nbtinsert.c

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/*-------------------------------------------------------------------------
 *
 * nbtinsert.c
 *    Item insertion in Lehman and Yao btrees for Postgres.
 *
 * Portions Copyright (c) 1996-2020, 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 BTStack _bt_search_insert(Relation rel, BTInsertState insertstate);
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,
                           Size itemsz,
                           OffsetNumber newitemoff,
                           int postingoff,
                           bool split_only_page);
static Buffer _bt_split(Relation rel, BTScanInsert itup_key, Buffer buf,
                        Buffer cbuf, OffsetNumber newitemoff, Size newitemsz,
                        IndexTuple newitem, IndexTuple orignewitem,
                        IndexTuple nposting, uint16 postingoff);
static void _bt_insert_parent(Relation rel, Buffer buf, Buffer rbuf,
                              BTStack stack, bool is_root, bool is_only);
static Buffer _bt_newroot(Relation rel, Buffer lbuf, Buffer rbuf);
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;
    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.
     *
     * Note that itemsz is passed down to lower level code that deals with
     * inserting the item.  It must be MAXALIGN()'d.  This ensures that space
     * accounting code consistently considers the alignment overhead that we
     * expect PageAddItem() will add later.  (Actually, index_form_tuple() is
     * already conservative about alignment, but we don't rely on that from
     * this distance.  Besides, preserving the "true" tuple size in index
     * tuple headers for the benefit of nbtsplitloc.c might happen someday.
     * Note that heapam does not MAXALIGN() each heap tuple's lp_len field.)
     */
    insertstate.itup = itup;
    insertstate.itemsz = MAXALIGN(IndexTupleSize(itup));
    insertstate.itup_key = itup_key;
    insertstate.bounds_valid = false;
    insertstate.buf = InvalidBuffer;
    insertstate.postingoff = 0;

search:

    /*
     * Find and lock the leaf page that the tuple should be added to by
     * searching from the root page.  insertstate.buf will hold a buffer that
     * is locked in exclusive mode afterwards.
     */
    stack = _bt_search_insert(rel, &insertstate);

    /*
     * checkingunique inserts are not allowed to go ahead when two tuples with
     * equal key attribute values would be visible to new MVCC snapshots once
     * the xact commits.  Check for conflicts in the locked page/buffer (if
     * needed) here.
     *
     * It might be necessary to check a page to the right in _bt_check_unique,
     * though that should be very rare.  In practice the first page the value
     * could be on (with scantid omitted) is almost always also the only page
     * that a matching tuple might be found on.  This is due to the behavior
     * of _bt_findsplitloc with duplicate tuples -- a group of duplicates can
     * only be allowed to cross a page boundary when there is no candidate
     * leaf page split point that avoids it.  Also, _bt_check_unique can use
     * the leaf page high key to determine that there will be no duplicates on
     * the right sibling without actually visiting it (it uses the high key in
     * cases where the new item happens to belong at the far right of the leaf
     * page).
     *
     * 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 perform a new search.
     *
     * 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 (unlikely(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 search;
        }

        /* 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, BufferGetBlockNumber(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, insertstate.itemsz, newitemoff,
                       insertstate.postingoff, 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_search_insert() -- _bt_search() wrapper for inserts
 *
 * Search the tree for a particular scankey, or more precisely for the first
 * leaf page it could be on.  Try to make use of the fastpath optimization's
 * rightmost leaf page cache before actually searching the tree from the root
 * page, though.
 *
 * Return value is a stack of parent-page pointers (though see notes about
 * fastpath optimization and page splits below).  insertstate->buf is set to
 * the address of the leaf-page buffer, which is write-locked and pinned in
 * all cases (if necessary by creating a new empty root page for caller).
 *
 * The fastpath optimization avoids most of the work of searching the tree
 * repeatedly when a single backend inserts successive new tuples on the
 * rightmost leaf page of an index.  A backend cache of the rightmost leaf
 * page is maintained within _bt_insertonpg(), and used here.  The cache is
 * invalidated here when an insert of a non-pivot tuple must take place on a
 * non-rightmost leaf page.
 *
 * The optimization helps with indexes on an auto-incremented field.  It also
 * helps with indexes on datetime columns, as well as indexes with lots of
 * NULL values.  (NULLs usually get inserted in the rightmost page for single
 * column indexes, since they usually get treated as coming after everything
 * else in the key space.  Individual NULL tuples will generally be placed on
 * the rightmost leaf page due to the influence of the heap TID column.)
 *
 * Note that we avoid applying the optimization when there is insufficient
 * space on the rightmost page to fit caller's new item.  This is necessary
 * because we'll need to return a real descent stack when a page split is
 * expected (actually, caller can cope with a leaf page split that uses a NULL
 * stack, but that's very slow and so must be avoided).  Note also that the
 * fastpath optimization acquires the lock on the page conditionally as a way
 * of reducing extra contention when there are concurrent insertions into the
 * rightmost page (we give up if we'd have to wait for the lock).  We assume
 * that it isn't useful to apply the optimization when there is contention,
 * since each per-backend cache won't stay valid for long.
 */
static BTStack
_bt_search_insert(Relation rel, BTInsertState insertstate)
{
    Assert(insertstate->buf == InvalidBuffer);
    Assert(!insertstate->bounds_valid);
    Assert(insertstate->postingoff == 0);

