nbtsearch.c

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/*-------------------------------------------------------------------------
 *
 * nbtsearch.c
 *    Search code for postgres btrees.
 *
 *
 * Portions Copyright (c) 1996-2026, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * IDENTIFICATION
 *    src/backend/access/nbtree/nbtsearch.c
 *
 *-------------------------------------------------------------------------
 */
 
#include "postgres.h"
 
#include "access/nbtree.h"
#include "access/relscan.h"
#include "access/xact.h"
#include "executor/instrument_node.h"
#include "miscadmin.h"
#include "pgstat.h"
#include "storage/predicate.h"
#include "utils/lsyscache.h"
#include "utils/rel.h"
 
 
static inline void _bt_drop_lock_and_maybe_pin(Relation rel, BTScanOpaque so);
static Buffer _bt_moveright(Relation rel, Relation heaprel, BTScanInsert key,
                            Buffer buf, bool forupdate, BTStack stack,
                            int access);
static OffsetNumber _bt_binsrch(Relation rel, BTScanInsert key, Buffer buf);
static int  _bt_binsrch_posting(BTScanInsert key, Page page,
                                OffsetNumber offnum);
static inline void _bt_returnitem(IndexScanDesc scan, BTScanOpaque so);
static bool _bt_steppage(IndexScanDesc scan, ScanDirection dir);
static bool _bt_readfirstpage(IndexScanDesc scan, OffsetNumber offnum,
                              ScanDirection dir);
static bool _bt_readnextpage(IndexScanDesc scan, BlockNumber blkno,
                             BlockNumber lastcurrblkno, ScanDirection dir,
                             bool seized);
static Buffer _bt_lock_and_validate_left(Relation rel, BlockNumber *blkno,
                                         BlockNumber lastcurrblkno);
static bool _bt_endpoint(IndexScanDesc scan, ScanDirection dir);
 
 
/*
 *  _bt_drop_lock_and_maybe_pin()
 *
 * Unlock so->currPos.buf.  If scan is so->dropPin, drop the pin, too.
 * Dropping the pin prevents VACUUM from blocking on acquiring a cleanup lock.
 */
static inline void
_bt_drop_lock_and_maybe_pin(Relation rel, BTScanOpaque so)
{
    if (!so->dropPin)
    {
        /* Just drop the lock (not the pin) */
        _bt_unlockbuf(rel, so->currPos.buf);
        return;
    }
 
    /*
     * Drop both the lock and the pin.
     *
     * Have to set so->currPos.lsn so that _bt_killitems has a way to detect
     * when concurrent heap TID recycling by VACUUM might have taken place.
     */
    so->currPos.lsn = BufferGetLSNAtomic(so->currPos.buf);
    _bt_relbuf(rel, so->currPos.buf);
    so->currPos.buf = InvalidBuffer;
}
 
/*
 *  _bt_search() -- Search the tree for a particular scankey,
 *      or more precisely for the first leaf page it could be on.
 *
 * The passed scankey is an insertion-type scankey (see nbtree/README),
 * but it can omit the rightmost column(s) of the index.
 *
 * If returnstack is true, return value is a stack of parent-page pointers
 * (i.e. there is no entry for the leaf level/page).  If returnstack is false,
 * we just return NULL.  This scheme allows callers that don't need a descent
 * stack to avoid palloc churn.
 *
 * When we return, *bufP is set to the address of the leaf-page buffer, which
 * is locked and pinned.  No locks are held on the parent pages, however!
 *
 * The returned buffer is locked according to access parameter.  Additionally,
 * access = BT_WRITE will allow an empty root page to be created and returned.
 * When access = BT_READ, an empty index will result in *bufP being set to
 * InvalidBuffer.  Also, in BT_WRITE mode, any incomplete splits encountered
 * during the search will be finished.
 *
 * heaprel must be provided by callers that pass access = BT_WRITE, since we
 * might need to allocate a new root page for caller -- see _bt_allocbuf.
 */
BTStack
_bt_search(Relation rel, Relation heaprel, BTScanInsert key, Buffer *bufP,
           int access, bool returnstack)
{
    BTStack     stack_in = NULL;
    int         page_access = BT_READ;
 
    /* heaprel must be set whenever _bt_allocbuf is reachable */
    Assert(access == BT_READ || access == BT_WRITE);
    Assert(access == BT_READ || heaprel != NULL);
 
    /* Get the root page to start with */
    *bufP = _bt_getroot(rel, heaprel, access);
 
    /* If index is empty and access = BT_READ, no root page is created. */
    if (!BufferIsValid(*bufP))
        return (BTStack) NULL;
 
    /* Loop iterates once per level descended in the tree */
    for (;;)
    {
        Page        page;
        BTPageOpaque opaque;
        OffsetNumber offnum;
        ItemId      itemid;
        IndexTuple  itup;
        BlockNumber child;
        BTStack     new_stack;
 
        /*
         * Race -- the page we just grabbed may have split since we read its
         * downlink in its parent page (or the metapage).  If it has, we may
         * need to move right to its new sibling.  Do that.
         *
         * In write-mode, allow _bt_moveright to finish any incomplete splits
         * along the way.  Strictly speaking, we'd only need to finish an
         * incomplete split on the leaf page we're about to insert to, not on
         * any of the upper levels (internal pages with incomplete splits are
         * also taken care of in _bt_getstackbuf).  But this is a good
         * opportunity to finish splits of internal pages too.
         */
        *bufP = _bt_moveright(rel, heaprel, key, *bufP, (access == BT_WRITE),
                              stack_in, page_access);
 
        /* if this is a leaf page, we're done */
        page = BufferGetPage(*bufP);
        opaque = BTPageGetOpaque(page);
        if (P_ISLEAF(opaque))
            break;
 
        /*
         * Find the appropriate pivot tuple on this page.  Its downlink points
         * to the child page that we're about to descend to.
         */
        offnum = _bt_binsrch(rel, key, *bufP);
        itemid = PageGetItemId(page, offnum);
        itup = (IndexTuple) PageGetItem(page, itemid);
        Assert(BTreeTupleIsPivot(itup) || !key->heapkeyspace);
        child = BTreeTupleGetDownLink(itup);
 
        /*
         * We need to save the location of the pivot tuple we chose in a new
         * stack entry for this page/level.  If caller ends up splitting a
         * page one level down, it usually ends up inserting a new pivot
         * tuple/downlink immediately after the location recorded here.
         */
        if (returnstack)
        {
            new_stack = (BTStack) palloc_object(BTStackData);
            new_stack->bts_blkno = BufferGetBlockNumber(*bufP);
            new_stack->bts_offset = offnum;
            new_stack->bts_parent = stack_in;
            stack_in = new_stack;
        }
 
        /*
         * Page level 1 is lowest non-leaf page level prior to leaves.  So, if
         * we're on the level 1 and asked to lock leaf page in write mode,
         * then lock next page in write mode, because it must be a leaf.
         */
        if (opaque->btpo_level == 1 && access == BT_WRITE)
            page_access = BT_WRITE;
 
        /* drop the read lock on the page, then acquire one on its child */
        *bufP = _bt_relandgetbuf(rel, *bufP, child, page_access);
 
        /* okay, all set to move down a level */
    }
 
    /*
     * If we're asked to lock leaf in write mode, but didn't manage to, then
     * relock.  This should only happen when the root page is a leaf page (and
     * the only page in the index other than the metapage).
     */
    if (access == BT_WRITE && page_access == BT_READ)
    {
        /* trade in our read lock for a write lock */
        _bt_unlockbuf(rel, *bufP);
        _bt_lockbuf(rel, *bufP, BT_WRITE);
 
        /*
         * Race -- the leaf page may have split after we dropped the read lock
         * but before we acquired a write lock.  If it has, we may need to
         * move right to its new sibling.  Do that.
         */
        *bufP = _bt_moveright(rel, heaprel, key, *bufP, true, stack_in, BT_WRITE);
    }
 
    return stack_in;
}
 
/*
 *  _bt_moveright() -- move right in the btree if necessary.
 *
 * When we follow a pointer to reach a page, it is possible that
 * the page has changed in the meanwhile.  If this happens, we're
 * guaranteed that the page has "split right" -- that is, that any
 * data that appeared on the page originally is either on the page
 * or strictly to the right of it.
 *
 * This routine decides whether or not we need to move right in the
 * tree by examining the high key entry on the page.  If that entry is
 * strictly less than the scankey, or <= the scankey in the
 * key.nextkey=true case, then we followed the wrong link and we need
 * to move right.
 *
 * The passed insertion-type scankey can omit the rightmost column(s) of the
 * index. (see nbtree/README)
 *
 * When key.nextkey is false (the usual case), we are looking for the first
 * item >= key.  When key.nextkey is true, we are looking for the first item
 * strictly greater than key.
 *
 * If forupdate is true, we will attempt to finish any incomplete splits
 * that we encounter.  This is required when locking a target page for an
 * insertion, because we don't allow inserting on a page before the split is
 * completed.  'heaprel' and 'stack' are only used if forupdate is true.
 *
 * On entry, we have the buffer pinned and a lock of the type specified by
 * 'access'.  If we move right, we release the buffer and lock and acquire
 * the same on the right sibling.  Return value is the buffer we stop at.
 */
static Buffer
_bt_moveright(Relation rel,
              Relation heaprel,
              BTScanInsert key,
              Buffer buf,
              bool forupdate,
              BTStack stack,
              int access)
{
    Page        page;
    BTPageOpaque opaque;
    int32       cmpval;
 
    Assert(!forupdate || heaprel != NULL);
 
