number of "duplicates" with NULL key values.
             */
            checkingunique = false;
            /* Tuple is unique in the sense that core code cares about */
            Assert(checkUnique != UNIQUE_CHECK_EXISTING);
            is_unique = true;
        }
    }

    /*
     * 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, with omitted/-inf value for the
     * 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 on for sure just yet in
         * checkingunique and !heapkeyspace cases, but it's okay to use the
         * first page the value could be on (with scantid omitted) instead.
         */
        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.
 *
 * Do not call here when there are NULL values in scan key.  NULL should be
 * considered unequal to NULL when checking for duplicates, but we are not
 * prepared to handle that correctly.
 */
static TransactionId
_bt_check_unique(Relation rel, BTInsertState insertstate, Relation heapRel,
                 IndexUniqueCheck checkUnique, bool *is_unique,
                 uint32 *speculativeToken)
{
    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.
     */
    Assert(!insertstate->bounds_valid);
    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->anynullkeys);
    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 allows us to avoid calling
             * _bt_compare() directly 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_compare(rel, itup_key, page, offset) < 0);
                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_compare() on
             * each killed item gets expensive.  Just advance over killed
             * items as quickly as we can.  We only apply _bt_compare() 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;

                if (_bt_compare(rel, itup_key, page, offset) != 0)
                    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. Don't invalidate binary search
                     * bounds.
                     */
                    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;
                        /* Caller releases lock on buf immediately */
                        insertstate->bounds_valid = false;
                        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;
                    insertstate->bounds_valid = false;

                    {
                        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);
            /* Don't invalidate binary search bounds */
        }
    }

    /*
     * 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 checkingunique=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.
 *----------
 */
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;
    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);
        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))));

        /* split the buffer into left and right halves */
        rbuf = _bt_split(rel, itup_key, buf, cbuf, newitemoff, itemsz, itup);
        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.
 *      newitemoff etc. tell us about the new item that must be inserted
 *      along with the data from the original 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 newitemoff, Size newitemsz, IndexTuple newitem)
{
    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 firstright;
    OffsetNumber maxoff;
    OffsetNumber i;
    bool        newitemonleft,
                isleaf;
    IndexTuple  lefthikey;
    int         indnatts = IndexRelationGetNumberOfAttributes(rel);
    int         indnkeyatts = IndexRelationGetNumberOfKeyAttributes(rel);

    /*
     * 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 will receive
     * the right-sibling data.
     *
     * leftpage is allocated after choosing a split point.  rightpage's new
     * buffer isn't acquired until after leftpage is initialized and has new
     * high key, the last point where splitting the page may fail (barring
     * corruption).  Failing before acquiring new buffer won't have lasting
     * consequences, since origpage won't have been modified and leftpage is
     * only workspace.
     */
    origpage = BufferGetPage(buf);
    oopaque = (BTPageOpaque) PageGetSpecialPointer(origpage);
    origpagenumber = BufferGetBlockNumber(buf);

    /*
     * Choose a point to split origpage at.
     *
     * A split point can be thought of as a point _between_ two existing
     * tuples on origpage (lastleft and firstright tuples), provided you
     * pretend that the new item that didn't fit is already on origpage.
     *
     * Since origpage does not actually contain newitem, the representation of
     * split points needs to work with two boundary cases: splits where
     * newitem is lastleft, and splits where newitem is firstright.
     * newitemonleft resolves the ambiguity that would otherwise exist when
     * newitemoff == firstright.  In all other cases it's clear which side of
     * the split every tuple goes on from context.  newitemonleft is usually
     * (but not always) redundant information.
     */
    firstright = _bt_findsplitloc(rel, origpage, newitemoff, newitemsz,
                                  newitem, &newitemonleft);

    /* Allocate temp buffer for leftpage */
    leftpage = PageGetTempPage(origpage);
    _bt_pageinit(leftpage, BufferGetPageSize(buf));
    lopaque = (BTPageOpaque) PageGetSpecialPointer(leftpage);

    /*
     * leftpage won't be the root when we're done.  Also, clear the SPLIT_END
     * and HAS_GARBAGE flags.
     */
    lopaque->btpo_flags = oopaque->btpo_flags;
    lopaque->btpo_flags &= ~(BTP_ROOT | BTP_SPLIT_END | BTP_HAS_GARBAGE);
    /* set flag in leftpage indicating that rightpage has no downlink yet */
    lopaque->btpo_flags |= BTP_INCOMPLETE_SPLIT;
    lopaque->btpo_prev = oopaque->btpo_prev;
    /* handle btpo_next after rightpage buffer acquired */
    lopaque->btpo.level = oopaque->btpo.level;
    /* handle btpo_cycleid after rightpage buffer acquired */

    /*
     * 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));
    isleaf = P_ISLEAF(oopaque);

    /*
     * The "high key" for the new left page will be the first key that's going
     * to go into the new right page, or a truncated version if this is a leaf
     * page split.
     *
     * 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.)
     */
    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;

    /*
     * Add new high key to leftpage
     */
    leftoff = P_HIKEY;

    Assert(BTreeTupleGetNAtts(lefthikey, rel) > 0);
    Assert(BTreeTupleGetNAtts(lefthikey, rel) <= indnkeyatts);
    if (PageAddItem(leftpage, (Item) lefthikey, itemsz, leftoff,
                    false, false) == InvalidOffsetNumber)
        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);