    if (RelationGetTargetBlock(rel) != InvalidBlockNumber)
    {
        /* Simulate a _bt_getbuf() call with conditional locking */
        insertstate->buf = ReadBuffer(rel, RelationGetTargetBlock(rel));
        if (ConditionalLockBuffer(insertstate->buf))
        {
            Page        page;
            BTPageOpaque lpageop;

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

            /*
             * Check if the page is still the rightmost leaf page and has
             * enough free space to accommodate the new tuple.  Also check
             * that the insertion scan key is strictly greater than the first
             * non-pivot tuple on the page.  (Note that we expect itup_key's
             * scantid to be unset when our caller is a checkingunique
             * inserter.)
             */
            if (P_RIGHTMOST(lpageop) &&
                P_ISLEAF(lpageop) &&
                !P_IGNORE(lpageop) &&
                PageGetFreeSpace(page) > insertstate->itemsz &&
                PageGetMaxOffsetNumber(page) >= P_HIKEY &&
                _bt_compare(rel, insertstate->itup_key, page, P_HIKEY) > 0)
            {
                /*
                 * Caller can use the fastpath optimization because cached
                 * block is still rightmost leaf page, which can fit caller's
                 * new tuple without splitting.  Keep block in local cache for
                 * next insert, and have caller use NULL stack.
                 *
                 * Note that _bt_insert_parent() has an assertion that catches
                 * leaf page splits that somehow follow from a fastpath insert
                 * (it should only be passed a NULL stack when it must deal
                 * with a concurrent root page split, and never because a NULL
                 * stack was returned here).
                 */
                return NULL;
            }

            /* Page unsuitable for caller, drop lock and pin */
            _bt_relbuf(rel, insertstate->buf);
        }
        else
        {
            /* Lock unavailable, drop pin */
            ReleaseBuffer(insertstate->buf);
        }

        /* Forget block, since cache doesn't appear to be useful */
        RelationSetTargetBlock(rel, InvalidBlockNumber);
    }

    /* Cannot use optimization -- descend tree, return proper descent stack */
    return _bt_search(rel, insertstate->itup_key, &insertstate->buf, BT_WRITE,
                      NULL);
}

/*
 *  _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;
    IndexTuple  curitup;
    ItemId      curitemid;
    BTScanInsert itup_key = insertstate->itup_key;
    SnapshotData SnapshotDirty;
    OffsetNumber offset;
    OffsetNumber maxoff;
    Page        page;
    BTPageOpaque opaque;
    Buffer      nbuf = InvalidBuffer;
    bool        found = false;
    bool        inposting = false;
    bool        prevalldead = true;
    int         curposti = 0;

    /* 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 (;;)
    {
        /*
         * Each iteration of the loop processes one heap TID, not one index
         * tuple.  Current offset number for page isn't usually advanced on
         * iterations that process heap TIDs from posting list tuples.
         *
         * "inposting" state is set when _inside_ a posting list --- not when
         * we're at the start (or end) of a posting list.  We advance curposti
         * at the end of the iteration when inside a posting list tuple.  In
         * general, every loop iteration either advances the page offset or
         * advances curposti --- an iteration that handles the rightmost/max
         * heap TID in a posting list finally advances the page offset (and
         * unsets "inposting").
         *
         * Make sure the offset points to an actual index tuple 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;
            }