    /*
     * When nextkey = false (normal case): if the scan key that brought us to
     * this page is > the high key stored on the page, then the page has split
     * and we need to move right.  (pg_upgrade'd !heapkeyspace indexes could
     * have some duplicates to the right as well as the left, but that's
     * something that's only ever dealt with on the leaf level, after
     * _bt_search has found an initial leaf page.)
     *
     * When nextkey = true: move right if the scan key is >= page's high key.
     * (Note that key.scantid cannot be set in this case.)
     *
     * The page could even have split more than once, so scan as far as
     * needed.
     *
     * We also have to move right if we followed a link that brought us to a
     * dead page.
     */
    cmpval = key->nextkey ? 0 : 1;
 
    for (;;)
    {
        page = BufferGetPage(buf);
        opaque = BTPageGetOpaque(page);
 
        if (P_RIGHTMOST(opaque))
            break;
 
        /*
         * Finish any incomplete splits we encounter along the way.
         */
        if (forupdate && P_INCOMPLETE_SPLIT(opaque))
        {
            BlockNumber blkno = BufferGetBlockNumber(buf);
 
            /* upgrade our lock if necessary */
            if (access == BT_READ)
            {
                _bt_unlockbuf(rel, buf);
                _bt_lockbuf(rel, buf, BT_WRITE);
            }
 
            if (P_INCOMPLETE_SPLIT(opaque))
                _bt_finish_split(rel, heaprel, buf, stack);
            else
                _bt_relbuf(rel, buf);
 
            /* re-acquire the lock in the right mode, and re-check */
            buf = _bt_getbuf(rel, blkno, access);
            continue;
        }
 
        if (P_IGNORE(opaque) || _bt_compare(rel, key, page, P_HIKEY) >= cmpval)
        {
            /* step right one page */
            buf = _bt_relandgetbuf(rel, buf, opaque->btpo_next, access);
            continue;
        }
        else
            break;
    }
 
    if (P_IGNORE(opaque))
        elog(ERROR, "fell off the end of index \"%s\"",
             RelationGetRelationName(rel));
 
    return buf;
}
 
/*
 *  _bt_binsrch() -- Do a binary search for a key on a particular page.
 *
 * On an internal (non-leaf) page, _bt_binsrch() returns the OffsetNumber
 * of the last key < given scankey, or last key <= given scankey if nextkey
 * is true.  (Since _bt_compare treats the first data key of such a page as
 * minus infinity, there will be at least one key < scankey, so the result
 * always points at one of the keys on the page.)
 *
 * On a leaf page, _bt_binsrch() returns the final result of the initial
 * positioning process that started with _bt_first's call to _bt_search.
 * We're returning a non-pivot tuple offset, so things are a little different.
 * It is possible that we'll return an offset that's either past the last
 * non-pivot slot, or (in the case of a backward scan) before the first slot.
 *
 * This procedure is not responsible for walking right, it just examines
 * the given page.  _bt_binsrch() has no lock or refcount side effects
 * on the buffer.
 */
static OffsetNumber
_bt_binsrch(Relation rel,
            BTScanInsert key,
            Buffer buf)
{
    Page        page;
    BTPageOpaque opaque;
    OffsetNumber low,
                high;
    int32       result,
                cmpval;
 
    page = BufferGetPage(buf);
    opaque = BTPageGetOpaque(page);
 
    /* Requesting nextkey semantics while using scantid seems nonsensical */
    Assert(!key->nextkey || key->scantid == NULL);
    /* scantid-set callers must use _bt_binsrch_insert() on leaf pages */
    Assert(!P_ISLEAF(opaque) || key->scantid == NULL);
 
    low = P_FIRSTDATAKEY(opaque);
    high = PageGetMaxOffsetNumber(page);
 
    /*
     * If there are no keys on the page, return the first available slot. Note
     * this covers two cases: the page is really empty (no keys), or it
     * contains only a high key.  The latter case is possible after vacuuming.
     * This can never happen on an internal page, however, since they are
     * never empty (an internal page must have at least one child).
     */
    if (unlikely(high < low))
        return low;
 
    /*
     * Binary search to find the first key on the page >= scan key, or first
     * key > scankey when nextkey is true.
     *
     * For nextkey=false (cmpval=1), the loop invariant is: all slots before
     * 'low' are < scan key, all slots at or after 'high' are >= scan key.
     *
     * For nextkey=true (cmpval=0), the loop invariant is: all slots before
     * 'low' are <= scan key, all slots at or after 'high' are > scan key.
     *
     * We can fall out when high == low.
     */
    high++;                     /* establish the loop invariant for high */
 
    cmpval = key->nextkey ? 0 : 1;  /* select comparison value */
 
    while (high > low)
    {
        OffsetNumber mid = low + ((high - low) / 2);
 
        /* We have low <= mid < high, so mid points at a real slot */
 
        result = _bt_compare(rel, key, page, mid);
 
        if (result >= cmpval)
            low = mid + 1;
        else
            high = mid;
    }
 
    /*
     * At this point we have high == low.
     *
     * On a leaf page we always return the first non-pivot tuple >= scan key
     * (resp. > scan key) for forward scan callers.  For backward scans, it's
     * always the _last_ non-pivot tuple < scan key (resp. <= scan key).
     */
    if (P_ISLEAF(opaque))
    {
        /*
         * In the backward scan case we're supposed to locate the last
         * matching tuple on the leaf level -- not the first matching tuple
         * (the last tuple will be the first one returned by the scan).
         *
         * At this point we've located the first non-pivot tuple immediately
         * after the last matching tuple (which might just be maxoff + 1).
         * Compensate by stepping back.
         */
        if (key->backward)
            return OffsetNumberPrev(low);
 
        return low;
    }
 
    /*
     * On a non-leaf page, return the last key < scan key (resp. <= scan key).
     * There must be one if _bt_compare() is playing by the rules.
     *
     * _bt_compare() will seldom see any exactly-matching pivot tuples, since
     * a truncated -inf heap TID is usually enough to prevent it altogether.
     * Even omitted scan key entries are treated as > truncated attributes.
     *
     * However, during backward scans _bt_compare() interprets omitted scan
     * key attributes as == corresponding truncated -inf attributes instead.
     * This works just like < would work here.  Under this scheme, < strategy
     * backward scans will always directly descend to the correct leaf page.
     * In particular, they will never incur an "extra" leaf page access with a
     * scan key that happens to contain the same prefix of values as some
     * pivot tuple's untruncated prefix.  VACUUM relies on this guarantee when
     * it uses a leaf page high key to "re-find" a page undergoing deletion.
     */
    Assert(low > P_FIRSTDATAKEY(opaque));
 
    return OffsetNumberPrev(low);
}
 
/*
 *
 *  _bt_binsrch_insert() -- Cacheable, incremental leaf page binary search.
 *
 * Like _bt_binsrch(), but with support for caching the binary search
 * bounds.  Only used during insertion, and only on the leaf page that it
 * looks like caller will insert tuple on.  Exclusive-locked and pinned
 * leaf page is contained within insertstate.
 *
 * Caches the bounds fields in insertstate so that a subsequent call can
 * reuse the low and strict high bounds of original binary search.  Callers
 * that use these fields directly must be prepared for the case where low
 * and/or stricthigh are not on the same page (one or both exceed maxoff
 * for the page).  The case where there are no items on the page (high <
 * low) makes bounds invalid.
 *
 * Caller is responsible for invalidating bounds when it modifies the page
 * before calling here a second time, and for dealing with posting list
 * tuple matches (callers can use insertstate's postingoff field to
 * determine which existing heap TID will need to be replaced by a posting
 * list split).
 */
OffsetNumber
_bt_binsrch_insert(Relation rel, BTInsertState insertstate)
{
    BTScanInsert key = insertstate->itup_key;
    Page        page;
    BTPageOpaque opaque;
    OffsetNumber low,
                high,
                stricthigh;
    int32       result,
                cmpval;
 
    page = BufferGetPage(insertstate->buf);
    opaque = BTPageGetOpaque(page);
 
    Assert(P_ISLEAF(opaque));
    Assert(!key->nextkey);
    Assert(insertstate->postingoff == 0);
 
    if (!insertstate->bounds_valid)
    {
        /* Start new binary search */
        low = P_FIRSTDATAKEY(opaque);
        high = PageGetMaxOffsetNumber(page);
    }
    else
    {
        /* Restore result of previous binary search against same page */
        low = insertstate->low;
        high = insertstate->stricthigh;
    }
 
    /* If there are no keys on the page, return the first available slot */
    if (unlikely(high < low))
    {
        /* Caller can't reuse bounds */
        insertstate->low = InvalidOffsetNumber;
        insertstate->stricthigh = InvalidOffsetNumber;
        insertstate->bounds_valid = false;
        return low;
    }
 
    /*
     * Binary search to find the first key on the page >= scan key. (nextkey
     * is always false when inserting).
     *
     * The loop invariant is: all slots before 'low' are < scan key, all slots
     * at or after 'high' are >= scan key.  'stricthigh' is > scan key, and is
     * maintained to save additional search effort for caller.
     *
     * We can fall out when high == low.
     */
    if (!insertstate->bounds_valid)
        high++;                 /* establish the loop invariant for high */
    stricthigh = high;          /* high initially strictly higher */
 
    cmpval = 1;                 /* !nextkey comparison value */
 
    while (high > low)
    {
        OffsetNumber mid = low + ((high - low) / 2);
 
        /* We have low <= mid < high, so mid points at a real slot */
 
        result = _bt_compare(rel, key, page, mid);
 
        if (result >= cmpval)
            low = mid + 1;
        else
        {
            high = mid;
            if (result != 0)
                stricthigh = high;
        }
 