    /*
     * Acquire a new right page to split into, now that left page has a new
     * high key.  From here on, it's not okay to throw an error without
     * zeroing rightpage first.  This coding rule ensures that we won't
     * confuse future VACUUM operations, which might otherwise try to re-find
     * a downlink to a leftover junk page as the page undergoes deletion.
     *
     * It would be reasonable to start the critical section just after the new
     * rightpage buffer is acquired instead; that would allow us to avoid
     * leftover junk pages without bothering to zero rightpage.  We do it this
     * way because it avoids an unnecessary PANIC when either origpage or its
     * existing sibling page are corrupt.
     */
    rbuf = _bt_getbuf(rel, P_NEW, BT_WRITE);
    rightpage = BufferGetPage(rbuf);
    rightpagenumber = BufferGetBlockNumber(rbuf);
    /* rightpage was initialized by _bt_getbuf */
    ropaque = (BTPageOpaque) PageGetSpecialPointer(rightpage);

    /*
     * Finish off remaining leftpage special area fields.  They cannot be set
     * before both origpage (leftpage) and rightpage buffers are acquired and
     * locked.
     */
    lopaque->btpo_next = rightpagenumber;
    lopaque->btpo_cycleid = _bt_vacuum_cycleid(rel);

    /*
     * rightpage won't be the root when we're done.  Also, clear the SPLIT_END
     * and HAS_GARBAGE flags.
     */
    ropaque->btpo_flags = oopaque->btpo_flags;
    ropaque->btpo_flags &= ~(BTP_ROOT | BTP_SPLIT_END | BTP_HAS_GARBAGE);
    ropaque->btpo_prev = origpagenumber;
    ropaque->btpo_next = oopaque->btpo_next;
    ropaque->btpo.level = oopaque->btpo.level;
    ropaque->btpo_cycleid = lopaque->btpo_cycleid;

    /*
     * Add new high key to rightpage where necessary.
     *
     * 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 from
     * origpage.
     */
    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);
    }

    /*
     * Now transfer all the data items (non-pivot tuples in isleaf case, or
     * additional pivot tuples in !isleaf case) 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)
            {
                Assert(newitemoff <= firstright);
                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
            {
                Assert(newitemoff >= firstright);
                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));
            ereport(ERROR,
                    (errcode(ERRCODE_INDEX_CORRUPTED),
                     errmsg_internal("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 line 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, completing split.
 *
 * On entry, buf and rbuf are the left and right split pages, which we
 * still hold write locks on.  Both locks will be released here.  We
 * release the rbuf lock once we have a write lock on the page that we
 * intend to insert a downlink to rbuf on (i.e. buf's current parent page).
 * The lock on buf is released at the same point as the lock on the parent
 * page, since buf's INCOMPLETE_SPLIT flag must be cleared by the same
 * atomic operation that completes the split by inserting a new 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_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);

        /*
         * Re-find and write lock the parent of buf.
         *
         * It's possible that the location of buf's downlink has changed since
         * our initial _bt_search() descent.  _bt_getstackbuf() will detect
         * and recover from this, updating the stack, which ensures that the
         * new downlink will be inserted at the correct offset. Even buf's
         * parent may have changed.
         */
        pbuf = _bt_getstackbuf(rel, stack, bknum);

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

        if (pbuf == InvalidBuffer)
            ereport(ERROR,
                    (errcode(ERRCODE_INDEX_CORRUPTED),
                     errmsg_internal("failed to re-find parent key in index \"%s\" for split pages %u/%u",
                                     RelationGetRelationName(rel), bknum, rbknum)));

        /* Recursively insert into 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 pivot
 *                       tuple whose downlink points to child page.
 *
 *      Caller passes child's block number, which is used to identify
 *      associated pivot tuple in parent page using a linear search that
 *      matches on pivot's downlink/block number.  The expected location of
 *      the pivot tuple is taken from the stack one level above the child
 *      page.  This is used as a starting point.  Insertions into the
 *      parent level could cause the pivot tuple to move right; deletions
 *      could cause it to move left, but not left of the page we previously
 *      found it on.
 *
 *      Caller can use its stack to relocate the pivot tuple/downlink for
 *      any same-level page to the right of the page found by its initial
 *      descent.  This is necessary because of the possibility that caller
 *      moved right to recover from a concurrent page split.  It's also
 *      convenient for certain callers to be able to step right when there
 *      wasn't a concurrent page split, while still using their original
 *      stack.  For example, the checkingunique _bt_doinsert() case may
 *      have to step right when there are many physical duplicates, and its
 *      scantid forces an insertion to the right of the "first page the
 *      value could be on".
 *
 *      Returns write-locked parent page buffer, or InvalidBuffer if pivot
 *      tuple not found (should not happen).  Adjusts bts_blkno &
 *      bts_offset if changed.  Page split caller should insert its new
 *      pivot tuple for its new right sibling page on parent page, at the
 *      offset number bts_offset + 1.
 */
Buffer
_bt_getstackbuf(Relation rel, BTStack stack, BlockNumber child)
{
    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) == child)
                {
                    /* 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) == child)
                {
                    /* 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.
         *
         * Lehman and Yao couple/chain locks when moving right here, which we
         * can avoid.  See nbtree/README.
         */
        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_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.
     */
}