            /*
             * We can skip items that are already 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.  We could reuse the bounds to
             * avoid _bt_compare() calls for known equal tuples, but it
             * doesn't seem worth it.  Workloads with heavy update activity
             * tend to have many deduplication passes, so we'll often avoid
             * most of those comparisons, too (we call _bt_compare() when the
             * posting list tuple is initially encountered, though not when
             * processing later TIDs from the same tuple).
             */
            if (!inposting)
                curitemid = PageGetItemId(page, offset);
            if (inposting || !ItemIdIsDead(curitemid))
            {
                ItemPointerData htid;
                bool        all_dead = false;

                if (!inposting)
                {
                    /* Plain tuple, or first TID in posting list tuple */
                    if (_bt_compare(rel, itup_key, page, offset) != 0)
                        break;  /* we're past all the equal tuples */

                    /* Advanced curitup */
                    curitup = (IndexTuple) PageGetItem(page, curitemid);
                    Assert(!BTreeTupleIsPivot(curitup));
                }

                /* okay, we gotta fetch the heap tuple using htid ... */
                if (!BTreeTupleIsPosting(curitup))
                {
                    /* ... htid is from simple non-pivot tuple */
                    Assert(!inposting);
                    htid = curitup->t_tid;
                }
                else if (!inposting)
                {
                    /* ... htid is first TID in new posting list */
                    inposting = true;
                    prevalldead = true;
                    curposti = 0;
                    htid = *BTreeTupleGetPostingN(curitup, 0);
                }
                else
                {
                    /* ... htid is second or subsequent TID in posting list */
                    Assert(curposti > 0);
                    htid = *BTreeTupleGetPostingN(curitup, curposti);
                }

                /*
                 * 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.
                     */
                    if (table_index_fetch_tuple_check(heapRel, &itup->t_tid,
                                                      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, BufferGetBlockNumber(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 && (!inposting ||
                                      (prevalldead &&
                                       curposti == BTreeTupleGetNPosting(curitup) - 1)))
                {
                    /*
                     * The conflicting tuple (or all HOT chains pointed to by
                     * all posting list TIDs) is dead to everyone, so 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);
                }

                /*
                 * Remember if posting list tuple has even a single HOT chain
                 * whose members are not all dead
                 */
                if (!all_dead && inposting)
                    prevalldead = false;
            }
        }

        if (inposting && curposti < BTreeTupleGetNPosting(curitup) - 1)
        {
            /* Advance to next TID in same posting list */
            curposti++;
            continue;
        }
        else if (offset < maxoff)
        {
            /* Advance to next tuple */
            curposti = 0;
            inposting = false;
            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 (;;)
            {
                BlockNumber 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));
            }
            /* Will also advance to next tuple */
            curposti = 0;
            inposting = false;
            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;
    OffsetNumber newitemoff;

    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);
    Assert(!itup_key->allequalimage || itup_key->heapkeyspace);

    if (itup_key->heapkeyspace)
    {
        /* Keep track of whether checkingunique duplicate seen */
        bool        uniquedup = false;

        /*
         * 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)
        {
            if (insertstate->low < insertstate->stricthigh)
            {
                /* Encountered a duplicate in _bt_check_unique() */
                Assert(insertstate->bounds_valid);
                uniquedup = true;
            }

            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);
                /* Assume duplicates (if checkingunique) */
                uniquedup = true;
            }
        }

        /*
         * If the target page is full, see if we can obtain enough space by
         * erasing LP_DEAD items.  If that fails to free enough space, see if
         * we can avoid a page split by performing a deduplication pass over
         * the page.
         *
         * We only perform a deduplication pass for a checkingunique caller
         * when the incoming item is a duplicate of an existing item on the
         * leaf page.  This heuristic avoids wasting cycles -- we only expect
         * to benefit from deduplicating a unique index page when most or all
         * recently added items are duplicates.  See nbtree/README.
         */
        if (PageGetFreeSpace(page) < insertstate->itemsz)
        {
            if (P_HAS_GARBAGE(lpageop))
            {
                _bt_vacuum_one_page(rel, insertstate->buf, heapRel);
                insertstate->bounds_valid = false;