        /*
         * If tuple at offset located by binary search is a posting list whose
         * TID range overlaps with caller's scantid, perform posting list
         * binary search to set postingoff for caller.  Caller must split the
         * posting list when postingoff is set.  This should happen
         * infrequently.
         */
        if (unlikely(result == 0 && key->scantid != NULL))
        {
            /*
             * postingoff should never be set more than once per leaf page
             * binary search.  That would mean that there are duplicate table
             * TIDs in the index, which is never okay.  Check for that here.
             */
            if (insertstate->postingoff != 0)
                ereport(ERROR,
                        (errcode(ERRCODE_INDEX_CORRUPTED),
                         errmsg_internal("table tid from new index tuple (%u,%u) cannot find insert offset between offsets %u and %u of block %u in index \"%s\"",
                                         ItemPointerGetBlockNumber(key->scantid),
                                         ItemPointerGetOffsetNumber(key->scantid),
                                         low, stricthigh,
                                         BufferGetBlockNumber(insertstate->buf),
                                         RelationGetRelationName(rel))));
 
            insertstate->postingoff = _bt_binsrch_posting(key, page, mid);
        }
    }
 
    /*
     * On a leaf page, a binary search always returns the first key >= scan
     * key (at least in !nextkey case), which could be the last slot + 1. This
     * is also the lower bound of cached search.
     *
     * stricthigh may also be the last slot + 1, which prevents caller from
     * using bounds directly, but is still useful to us if we're called a
     * second time with cached bounds (cached low will be < stricthigh when
     * that happens).
     */
    insertstate->low = low;
    insertstate->stricthigh = stricthigh;
    insertstate->bounds_valid = true;
 
    return low;
}
 
/*----------
 *  _bt_binsrch_posting() -- posting list binary search.
 *
 * Helper routine for _bt_binsrch_insert().
 *
 * Returns offset into posting list where caller's scantid belongs.
 *----------
 */
static int
_bt_binsrch_posting(BTScanInsert key, Page page, OffsetNumber offnum)
{
    IndexTuple  itup;
    ItemId      itemid;
    int         low,
                high,
                mid,
                res;
 
    /*
     * If this isn't a posting tuple, then the index must be corrupt (if it is
     * an ordinary non-pivot tuple then there must be an existing tuple with a
     * heap TID that equals inserter's new heap TID/scantid).  Defensively
     * check that tuple is a posting list tuple whose posting list range
     * includes caller's scantid.
     *
     * (This is also needed because contrib/amcheck's rootdescend option needs
     * to be able to relocate a non-pivot tuple using _bt_binsrch_insert().)
     */
    itemid = PageGetItemId(page, offnum);
    itup = (IndexTuple) PageGetItem(page, itemid);
    if (!BTreeTupleIsPosting(itup))
        return 0;
 
    Assert(key->heapkeyspace && key->allequalimage);
 
    /*
     * In the event that posting list tuple has LP_DEAD bit set, indicate this
     * to _bt_binsrch_insert() caller by returning -1, a sentinel value.  A
     * second call to _bt_binsrch_insert() can take place when its caller has
     * removed the dead item.
     */
    if (ItemIdIsDead(itemid))
        return -1;
 
    /* "high" is past end of posting list for loop invariant */
    low = 0;
    high = BTreeTupleGetNPosting(itup);
    Assert(high >= 2);
 
    while (high > low)
    {
        mid = low + ((high - low) / 2);
        res = ItemPointerCompare(key->scantid,
                                 BTreeTupleGetPostingN(itup, mid));
 
        if (res > 0)
            low = mid + 1;
        else if (res < 0)
            high = mid;
        else
            return mid;
    }
 
    /* Exact match not found */
    return low;
}
 
/*----------
 *  _bt_compare() -- Compare insertion-type scankey to tuple on a page.
 *
 *  page/offnum: location of btree item to be compared to.
 *
 *      This routine returns:
 *          <0 if scankey < tuple at offnum;
 *           0 if scankey == tuple at offnum;
 *          >0 if scankey > tuple at offnum.
 *
 * NULLs in the keys are treated as sortable values.  Therefore
 * "equality" does not necessarily mean that the item should be returned
 * to the caller as a matching key.  Similarly, an insertion scankey
 * with its scantid set is treated as equal to a posting tuple whose TID
 * range overlaps with their scantid.  There generally won't be a
 * matching TID in the posting tuple, which caller must handle
 * themselves (e.g., by splitting the posting list tuple).
 *
 * CRUCIAL NOTE: on a non-leaf page, the first data key is assumed to be
 * "minus infinity": this routine will always claim it is less than the
 * scankey.  The actual key value stored is explicitly truncated to 0
 * attributes (explicitly minus infinity) with version 3+ indexes, but
 * that isn't relied upon.  This allows us to implement the Lehman and
 * Yao convention that the first down-link pointer is before the first
 * key.  See backend/access/nbtree/README for details.
 *----------
 */
int32
_bt_compare(Relation rel,
            BTScanInsert key,
            Page page,
            OffsetNumber offnum)
{
    TupleDesc   itupdesc = RelationGetDescr(rel);
    BTPageOpaque opaque = BTPageGetOpaque(page);
    IndexTuple  itup;
    ItemPointer heapTid;
    ScanKey     scankey;
    int         ncmpkey;
    int         ntupatts;
    int32       result;
 
    Assert(_bt_check_natts(rel, key->heapkeyspace, page, offnum));
    Assert(key->keysz <= IndexRelationGetNumberOfKeyAttributes(rel));
    Assert(key->heapkeyspace || key->scantid == NULL);
 
    /*
     * Force result ">" if target item is first data item on an internal page
     * --- see NOTE above.
     */
    if (!P_ISLEAF(opaque) && offnum == P_FIRSTDATAKEY(opaque))
        return 1;
 
    itup = (IndexTuple) PageGetItem(page, PageGetItemId(page, offnum));
    ntupatts = BTreeTupleGetNAtts(itup, rel);
 
    /*
     * The scan key is set up with the attribute number associated with each
     * term in the key.  It is important that, if the index is multi-key, the
     * scan contain the first k key attributes, and that they be in order.  If
     * you think about how multi-key ordering works, you'll understand why
     * this is.
     *
     * We don't test for violation of this condition here, however.  The
     * initial setup for the index scan had better have gotten it right (see
     * _bt_first).
     */
 
    ncmpkey = Min(ntupatts, key->keysz);
    Assert(key->heapkeyspace || ncmpkey == key->keysz);
    Assert(!BTreeTupleIsPosting(itup) || key->allequalimage);
    scankey = key->scankeys;
    for (int i = 1; i <= ncmpkey; i++)
    {
        Datum       datum;
        bool        isNull;
 
        datum = index_getattr(itup, scankey->sk_attno, itupdesc, &isNull);
 
        if (scankey->sk_flags & SK_ISNULL)  /* key is NULL */
        {
            if (isNull)
                result = 0;     /* NULL "=" NULL */
            else if (scankey->sk_flags & SK_BT_NULLS_FIRST)
                result = -1;    /* NULL "<" NOT_NULL */
            else
                result = 1;     /* NULL ">" NOT_NULL */
        }
        else if (isNull)        /* key is NOT_NULL and item is NULL */
        {
            if (scankey->sk_flags & SK_BT_NULLS_FIRST)
                result = 1;     /* NOT_NULL ">" NULL */
            else
                result = -1;    /* NOT_NULL "<" NULL */
        }
        else
        {
            /*
             * The sk_func needs to be passed the index value as left arg and
             * the sk_argument as right arg (they might be of different
             * types).  Since it is convenient for callers to think of
             * _bt_compare as comparing the scankey to the index item, we have
             * to flip the sign of the comparison result.  (Unless it's a DESC
             * column, in which case we *don't* flip the sign.)
             */
            result = DatumGetInt32(FunctionCall2Coll(&scankey->sk_func,
                                                     scankey->sk_collation,
                                                     datum,
                                                     scankey->sk_argument));
 
            if (!(scankey->sk_flags & SK_BT_DESC))
                INVERT_COMPARE_RESULT(result);
        }
 
        /* if the keys are unequal, return the difference */
        if (result != 0)
            return result;
 
        scankey++;
    }
 
    /*
     * All non-truncated attributes (other than heap TID) were found to be
     * equal.  Treat truncated attributes as minus infinity when scankey has a
     * key attribute value that would otherwise be compared directly.
     *
     * Note: it doesn't matter if ntupatts includes non-key attributes;
     * scankey won't, so explicitly excluding non-key attributes isn't
     * necessary.
     */
    if (key->keysz > ntupatts)
        return 1;
 
    /*
     * Use the heap TID attribute and scantid to try to break the tie.  The
     * rules are the same as any other key attribute -- only the
     * representation differs.
     */
    heapTid = BTreeTupleGetHeapTID(itup);
    if (key->scantid == NULL)
    {
        /*
         * Forward scans have a scankey that is considered greater than a
         * truncated pivot tuple if and when the scankey has equal values for
         * attributes up to and including the least significant untruncated
         * attribute in tuple.  Even attributes that were omitted from the
         * scan key are considered greater than -inf truncated attributes.
         * (See _bt_binsrch for an explanation of our backward scan behavior.)
         *
         * For example, if an index has the minimum two attributes (single
         * user key attribute, plus heap TID attribute), and a page's high key
         * is ('foo', -inf), and scankey is ('foo', <omitted>), the search
         * will not descend to the page to the left.  The search will descend
         * right instead.  The truncated attribute in pivot tuple means that
         * all non-pivot tuples on the page to the left are strictly < 'foo',
         * so it isn't necessary to descend left.  In other words, search
         * doesn't have to descend left because it isn't interested in a match
         * that has a heap TID value of -inf.
         *
         * Note: the heap TID part of the test ensures that scankey is being
         * compared to a pivot tuple with one or more truncated -inf key
         * attributes.  The heap TID attribute is the last key attribute in
         * every index, of course, but other than that it isn't special.
         */
        if (!key->backward && key->keysz == ntupatts && heapTid == NULL &&
            key->heapkeyspace)
            return 1;
 
        /* All provided scankey arguments found to be equal */
        return 0;
    }
 
    /*
     * Treat truncated heap TID as minus infinity, since scankey has a key
     * attribute value (scantid) that would otherwise be compared directly
     */
    Assert(key->keysz == IndexRelationGetNumberOfKeyAttributes(rel));
    if (heapTid == NULL)
        return 1;
 
    /*
     * Scankey must be treated as equal to a posting list tuple if its scantid
     * value falls within the range of the posting list.  In all other cases
     * there can only be a single heap TID value, which is compared directly
     * with scantid.
     */
    Assert(ntupatts >= IndexRelationGetNumberOfKeyAttributes(rel));
    result = ItemPointerCompare(key->scantid, heapTid);
    if (result <= 0 || !BTreeTupleIsPosting(itup))
        return result;
    else
    {
        result = ItemPointerCompare(key->scantid,
                                    BTreeTupleGetMaxHeapTID(itup));
        if (result > 0)
            return 1;
    }
 
    return 0;
}
 
/*
 *  _bt_first() -- Find the first item in a scan.
 *
 *      We need to be clever about the direction of scan, the search
 *      conditions, and the tree ordering.  We find the first item (or,
 *      if backwards scan, the last item) in the tree that satisfies the
 *      qualifications in the scan key.  On success exit, data about the
 *      matching tuple(s) on the page has been loaded into so->currPos.  We'll
 *      drop all locks and hold onto a pin on page's buffer, except during
 *      so->dropPin scans, when we drop both the lock and the pin.
 *      _bt_returnitem sets the next item to return to scan on success exit.
 *
 * If there are no matching items in the index, we return false, with no
 * pins or locks held.  so->currPos will remain invalid.
 *
 * Note that scan->keyData[], and the so->keyData[] scankey built from it,
 * are both search-type scankeys (see nbtree/README for more about this).
 * Within this routine, we build a temporary insertion-type scankey to use
 * in locating the scan start position.
 */
bool
_bt_first(IndexScanDesc scan, ScanDirection dir)
{
    Relation    rel = scan->indexRelation;
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    OffsetNumber offnum;
    BTScanInsertData inskey;
    ScanKey     startKeys[INDEX_MAX_KEYS];
    ScanKeyData notnullkey;
    int         keysz = 0;
    StrategyNumber strat_total = InvalidStrategy;
    BlockNumber blkno = InvalidBlockNumber,
                lastcurrblkno;
 
    Assert(!BTScanPosIsValid(so->currPos));
 
    /*
     * Examine the scan keys and eliminate any redundant keys; also mark the
     * keys that must be matched to continue the scan.
     */
    _bt_preprocess_keys(scan);
 
    /*
     * Quit now if _bt_preprocess_keys() discovered that the scan keys can
     * never be satisfied (eg, x == 1 AND x > 2).
     */
    if (!so->qual_ok)
    {
        Assert(!so->needPrimScan);
        _bt_parallel_done(scan);
        return false;
    }
 
    /*
     * If this is a parallel scan, we must seize the scan.  _bt_readfirstpage
     * will likely release the parallel scan later on.
     */
    if (scan->parallel_scan != NULL &&
        !_bt_parallel_seize(scan, &blkno, &lastcurrblkno, true))
        return false;
 
    /*
     * Initialize the scan's arrays (if any) for the current scan direction
     * (except when they were already set to later values as part of
     * scheduling the primitive index scan that is now underway)
     */
    if (so->numArrayKeys && !so->needPrimScan)
        _bt_start_array_keys(scan, dir);
 
    if (blkno != InvalidBlockNumber)
    {
        /*
         * We anticipated calling _bt_search, but another worker bet us to it.
         * _bt_readnextpage releases the scan for us (not _bt_readfirstpage).
         */
        Assert(scan->parallel_scan != NULL);
        Assert(!so->needPrimScan);
        Assert(blkno != P_NONE);
 
        if (!_bt_readnextpage(scan, blkno, lastcurrblkno, dir, true))
            return false;
 
        _bt_returnitem(scan, so);
        return true;
    }
 
    /*
     * Count an indexscan for stats, now that we know that we'll call
     * _bt_search/_bt_endpoint below
     */
    pgstat_count_index_scan(rel);
    if (scan->instrument)
        scan->instrument->nsearches++;
 
    /*----------
     * Examine the scan keys to discover where we need to start the scan.
     * The selected scan keys (at most one per index column) are remembered by
     * storing their addresses into the local startKeys[] array.  The final
     * startKeys[] entry's strategy is set in strat_total. (Actually, there
     * are a couple of cases where we force a less/more restrictive strategy.)
     *
     * We must use the key that was marked required (in the direction opposite
     * our own scan's) during preprocessing.  Each index attribute can only
     * have one such required key.  In general, the keys that we use to find
     * an initial position when scanning forwards are the same keys that end
     * the scan on the leaf level when scanning backwards (and vice-versa).
     *
     * When the scan keys include cross-type operators, _bt_preprocess_keys
     * may not be able to eliminate redundant keys; in such cases it will
     * arbitrarily pick a usable key for each attribute (and scan direction),
     * ensuring that there is no more than one key required in each direction.
     * We stop considering further keys once we reach the first nonrequired
     * key (which must come after all required keys), so this can't affect us.
     *
     * The required keys that we use as starting boundaries have to be =, >,
     * or >= keys for a forward scan or =, <, <= keys for a backwards scan.
     * We can use keys for multiple attributes so long as the prior attributes
     * had only =, >= (resp. =, <=) keys.  These rules are very similar to the
     * rules that preprocessing used to determine which keys to mark required.
     * We cannot always use every required key as a positioning key, though.
     * Skip arrays necessitate independently applying our own rules here.
     * Skip arrays are always generally considered = array keys, but we'll
     * nevertheless treat them as inequalities at certain points of the scan.
     * When that happens, it _might_ have implications for the number of
     * required keys that we can safely use for initial positioning purposes.
     *
     * For example, a forward scan with a skip array on its leading attribute
     * (with no low_compare/high_compare) will have at least two required scan
     * keys, but we won't use any of them as boundary keys during the scan's
     * initial call here.  Our positioning key during the first call here can
     * be thought of as representing "> -infinity".  Similarly, if such a skip
     * array's low_compare is "a > 'foo'", then we position using "a > 'foo'"
     * during the scan's initial call here; a lower-order key such as "b = 42"
     * can't be used until the "a" array advances beyond MINVAL/low_compare.
     *
     * On the other hand, if such a skip array's low_compare was "a >= 'foo'",
     * then we _can_ use "a >= 'foo' AND b = 42" during the initial call here.
     * A subsequent call here might have us use "a = 'fop' AND b = 42".  Note
     * that we treat = and >= as equivalent when scanning forwards (just as we
     * treat = and <= as equivalent when scanning backwards).  We effectively
     * do the same thing (though with a distinct "a" element/value) each time.
     *
     * All keys (with the exception of SK_SEARCHNULL keys and SK_BT_SKIP
     * array keys whose array is "null_elem=true") imply a NOT NULL qualifier.
     * If the index stores nulls at the end of the index we'll be starting
     * from, and we have no boundary key for the column (which means the key
     * we deduced NOT NULL from is an inequality key that constrains the other
     * end of the index), then we cons up an explicit SK_SEARCHNOTNULL key to
     * use as a boundary key.  If we didn't do this, we might find ourselves
     * traversing a lot of null entries at the start of the scan.
     *
     * In this loop, row-comparison keys are treated the same as keys on their
     * first (leftmost) columns.  We'll add all lower-order columns of the row
     * comparison that were marked required during preprocessing below.
     *
     * _bt_advance_array_keys needs to know exactly how we'll reposition the
     * scan (should it opt to schedule another primitive index scan).  It is
     * critical that primscans only be scheduled when they'll definitely make
     * some useful progress.  _bt_advance_array_keys does this by calling
     * _bt_checkkeys routines that report whether a tuple is past the end of
     * matches for the scan's keys (given the scan's current array elements).
     * If the page's final tuple is "after the end of matches" for a scan that
     * uses the *opposite* scan direction, then it must follow that it's also
     * "before the start of matches" for the actual current scan direction.
     * It is therefore essential that all of our initial positioning rules are
     * symmetric with _bt_checkkeys's corresponding continuescan=false rule.
     * If you update anything here, _bt_checkkeys/_bt_advance_array_keys might
     * need to be kept in sync.
     *----------
     */
    if (so->numberOfKeys > 0)
    {
        AttrNumber  curattr;
        ScanKey     bkey;
        ScanKey     impliesNN;
        ScanKey     cur;
 
        /*
         * bkey will be set to the key that preprocessing left behind as the
         * boundary key for this attribute, in this scan direction (if any)
         */
        cur = so->keyData;
        curattr = 1;
        bkey = NULL;
        /* Also remember any scankey that implies a NOT NULL constraint */
        impliesNN = NULL;
 
        /*
         * Loop iterates from 0 to numberOfKeys inclusive; we use the last
         * pass to handle after-last-key processing.  Actual exit from the
         * loop is at one of the "break" statements below.
         */
        for (int i = 0;; cur++, i++)
        {
            if (i >= so->numberOfKeys || cur->sk_attno != curattr)
            {
                /* Done looking for the curattr boundary key */
                Assert(bkey == NULL ||
                       (bkey->sk_attno == curattr &&
                        (bkey->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD))));
                Assert(impliesNN == NULL ||
                       (impliesNN->sk_attno == curattr &&
                        (impliesNN->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD))));
 