                /* Might as well assume duplicates (if checkingunique) */
                uniquedup = true;
            }

            if (itup_key->allequalimage && BTGetDeduplicateItems(rel) &&
                (!checkingunique || uniquedup) &&
                PageGetFreeSpace(page) < insertstate->itemsz)
            {
                _bt_dedup_one_page(rel, insertstate->buf, heapRel,
                                   insertstate->itup, insertstate->itemsz,
                                   checkingunique);
                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);

    newitemoff = _bt_binsrch_insert(rel, insertstate);

    if (insertstate->postingoff == -1)
    {
        /*
         * There is an overlapping posting list tuple with its LP_DEAD bit
         * set.  We don't want to unnecessarily unset its LP_DEAD bit while
         * performing a posting list split, so delete all LP_DEAD items early.
         * This is the only case where LP_DEAD deletes happen even though
         * there is space for newitem on the page.
         */
        _bt_vacuum_one_page(rel, insertstate->buf, heapRel);

        /*
         * Do new binary search.  New insert location cannot overlap with any
         * posting list now.
         */
        insertstate->bounds_valid = false;
        insertstate->postingoff = 0;
        newitemoff = _bt_binsrch_insert(rel, insertstate);
        Assert(insertstate->postingoff == 0);
    }

    return newitemoff;
}

/*
 * 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 postingoff != 0, splits existing posting list tuple
 *             (since it overlaps with new 'itup' tuple).
 *          +  if necessary, splits the target page, using 'itup_key' for
 *             suffix truncation on leaf pages (caller passes NULL for
 *             non-leaf pages).
 *          +  inserts the new tuple (might be split from posting list).
 *          +  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,
               Size itemsz,
               OffsetNumber newitemoff,
               int postingoff,
               bool split_only_page)
{
    Page        page;
    BTPageOpaque lpageop;
    IndexTuple  oposting = NULL;
    IndexTuple  origitup = NULL;
    IndexTuple  nposting = NULL;

    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));
    Assert(!BTreeTupleIsPosting(itup));
    Assert(MAXALIGN(IndexTupleSize(itup)) == itemsz);

    /*
     * 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.
     */
    Assert(P_ISLEAF(lpageop) || newitemoff > P_FIRSTDATAKEY(lpageop));

    /* 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));

    /*
     * Do we need to split an existing posting list item?
     */
    if (postingoff != 0)
    {
        ItemId      itemid = PageGetItemId(page, newitemoff);

        /*
         * The new tuple is a duplicate with a heap TID that falls inside the
         * range of an existing posting list tuple on a leaf page.  Prepare to
         * split an existing posting list.  Overwriting the posting list with
         * its post-split version is treated as an extra step in either the
         * insert or page split critical section.
         */
        Assert(P_ISLEAF(lpageop) && !ItemIdIsDead(itemid));
        Assert(itup_key->heapkeyspace && itup_key->allequalimage);
        oposting = (IndexTuple) PageGetItem(page, itemid);

        /* use a mutable copy of itup as our itup from here on */
        origitup = itup;
        itup = CopyIndexTuple(origitup);
        nposting = _bt_swap_posting(itup, oposting, postingoff);
        /* itup now contains rightmost/max TID from oposting */

        /* Alter offset so that newitem goes after posting list */
        newitemoff = OffsetNumberNext(newitemoff);
    }

    /*
     * 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;

        /* split the buffer into left and right halves */
        rbuf = _bt_split(rel, itup_key, buf, cbuf, newitemoff, itemsz, itup,
                         origitup, nposting, postingoff);
        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
    {
        bool        isleaf = P_ISLEAF(lpageop);
        bool        isrightmost = P_RIGHTMOST(lpageop);
        Buffer      metabuf = InvalidBuffer;
        Page        metapg = NULL;
        BTMetaPageData *metad = NULL;
        BlockNumber blockcache;

        /*
         * 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(!isleaf);
            Assert(BufferIsValid(cbuf));

            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;
            }
        }

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

        if (postingoff != 0)
            memcpy(oposting, nposting, MAXALIGN(IndexTupleSize(nposting)));

        if (PageAddItem(page, (Item) itup, itemsz, newitemoff, false,
                        false) == InvalidOffsetNumber)
            elog(PANIC, "failed to add new item to block %u in index \"%s\"",
                 BufferGetBlockNumber(buf), 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 = BufferGetBlockNumber(buf);
            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);
        }

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

            xlrec.offnum = newitemoff;