                /*
                 * If this is a scan key for a skip array whose current
                 * element is MINVAL, choose low_compare (when scanning
                 * backwards it'll be MAXVAL, and we'll choose high_compare).
                 *
                 * Note: if the array's low_compare key makes 'bkey' NULL,
                 * then we behave as if the array's first element is -inf,
                 * except when !array->null_elem implies a usable NOT NULL
                 * constraint.
                 */
                if (bkey != NULL &&
                    (bkey->sk_flags & (SK_BT_MINVAL | SK_BT_MAXVAL)))
                {
                    int         ikey = bkey - so->keyData;
                    ScanKey     skipequalitykey = bkey;
                    BTArrayKeyInfo *array = NULL;
 
                    for (int arridx = 0; arridx < so->numArrayKeys; arridx++)
                    {
                        array = &so->arrayKeys[arridx];
                        if (array->scan_key == ikey)
                            break;
                    }
 
                    if (ScanDirectionIsForward(dir))
                    {
                        Assert(!(skipequalitykey->sk_flags & SK_BT_MAXVAL));
                        bkey = array->low_compare;
                    }
                    else
                    {
                        Assert(!(skipequalitykey->sk_flags & SK_BT_MINVAL));
                        bkey = array->high_compare;
                    }
 
                    Assert(bkey == NULL ||
                           bkey->sk_attno == skipequalitykey->sk_attno);
 
                    if (!array->null_elem)
                        impliesNN = skipequalitykey;
                    else
                        Assert(bkey == NULL && impliesNN == NULL);
                }
 
                /*
                 * If we didn't find a usable boundary key, see if we can
                 * deduce a NOT NULL key
                 */
                if (bkey == NULL && impliesNN != NULL &&
                    ((impliesNN->sk_flags & SK_BT_NULLS_FIRST) ?
                     ScanDirectionIsForward(dir) :
                     ScanDirectionIsBackward(dir)))
                {
                    /* Final startKeys[] entry will be deduced NOT NULL key */
                    bkey = &notnullkey;
                    ScanKeyEntryInitialize(bkey,
                                           (SK_SEARCHNOTNULL | SK_ISNULL |
                                            (impliesNN->sk_flags &
                                             (SK_BT_DESC | SK_BT_NULLS_FIRST))),
                                           curattr,
                                           ScanDirectionIsForward(dir) ?
                                           BTGreaterStrategyNumber : BTLessStrategyNumber,
                                           InvalidOid,
                                           InvalidOid,
                                           InvalidOid,
                                           (Datum) 0);
                }
 
                /*
                 * If preprocessing didn't leave a usable boundary key, quit;
                 * else save the boundary key pointer in startKeys[]
                 */
                if (bkey == NULL)
                    break;
                startKeys[keysz++] = bkey;
 
                /*
                 * We can only consider adding more boundary keys when the one
                 * that we just chose to add uses either the = or >= strategy
                 * (during backwards scans we can only do so when the key that
                 * we just added to startKeys[] uses the = or <= strategy)
                 */
                strat_total = bkey->sk_strategy;
                if (strat_total == BTGreaterStrategyNumber ||
                    strat_total == BTLessStrategyNumber)
                    break;
 
                /*
                 * If the key that we just added to startKeys[] is a skip
                 * array = key whose current element is marked NEXT or PRIOR,
                 * make strat_total > or < (and stop adding boundary keys).
                 * This can only happen with opclasses that lack skip support.
                 */
                if (bkey->sk_flags & (SK_BT_NEXT | SK_BT_PRIOR))
                {
                    Assert(bkey->sk_flags & SK_BT_SKIP);
                    Assert(strat_total == BTEqualStrategyNumber);
 
                    if (ScanDirectionIsForward(dir))
                    {
                        Assert(!(bkey->sk_flags & SK_BT_PRIOR));
                        strat_total = BTGreaterStrategyNumber;
                    }
                    else
                    {
                        Assert(!(bkey->sk_flags & SK_BT_NEXT));
                        strat_total = BTLessStrategyNumber;
                    }
 
                    /*
                     * We're done.  We'll never find an exact = match for a
                     * NEXT or PRIOR sentinel sk_argument value.  There's no
                     * sense in trying to add more keys to startKeys[].
                     */
                    break;
                }
 
                /*
                 * Done if that was the last scan key output by preprocessing.
                 * Also done if we've now examined all keys marked required.
                 */
                if (i >= so->numberOfKeys ||
                    !(cur->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD)))
                    break;
 
                /*
                 * Reset for next attr.
                 */
                Assert(cur->sk_attno == curattr + 1);
                curattr = cur->sk_attno;
                bkey = NULL;
                impliesNN = NULL;
            }
 
            /*
             * If we've located the starting boundary key for curattr, we have
             * no interest in curattr's other required key
             */
            if (bkey != NULL)
                continue;
 
            /*
             * Is this key the starting boundary key for curattr?
             *
             * If not, does it imply a NOT NULL constraint?  (Because
             * SK_SEARCHNULL keys are always assigned BTEqualStrategyNumber,
             * *any* inequality key works for that; we need not test.)
             */
            switch (cur->sk_strategy)
            {
                case BTLessStrategyNumber:
                case BTLessEqualStrategyNumber:
                    if (ScanDirectionIsBackward(dir))
                        bkey = cur;
                    else if (impliesNN == NULL)
                        impliesNN = cur;
                    break;
                case BTEqualStrategyNumber:
                    bkey = cur;
                    break;
                case BTGreaterEqualStrategyNumber:
                case BTGreaterStrategyNumber:
                    if (ScanDirectionIsForward(dir))
                        bkey = cur;
                    else if (impliesNN == NULL)
                        impliesNN = cur;
                    break;
            }
        }
    }
 
    /*
     * If we found no usable boundary keys, we have to start from one end of
     * the tree.  Walk down that edge to the first or last key, and scan from
     * there.
     *
     * Note: calls _bt_readfirstpage for us, which releases the parallel scan.
     */
    if (keysz == 0)
        return _bt_endpoint(scan, dir);
 
    /*
     * We want to start the scan somewhere within the index.  Set up an
     * insertion scankey we can use to search for the boundary point we
     * identified above.  The insertion scankey is built using the keys
     * identified by startKeys[].  (Remaining insertion scankey fields are
     * initialized after initial-positioning scan keys are finalized.)
     */
    Assert(keysz <= INDEX_MAX_KEYS);
    for (int i = 0; i < keysz; i++)
    {
        ScanKey     bkey = startKeys[i];
 
        Assert(bkey->sk_attno == i + 1);
 
        if (bkey->sk_flags & SK_ROW_HEADER)
        {
            /*
             * Row comparison header: look to the first row member instead
             */
            ScanKey     subkey = (ScanKey) DatumGetPointer(bkey->sk_argument);
            bool        loosen_strat = false,
                        tighten_strat = false;
 
            /*
             * Cannot be a NULL in the first row member: _bt_preprocess_keys
             * would've marked the qual as unsatisfiable, preventing us from
             * ever getting this far
             */
            Assert(subkey->sk_flags & SK_ROW_MEMBER);
            Assert(subkey->sk_attno == bkey->sk_attno);
            Assert(!(subkey->sk_flags & SK_ISNULL));
 
            /*
             * This is either a > or >= key (during backwards scans it is
             * either < or <=) that was marked required during preprocessing.
             * Later so->keyData[] keys can't have been marked required, so
             * our row compare header key must be the final startKeys[] entry.
             */
            Assert(subkey->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD));
            Assert(subkey->sk_strategy == bkey->sk_strategy);
            Assert(subkey->sk_strategy == strat_total);
            Assert(i == keysz - 1);
 
            /*
             * The member scankeys are already in insertion format (ie, they
             * have sk_func = 3-way-comparison function)
             */
            memcpy(inskey.scankeys + i, subkey, sizeof(ScanKeyData));
 
            /*
             * Now look to later row compare members.
             *
             * If there's an "index attribute gap" between two row compare
             * members, the second member won't have been marked required, and
             * so can't be used as a starting boundary key here.  The part of
             * the row comparison that we do still use has to be treated as a
             * ">=" or "<=" condition.  For example, a qual "(a, c) > (1, 42)"
             * with an omitted intervening index attribute "b" will use an
             * insertion scan key "a >= 1".  Even the first "a = 1" tuple on
             * the leaf level might satisfy the row compare qual.
             *
             * We're able to use a _more_ restrictive strategy when we reach a
             * NULL row compare member, since they're always unsatisfiable.
             * For example, a qual "(a, b, c) >= (1, NULL, 77)" will use an
             * insertion scan key "a > 1".  All tuples where "a = 1" cannot
             * possibly satisfy the row compare qual, so this is safe.
             */
            Assert(!(subkey->sk_flags & SK_ROW_END));
            for (;;)
            {
                subkey++;
                Assert(subkey->sk_flags & SK_ROW_MEMBER);
 
                if (subkey->sk_flags & SK_ISNULL)
                {
                    /*
                     * NULL member key, can only use earlier keys.
                     *
                     * We deliberately avoid checking if this key is marked
                     * required.  All earlier keys are required, and this key
                     * is unsatisfiable either way, so we can't miss anything.
                     */
                    tighten_strat = true;
                    break;
                }
 
                if (!(subkey->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD)))
                {
                    /* nonrequired member key, can only use earlier keys */
                    loosen_strat = true;
                    break;
                }
 
                Assert(subkey->sk_attno == keysz + 1);
                Assert(subkey->sk_strategy == bkey->sk_strategy);
                Assert(keysz < INDEX_MAX_KEYS);
 
                memcpy(inskey.scankeys + keysz, subkey, sizeof(ScanKeyData));
                keysz++;
 
                if (subkey->sk_flags & SK_ROW_END)
                    break;
            }
            Assert(!(loosen_strat && tighten_strat));
            if (loosen_strat)
            {
                /* Use less restrictive strategy (and fewer member keys) */
                switch (strat_total)
                {
                    case BTLessStrategyNumber:
                        strat_total = BTLessEqualStrategyNumber;
                        break;
                    case BTGreaterStrategyNumber:
                        strat_total = BTGreaterEqualStrategyNumber;
                        break;
                }
            }
            if (tighten_strat)
            {
                /* Use more restrictive strategy (and fewer member keys) */
                switch (strat_total)
                {
                    case BTLessEqualStrategyNumber:
                        strat_total = BTLessStrategyNumber;
                        break;
                    case BTGreaterEqualStrategyNumber:
                        strat_total = BTGreaterStrategyNumber;
                        break;
                }
            }
 
            /* Done (row compare header key is always last startKeys[] key) */
            break;
        }
 
        /*
         * Ordinary comparison key/search-style key.
         *
         * Transform the search-style scan key to an insertion scan key by
         * replacing the sk_func with the appropriate btree 3-way-comparison
         * function.
         *
         * If scankey operator is not a cross-type comparison, we can use the
         * cached comparison function; otherwise gotta look it up in the
         * catalogs.  (That can't lead to infinite recursion, since no
         * indexscan initiated by syscache lookup will use cross-data-type
         * operators.)
         *
         * We support the convention that sk_subtype == InvalidOid means the
         * opclass input type; this hack simplifies life for ScanKeyInit().
         */
        if (bkey->sk_subtype == rel->rd_opcintype[i] ||
            bkey->sk_subtype == InvalidOid)
        {
            FmgrInfo   *procinfo;
 
            procinfo = index_getprocinfo(rel, bkey->sk_attno, BTORDER_PROC);
            ScanKeyEntryInitializeWithInfo(inskey.scankeys + i,
                                           bkey->sk_flags,
                                           bkey->sk_attno,
                                           InvalidStrategy,
                                           bkey->sk_subtype,
                                           bkey->sk_collation,
                                           procinfo,
                                           bkey->sk_argument);
        }
        else
        {
            RegProcedure cmp_proc;
 
            cmp_proc = get_opfamily_proc(rel->rd_opfamily[i],
                                         rel->rd_opcintype[i],
                                         bkey->sk_subtype, BTORDER_PROC);
            if (!RegProcedureIsValid(cmp_proc))
                elog(ERROR, "missing support function %d(%u,%u) for attribute %d of index \"%s\"",
                     BTORDER_PROC, rel->rd_opcintype[i], bkey->sk_subtype,
                     bkey->sk_attno, RelationGetRelationName(rel));
            ScanKeyEntryInitialize(inskey.scankeys + i,
                                   bkey->sk_flags,
                                   bkey->sk_attno,
                                   InvalidStrategy,
                                   bkey->sk_subtype,
                                   bkey->sk_collation,
                                   cmp_proc,
                                   bkey->sk_argument);
        }
    }
 
    /*----------
     * Examine the selected initial-positioning strategy to determine exactly
     * where we need to start the scan, and set flag variables to control the
     * initial descent by _bt_search (and our _bt_binsrch call for the leaf
     * page _bt_search returns).
     *----------
     */
    _bt_metaversion(rel, &inskey.heapkeyspace, &inskey.allequalimage);
    inskey.anynullkeys = false; /* unused */
    inskey.scantid = NULL;
    inskey.keysz = keysz;
    switch (strat_total)
    {
        case BTLessStrategyNumber:
 
            inskey.nextkey = false;
            inskey.backward = true;
            break;
 
        case BTLessEqualStrategyNumber:
 
            inskey.nextkey = true;
            inskey.backward = true;
            break;
 
        case BTEqualStrategyNumber:
 
            /*
             * If a backward scan was specified, need to start with last equal
             * item not first one.
             */
            if (ScanDirectionIsBackward(dir))
            {
                /*
                 * This is the same as the <= strategy
                 */
                inskey.nextkey = true;
                inskey.backward = true;
            }
            else
            {
                /*
                 * This is the same as the >= strategy
                 */
                inskey.nextkey = false;
                inskey.backward = false;
            }
            break;
 
        case BTGreaterEqualStrategyNumber:
 
            /*
             * Find first item >= scankey
             */
            inskey.nextkey = false;
            inskey.backward = false;
            break;
 
        case BTGreaterStrategyNumber:
 
            /*
             * Find first item > scankey
             */
            inskey.nextkey = true;
            inskey.backward = false;
            break;
 
        default:
            /* can't get here, but keep compiler quiet */
            elog(ERROR, "unrecognized strat_total: %d", (int) strat_total);
            return false;
    }
 
    /*
     * Use the manufactured insertion scan key to descend the tree and
     * position ourselves on the target leaf page.
     */
    Assert(ScanDirectionIsBackward(dir) == inskey.backward);
    _bt_search(rel, NULL, &inskey, &so->currPos.buf, BT_READ, false);
 
    if (!BufferIsValid(so->currPos.buf))
    {
        Assert(!so->needPrimScan);
 
        /*
         * We only get here if the index is completely empty. Lock relation
         * because nothing finer to lock exists.  Without a buffer lock, it's
         * possible for another transaction to insert data between
         * _bt_search() and PredicateLockRelation().  We have to try again
         * after taking the relation-level predicate lock, to close a narrow
         * window where we wouldn't scan concurrently inserted tuples, but the
         * writer wouldn't see our predicate lock.
         */
        if (IsolationIsSerializable())
        {
            PredicateLockRelation(rel, scan->xs_snapshot);
            _bt_search(rel, NULL, &inskey, &so->currPos.buf, BT_READ, false);
        }
 
        if (!BufferIsValid(so->currPos.buf))
        {
            _bt_parallel_done(scan);
            return false;
        }
    }
 
    /* position to the precise item on the page */
    offnum = _bt_binsrch(rel, &inskey, so->currPos.buf);
 
    /*
     * Now load data from the first page of the scan (usually the page
     * currently in so->currPos.buf).
     *
     * If inskey.nextkey = false and inskey.backward = false, offnum is
     * positioned at the first non-pivot tuple >= inskey.scankeys.
     *
     * If inskey.nextkey = false and inskey.backward = true, offnum is
     * positioned at the last non-pivot tuple < inskey.scankeys.
     *
     * If inskey.nextkey = true and inskey.backward = false, offnum is
     * positioned at the first non-pivot tuple > inskey.scankeys.
     *
     * If inskey.nextkey = true and inskey.backward = true, offnum is
     * positioned at the last non-pivot tuple <= inskey.scankeys.
     *
     * It's possible that _bt_binsrch returned an offnum that is out of bounds
     * for the page.  For example, when inskey is both < the leaf page's high
     * key and > all of its non-pivot tuples, offnum will be "maxoff + 1".
     */
    if (!_bt_readfirstpage(scan, offnum, dir))
        return false;
 
    _bt_returnitem(scan, so);
    return true;
}
 
/*
 *  _bt_next() -- Get the next item in a scan.
 *
 *      On entry, so->currPos describes the current page, which may be pinned
 *      but is not locked, and so->currPos.itemIndex identifies which item was
 *      previously returned.
 *
 *      On success exit, so->currPos is updated as needed, and _bt_returnitem
 *      sets the next item to return to the scan.  so->currPos remains valid.
 *
 *      On failure exit (no more tuples), we invalidate so->currPos.  It'll
 *      still be possible for the scan to return tuples by changing direction,
 *      though we'll need to call _bt_first anew in that other direction.
 */
bool
_bt_next(IndexScanDesc scan, ScanDirection dir)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
 
    Assert(BTScanPosIsValid(so->currPos));
 
    /*
     * Advance to next tuple on current page; or if there's no more, try to
     * step to the next page with data.
     */
    if (ScanDirectionIsForward(dir))
    {
        if (++so->currPos.itemIndex > so->currPos.lastItem)
        {
            if (!_bt_steppage(scan, dir))
                return false;
        }
    }
    else
    {
        if (--so->currPos.itemIndex < so->currPos.firstItem)
        {
            if (!_bt_steppage(scan, dir))
                return false;
        }
    }
 
    _bt_returnitem(scan, so);
    return true;
}
 
/*
 * Return the index item from so->currPos.items[so->currPos.itemIndex] to the
 * index scan by setting the relevant fields in caller's index scan descriptor
 */
static inline void
_bt_returnitem(IndexScanDesc scan, BTScanOpaque so)
{
    BTScanPosItem *currItem = &so->currPos.items[so->currPos.itemIndex];
 
    /* Most recent _bt_readpage must have succeeded */
    Assert(BTScanPosIsValid(so->currPos));
    Assert(so->currPos.itemIndex >= so->currPos.firstItem);
    Assert(so->currPos.itemIndex <= so->currPos.lastItem);
 
    /* Return next item, per amgettuple contract */
    scan->xs_heaptid = currItem->heapTid;
    if (so->currTuples)
        scan->xs_itup = (IndexTuple) (so->currTuples + currItem->tupleOffset);
}
 
/*
 *  _bt_steppage() -- Step to next page containing valid data for scan
 *
 * Wrapper on _bt_readnextpage that performs final steps for the current page.
 *
 * On entry, so->currPos must be valid.  Its buffer will be pinned, though
 * never locked. (Actually, when so->dropPin there won't even be a pin held,
 * though so->currPos.currPage must still be set to a valid block number.)
 */
static bool
_bt_steppage(IndexScanDesc scan, ScanDirection dir)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    BlockNumber blkno,
                lastcurrblkno;
 
    Assert(BTScanPosIsValid(so->currPos));
 