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

            if (isleaf && postingoff == 0)
            {
                /* Simple leaf insert */
                xlinfo = XLOG_BTREE_INSERT_LEAF;
            }
            else if (postingoff != 0)
            {
                /*
                 * Leaf insert with posting list split.  Must include
                 * postingoff field before newitem/orignewitem.
                 */
                xlinfo = XLOG_BTREE_INSERT_POST;
            }
            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;
                xlmeta.allequalimage = metad->btm_allequalimage;

                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);
            if (postingoff == 0)
            {
                /* Simple, common case -- log itup from caller */
                XLogRegisterBufData(0, (char *) itup, IndexTupleSize(itup));
            }
            else
            {
                /*
                 * Insert with posting list split (XLOG_BTREE_INSERT_POST
                 * record) case.
                 *
                 * Log postingoff.  Also log origitup, not itup.  REDO routine
                 * must reconstruct final itup (as well as nposting) using
                 * _bt_swap_posting().
                 */
                uint16      upostingoff = postingoff;

                XLogRegisterBufData(0, (char *) &upostingoff, sizeof(uint16));
                XLogRegisterBufData(0, (char *) origitup,
                                    IndexTupleSize(origitup));
            }

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

        /*
         * Cache the block number if this is the rightmost leaf page.  Cache
         * may be used by a future inserter within _bt_search_insert().
         */
        blockcache = InvalidBlockNumber;
        if (isrightmost && isleaf && !P_ISROOT(lpageop))
            blockcache = BufferGetBlockNumber(buf);

        /* Release buffer for insertion target block */
        _bt_relbuf(rel, buf);

        /*
         * If we decided to cache the insertion target block before releasing
         * its buffer lock, then cache it now.  Check the height of the tree
         * first, though.  We don't go for the optimization with small
         * indexes.  Defer final check to this point to ensure that we don't
         * call _bt_getrootheight while holding a buffer lock.
         */
        if (BlockNumberIsValid(blockcache) &&
            _bt_getrootheight(rel) >= BTREE_FASTPATH_MIN_LEVEL)
            RelationSetTargetBlock(rel, blockcache);
    }

    /* be tidy */
    if (postingoff != 0)
    {
        /* itup is actually a modified copy of caller's original */
        pfree(nposting);
        pfree(itup);
    }
}

/*
 *  _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.
 *
 *      orignewitem, nposting, and postingoff are needed when an insert of
 *      orignewitem results in both a posting list split and a page split.
 *      These extra posting list split details are used here in the same
 *      way as they are used in the more common case where a posting list
 *      split does not coincide with a page split.  We need to deal with
 *      posting list splits directly in order to ensure that everything
 *      that follows from the insert of orignewitem is handled as a single
 *      atomic operation (though caller's insert of a new pivot/downlink
 *      into parent page will still be a separate operation).  See
 *      nbtree/README for details on the design of posting list splits.
 *
 *      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,
          IndexTuple orignewitem, IndexTuple nposting, uint16 postingoff)
{
    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 origpagepostingoff;
    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);

    /*
     * Determine page offset number of existing overlapped-with-orignewitem
     * posting list when it is necessary to perform a posting list split in
     * passing.  Note that newitem was already changed by caller (newitem no
     * longer has the orignewitem TID).
     *
     * This page offset number (origpagepostingoff) will be used to pretend
     * that the posting split has already taken place, even though the
     * required modifications to origpage won't occur until we reach the
     * critical section.  The lastleft and firstright tuples of our page split
     * point should, in effect, come from an imaginary version of origpage
     * that has the nposting tuple instead of the original posting list tuple.
     *
     * Note: _bt_findsplitloc() should have compensated for coinciding posting
     * list splits in just the same way, at least in theory.  It doesn't
     * bother with that, though.  In practice it won't affect its choice of
     * split point.
     */
    origpagepostingoff = InvalidOffsetNumber;
    if (postingoff != 0)
    {
        Assert(isleaf);
        Assert(ItemPointerCompare(&orignewitem->t_tid,
                                  &newitem->t_tid) < 0);
        Assert(BTreeTupleIsPosting(nposting));
        origpagepostingoff = OffsetNumberPrev(newitemoff);
    }

    /*
     * 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);
        if (firstright == origpagepostingoff)
            item = nposting;
    }

    /*
     * 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);
            if (lastleftoff == origpagepostingoff)
                lastleft = nposting;
        }

        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);

        /* replace original item with nposting due to posting split? */
        if (i == origpagepostingoff)
        {
            Assert(BTreeTupleIsPosting(item));
            Assert(itemsz == MAXALIGN(IndexTupleSize(nposting)));
            item = nposting;
        }