    /* Before leaving current page, deal with any killed items */
    if (so->numKilled > 0)
        _bt_killitems(scan);
 
    /*
     * Before we modify currPos, make a copy of the page data if there was a
     * mark position that needs it.
     */
    if (so->markItemIndex >= 0)
    {
        /* bump pin on current buffer for assignment to mark buffer */
        if (BTScanPosIsPinned(so->currPos))
            IncrBufferRefCount(so->currPos.buf);
        memcpy(&so->markPos, &so->currPos,
               offsetof(BTScanPosData, items[1]) +
               so->currPos.lastItem * sizeof(BTScanPosItem));
        if (so->markTuples)
            memcpy(so->markTuples, so->currTuples,
                   so->currPos.nextTupleOffset);
        so->markPos.itemIndex = so->markItemIndex;
        so->markItemIndex = -1;
 
        /*
         * If we're just about to start the next primitive index scan
         * (possible with a scan that has arrays keys, and needs to skip to
         * continue in the current scan direction), moreLeft/moreRight only
         * indicate the end of the current primitive index scan.  They must
         * never be taken to indicate that the top-level index scan has ended
         * (that would be wrong).
         *
         * We could handle this case by treating the current array keys as
         * markPos state.  But depending on the current array state like this
         * would add complexity.  Instead, we just unset markPos's copy of
         * moreRight or moreLeft (whichever might be affected), while making
         * btrestrpos reset the scan's arrays to their initial scan positions.
         * In effect, btrestrpos leaves advancing the arrays up to the first
         * _bt_readpage call (that takes place after it has restored markPos).
         */
        if (so->needPrimScan)
        {
            if (ScanDirectionIsForward(so->currPos.dir))
                so->markPos.moreRight = true;
            else
                so->markPos.moreLeft = true;
        }
 
        /* mark/restore not supported by parallel scans */
        Assert(!scan->parallel_scan);
    }
 
    BTScanPosUnpinIfPinned(so->currPos);
 
    /* Walk to the next page with data */
    if (ScanDirectionIsForward(dir))
        blkno = so->currPos.nextPage;
    else
        blkno = so->currPos.prevPage;
    lastcurrblkno = so->currPos.currPage;
 
    /*
     * Cancel primitive index scans that were scheduled when the call to
     * _bt_readpage for currPos happened to use the opposite direction to the
     * one that we're stepping in now.  (It's okay to leave the scan's array
     * keys as-is, since the next _bt_readpage will advance them.)
     */
    if (so->currPos.dir != dir)
        so->needPrimScan = false;
 
    return _bt_readnextpage(scan, blkno, lastcurrblkno, dir, false);
}
 
/*
 *  _bt_readfirstpage() -- Read first page containing valid data for _bt_first
 *
 * _bt_first caller passes us an offnum returned by _bt_binsrch, which might
 * be an out of bounds offnum such as "maxoff + 1" in certain corner cases.
 * When we're passed an offnum past the end of the page, we might still manage
 * to stop the scan on this page by calling _bt_checkkeys against the high
 * key.  See _bt_readpage for full details.
 *
 * On entry, so->currPos must be pinned and locked (so offnum stays valid).
 * Parallel scan callers must have seized the scan before calling here.
 *
 * On exit, we'll have updated so->currPos and retained locks and pins
 * according to the same rules as those laid out for _bt_readnextpage exit.
 * Like _bt_readnextpage, our return value indicates if there are any matching
 * records in the given direction.
 *
 * We always release the scan for a parallel scan caller, regardless of
 * success or failure; we'll call _bt_parallel_release as soon as possible.
 */
static bool
_bt_readfirstpage(IndexScanDesc scan, OffsetNumber offnum, ScanDirection dir)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
 
    so->numKilled = 0;          /* just paranoia */
    so->markItemIndex = -1;     /* ditto */
 
    /* Initialize so->currPos for the first page (page in so->currPos.buf) */
    if (so->needPrimScan)
    {
        Assert(so->numArrayKeys);
 
        so->currPos.moreLeft = true;
        so->currPos.moreRight = true;
        so->needPrimScan = false;
    }
    else if (ScanDirectionIsForward(dir))
    {
        so->currPos.moreLeft = false;
        so->currPos.moreRight = true;
    }
    else
    {
        so->currPos.moreLeft = true;
        so->currPos.moreRight = false;
    }
 
    /*
     * Attempt to load matching tuples from the first page.
     *
     * Note that _bt_readpage will finish initializing the so->currPos fields.
     * _bt_readpage also releases parallel scan (even when it returns false).
     */
    if (_bt_readpage(scan, dir, offnum, true))
    {
        Relation    rel = scan->indexRelation;
 
        /*
         * _bt_readpage succeeded.  Drop the lock (and maybe the pin) on
         * so->currPos.buf in preparation for btgettuple returning tuples.
         */
        Assert(BTScanPosIsPinned(so->currPos));
        _bt_drop_lock_and_maybe_pin(rel, so);
        return true;
    }
 
    /* There's no actually-matching data on the page in so->currPos.buf */
    _bt_unlockbuf(scan->indexRelation, so->currPos.buf);
 
    /* Call _bt_readnextpage using its _bt_steppage wrapper function */
    if (!_bt_steppage(scan, dir))
        return false;
 
    /* _bt_readpage for a later page (now in so->currPos) succeeded */
    return true;
}
 
/*
 *  _bt_readnextpage() -- Read next page containing valid data for _bt_next
 *
 * Caller's blkno is the next interesting page's link, taken from either the
 * previously-saved right link or left link.  lastcurrblkno is the page that
 * was current at the point where the blkno link was saved, which we use to
 * reason about concurrent page splits/page deletions during backwards scans.
 * In the common case where seized=false, blkno is either so->currPos.nextPage
 * or so->currPos.prevPage, and lastcurrblkno is so->currPos.currPage.
 *
 * On entry, so->currPos shouldn't be locked by caller.  so->currPos.buf must
 * be InvalidBuffer/unpinned as needed by caller (note that lastcurrblkno
 * won't need to be read again in almost all cases).  Parallel scan callers
 * that seized the scan before calling here should pass seized=true; such a
 * caller's blkno and lastcurrblkno arguments come from the seized scan.
 * seized=false callers just pass us the blkno/lastcurrblkno taken from their
 * so->currPos, which (along with so->currPos itself) can be used to end the
 * scan.  A seized=false caller's blkno can never be assumed to be the page
 * that must be read next during a parallel scan, though.  We must figure that
 * part out for ourselves by seizing the scan (the correct page to read might
 * already be beyond the seized=false caller's blkno during a parallel scan,
 * unless blkno/so->currPos.nextPage/so->currPos.prevPage is already P_NONE,
 * or unless so->currPos.moreRight/so->currPos.moreLeft is already unset).
 *
 * On success exit, so->currPos is updated to contain data from the next
 * interesting page, and we return true.  We hold a pin on the buffer on
 * success exit (except during so->dropPin index scans, when we drop the pin
 * eagerly to avoid blocking VACUUM).
 *
 * If there are no more matching records in the given direction, we invalidate
 * so->currPos (while ensuring it retains no locks or pins), and return false.
 *
 * We always release the scan for a parallel scan caller, regardless of
 * success or failure; we'll call _bt_parallel_release as soon as possible.
 */
static bool
_bt_readnextpage(IndexScanDesc scan, BlockNumber blkno,
                 BlockNumber lastcurrblkno, ScanDirection dir, bool seized)
{
    Relation    rel = scan->indexRelation;
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
 
    Assert(so->currPos.currPage == lastcurrblkno || seized);
    Assert(!(blkno == P_NONE && seized));
    Assert(!BTScanPosIsPinned(so->currPos));
 
    /*
     * Remember that the scan already read lastcurrblkno, a page to the left
     * of blkno (or remember reading a page to the right, for backwards scans)
     */
    if (ScanDirectionIsForward(dir))
        so->currPos.moreLeft = true;
    else
        so->currPos.moreRight = true;
 
    for (;;)
    {
        Page        page;
        BTPageOpaque opaque;
 
        if (blkno == P_NONE ||
            (ScanDirectionIsForward(dir) ?
             !so->currPos.moreRight : !so->currPos.moreLeft))
        {
            /* most recent _bt_readpage call (for lastcurrblkno) ended scan */
            Assert(so->currPos.currPage == lastcurrblkno && !seized);
            BTScanPosInvalidate(so->currPos);
            _bt_parallel_done(scan);    /* iff !so->needPrimScan */
            return false;
        }
 
        Assert(!so->needPrimScan);
 
        /* parallel scan must never actually visit so->currPos blkno */
        if (!seized && scan->parallel_scan != NULL &&
            !_bt_parallel_seize(scan, &blkno, &lastcurrblkno, false))
        {
            /* whole scan is now done (or another primitive scan required) */
            BTScanPosInvalidate(so->currPos);
            return false;
        }
 
        if (ScanDirectionIsForward(dir))
        {
            /* read blkno, but check for interrupts first */
            CHECK_FOR_INTERRUPTS();
            so->currPos.buf = _bt_getbuf(rel, blkno, BT_READ);
        }
        else
        {
            /* read blkno, avoiding race (also checks for interrupts) */
            so->currPos.buf = _bt_lock_and_validate_left(rel, &blkno,
                                                         lastcurrblkno);
            if (so->currPos.buf == InvalidBuffer)
            {
                /* must have been a concurrent deletion of leftmost page */
                BTScanPosInvalidate(so->currPos);
                _bt_parallel_done(scan);
                return false;
            }
        }
 
        page = BufferGetPage(so->currPos.buf);
        opaque = BTPageGetOpaque(page);
        lastcurrblkno = blkno;
        if (likely(!P_IGNORE(opaque)))
        {
            /* see if there are any matches on this page */
            if (ScanDirectionIsForward(dir))
            {
                /* note that this will clear moreRight if we can stop */
                if (_bt_readpage(scan, dir, P_FIRSTDATAKEY(opaque), seized))
                    break;
                blkno = so->currPos.nextPage;
            }
            else
            {
                /* note that this will clear moreLeft if we can stop */
                if (_bt_readpage(scan, dir, PageGetMaxOffsetNumber(page), seized))
                    break;
                blkno = so->currPos.prevPage;
            }
        }
        else
        {
            /* _bt_readpage not called, so do all this for ourselves */
            if (ScanDirectionIsForward(dir))
                blkno = opaque->btpo_next;
            else
                blkno = opaque->btpo_prev;
            if (scan->parallel_scan != NULL)
                _bt_parallel_release(scan, blkno, lastcurrblkno);
        }
 