        /* does new item belong before this one? */
        else 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;
        /* See comments below on newitem, orignewitem, and posting lists */
        xlrec.firstright = firstright;
        xlrec.newitemoff = newitemoff;
        xlrec.postingoff = 0;
        if (postingoff != 0 && origpagepostingoff < firstright)
            xlrec.postingoff = postingoff;

        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 always store newitemoff in the record, though.
         *
         * The details are sometimes slightly different for page splits that
         * coincide with a posting list split.  If both the replacement
         * posting list and newitem go on the right page, then we don't need
         * to log anything extra, just like the simple !newitemonleft
         * no-posting-split case (postingoff is set to zero in the WAL record,
         * so recovery doesn't need to process a posting list split at all).
         * Otherwise, we set postingoff and log orignewitem instead of
         * newitem, despite having actually inserted newitem.  REDO routine
         * must reconstruct nposting and newitem using _bt_swap_posting().
         *
         * Note: It's possible that our page split point is the point that
         * makes the posting list lastleft and newitem firstright.  This is
         * the only case where we log orignewitem/newitem despite newitem
         * going on the right page.  If XLogInsert decides that it can omit
         * orignewitem due to logging a full-page image of the left page,
         * everything still works out, since recovery only needs to log
         * orignewitem for items on the left page (just like the regular
         * newitem-logged case).
         */
        if (newitemonleft && xlrec.postingoff == 0)
            XLogRegisterBufData(0, (char *) newitem, MAXALIGN(newitemsz));
        else if (xlrec.postingoff != 0)
        {
            Assert(newitemonleft || firstright == newitemoff);
            Assert(MAXALIGN(newitemsz) == IndexTupleSize(orignewitem));
            XLogRegisterBufData(0, (char *) orignewitem, 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);

            /*
             * We should never reach here when a leaf page split takes place
             * despite the insert of newitem being able to apply the fastpath
             * optimization.  Make sure of that with an assertion.
             *
             * This is more of a performance issue than a correctness issue.
             * The fastpath won't have a descent stack.  Using a phony stack
             * here works, but never rely on that.  The fastpath should be
             * rejected within _bt_search_insert() when the rightmost leaf
             * page will split, since it's faster to go through _bt_search()
             * and get a stack in the usual way.
             */
            Assert(!(P_ISLEAF(lpageop) &&
                     BlockNumberIsValid(RelationGetTargetBlock(rel))));

            /* 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);
        BTreeTupleSetDownLink(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);

        /*
         * Unlock the right child.  The left child will be unlocked in
         * _bt_insertonpg().
         *
         * Unlocking the right child must be delayed until here to ensure that
         * no concurrent VACUUM operation can become confused.  Page deletion
         * cannot be allowed to fail to re-find a downlink for the rbuf page.
         * (Actually, this is just a vestige of how things used to work.  The
         * page deletion code is expected to check for the INCOMPLETE_SPLIT
         * flag on the left child.  It won't attempt deletion of the right
         * child until the split is complete.  Despite all this, we opt to
         * conservatively delay unlocking the right child until here.)
         */
        _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, MAXALIGN(IndexTupleSize(new_item)),
                       stack->bts_offset + 1, 0, 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 (BTreeTupleGetDownLink(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 (BTreeTupleGetDownLink(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;
    BTreeTupleSetDownLink(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);
    BTreeTupleSetDownLink(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;
        md.allequalimage = metad->btm_allequalimage;

        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 data item to a particular page during split.
 *
 *      The difference between this routine and a bare PageAddItem call is
 *      that this code knows that the leftmost data item on an internal
 *      btree page has a key that must be treated as minus infinity.
 *      Therefore, it truncates away all attributes.  This extra step is
 *      only needed during internal page splits.
 *
 *      Truncation of an internal page data item can be thought of as one
 *      of the steps used to "move" a boundary separator key during an
 *      internal page split.  Conceptually, _bt_split() caller splits
 *      internal pages "inside" the firstright data item: firstright's
 *      separator key is used as the high key for the left page, while its
 *      downlink is used within the first data item (also the negative
 *      infinity item) for the right page.  Each distinct separator key
 *      should appear no more than once per level of the tree.
 *
 *      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);
        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[MaxIndexTuplesPerPage];
    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, or when deduplication runs.
     */
}