        /* no matching tuples on this page */
        _bt_relbuf(rel, so->currPos.buf);
        seized = false;         /* released by _bt_readpage (or by us) */
    }
 
    /*
     * _bt_readpage succeeded.  Drop the lock (and maybe the pin) on
     * so->currPos.buf in preparation for btgettuple returning tuples.
     */
    Assert(so->currPos.currPage == blkno);
    Assert(BTScanPosIsPinned(so->currPos));
    _bt_drop_lock_and_maybe_pin(rel, so);
 
    return true;
}
 
/*
 * _bt_lock_and_validate_left() -- lock caller's left sibling blkno,
 * recovering from concurrent page splits/page deletions when necessary
 *
 * Called during backwards scans, to deal with their unique concurrency rules.
 *
 * blkno points to the block number of the page that we expect to move the
 * scan to.  We'll successfully move the scan there when we find that its
 * right sibling link still points to lastcurrblkno (the page we just read).
 * Otherwise, we have to figure out which page is the correct one for the scan
 * to now read the hard way, reasoning about concurrent splits and deletions.
 * See nbtree/README.
 *
 * On return, we have both a pin and a read lock on the returned page, whose
 * block number will be set in *blkno.  Returns InvalidBuffer if there is no
 * page to the left (no lock or pin is held in that case).
 *
 * It is possible for the returned leaf page to be half-dead; caller must
 * check that condition and step left again when required.
 */
static Buffer
_bt_lock_and_validate_left(Relation rel, BlockNumber *blkno,
                           BlockNumber lastcurrblkno)
{
    BlockNumber origblkno = *blkno; /* detects circular links */
 
    for (;;)
    {
        Buffer      buf;
        Page        page;
        BTPageOpaque opaque;
        int         tries;
 
        /* check for interrupts while we're not holding any buffer lock */
        CHECK_FOR_INTERRUPTS();
        buf = _bt_getbuf(rel, *blkno, BT_READ);
        page = BufferGetPage(buf);
        opaque = BTPageGetOpaque(page);
 
        /*
         * If this isn't the page we want, walk right till we find what we
         * want --- but go no more than four hops (an arbitrary limit). If we
         * don't find the correct page by then, the most likely bet is that
         * lastcurrblkno got deleted and isn't in the sibling chain at all
         * anymore, not that its left sibling got split more than four times.
         *
         * Note that it is correct to test P_ISDELETED not P_IGNORE here,
         * because half-dead pages are still in the sibling chain.
         */
        tries = 0;
        for (;;)
        {
            if (likely(!P_ISDELETED(opaque) &&
                       opaque->btpo_next == lastcurrblkno))
            {
                /* Found desired page, return it */
                return buf;
            }
            if (P_RIGHTMOST(opaque) || ++tries > 4)
                break;
            /* step right */
            *blkno = opaque->btpo_next;
            buf = _bt_relandgetbuf(rel, buf, *blkno, BT_READ);
            page = BufferGetPage(buf);
            opaque = BTPageGetOpaque(page);
        }
 
        /*
         * Return to the original page (usually the page most recently read by
         * _bt_readpage, which is passed by caller as lastcurrblkno) to see
         * what's up with its prev sibling link
         */
        buf = _bt_relandgetbuf(rel, buf, lastcurrblkno, BT_READ);
        page = BufferGetPage(buf);
        opaque = BTPageGetOpaque(page);
        if (P_ISDELETED(opaque))
        {
            /*
             * It was deleted.  Move right to first nondeleted page (there
             * must be one); that is the page that has acquired the deleted
             * one's keyspace, so stepping left from it will take us where we
             * want to be.
             */
            for (;;)
            {
                if (P_RIGHTMOST(opaque))
                    elog(ERROR, "fell off the end of index \"%s\"",
                         RelationGetRelationName(rel));
                lastcurrblkno = opaque->btpo_next;
                buf = _bt_relandgetbuf(rel, buf, lastcurrblkno, BT_READ);
                page = BufferGetPage(buf);
                opaque = BTPageGetOpaque(page);
                if (!P_ISDELETED(opaque))
                    break;
            }
        }
        else
        {
            /*
             * Original lastcurrblkno wasn't deleted; the explanation had
             * better be that the page to the left got split or deleted.
             * Without this check, we risk going into an infinite loop.
             */
            if (opaque->btpo_prev == origblkno)
                elog(ERROR, "could not find left sibling of block %u in index \"%s\"",
                     lastcurrblkno, RelationGetRelationName(rel));
            /* Okay to try again, since left sibling link changed */
        }
 
        /*
         * Original lastcurrblkno from caller was concurrently deleted (could
         * also have been a great many concurrent left sibling page splits).
         * Found a non-deleted page that should now act as our lastcurrblkno.
         */
        if (P_LEFTMOST(opaque))
        {
            /* New lastcurrblkno has no left sibling (concurrently deleted) */
            _bt_relbuf(rel, buf);
            break;
        }
 
        /* Start from scratch with new lastcurrblkno's blkno/prev link */
        *blkno = origblkno = opaque->btpo_prev;
        _bt_relbuf(rel, buf);
    }
 
    return InvalidBuffer;
}
 
/*
 * _bt_get_endpoint() -- Find the first or last page on a given tree level
 *
 * If the index is empty, we will return InvalidBuffer; any other failure
 * condition causes ereport().  We will not return a dead page.
 *
 * The returned buffer is pinned and read-locked.
 */
Buffer
_bt_get_endpoint(Relation rel, uint32 level, bool rightmost)
{
    Buffer      buf;
    Page        page;
    BTPageOpaque opaque;
    OffsetNumber offnum;
    BlockNumber blkno;
    IndexTuple  itup;
 
    /*
     * If we are looking for a leaf page, okay to descend from fast root;
     * otherwise better descend from true root.  (There is no point in being
     * smarter about intermediate levels.)
     */
    if (level == 0)
        buf = _bt_getroot(rel, NULL, BT_READ);
    else
        buf = _bt_gettrueroot(rel);
 
    if (!BufferIsValid(buf))
        return InvalidBuffer;
 
    page = BufferGetPage(buf);
    opaque = BTPageGetOpaque(page);
 
    for (;;)
    {
        /*
         * If we landed on a deleted page, step right to find a live page
         * (there must be one).  Also, if we want the rightmost page, step
         * right if needed to get to it (this could happen if the page split
         * since we obtained a pointer to it).
         */
        while (P_IGNORE(opaque) ||
               (rightmost && !P_RIGHTMOST(opaque)))
        {
            blkno = opaque->btpo_next;
            if (blkno == P_NONE)
                elog(ERROR, "fell off the end of index \"%s\"",
                     RelationGetRelationName(rel));
            buf = _bt_relandgetbuf(rel, buf, blkno, BT_READ);
            page = BufferGetPage(buf);
            opaque = BTPageGetOpaque(page);
        }
 
        /* Done? */
        if (opaque->btpo_level == level)
            break;
        if (opaque->btpo_level < level)
            ereport(ERROR,
                    (errcode(ERRCODE_INDEX_CORRUPTED),
                     errmsg_internal("btree level %u not found in index \"%s\"",
                                     level, RelationGetRelationName(rel))));
 
        /* Descend to leftmost or rightmost child page */
        if (rightmost)
            offnum = PageGetMaxOffsetNumber(page);
        else
            offnum = P_FIRSTDATAKEY(opaque);
 
        if (offnum < 1 || offnum > PageGetMaxOffsetNumber(page))
            elog(PANIC, "offnum out of range");
 
        itup = (IndexTuple) PageGetItem(page, PageGetItemId(page, offnum));
        blkno = BTreeTupleGetDownLink(itup);
 
        buf = _bt_relandgetbuf(rel, buf, blkno, BT_READ);
        page = BufferGetPage(buf);
        opaque = BTPageGetOpaque(page);
    }
 
    return buf;
}
 
/*
 *  _bt_endpoint() -- Find the first or last page in the index, and scan
 * from there to the first key satisfying all the quals.
 *
 * This is used by _bt_first() to set up a scan when we've determined
 * that the scan must start at the beginning or end of the index (for
 * a forward or backward scan respectively).
 *
 * Parallel scan callers must have seized the scan before calling here.
 * Exit conditions are the same as for _bt_first().
 */
static bool
_bt_endpoint(IndexScanDesc scan, ScanDirection dir)
{
    Relation    rel = scan->indexRelation;
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    Page        page;
    BTPageOpaque opaque;
    OffsetNumber start;
 
    Assert(!BTScanPosIsValid(so->currPos));
    Assert(!so->needPrimScan);
 
    /*
     * Scan down to the leftmost or rightmost leaf page.  This is a simplified
     * version of _bt_search().
     */
    so->currPos.buf = _bt_get_endpoint(rel, 0, ScanDirectionIsBackward(dir));
 
    if (!BufferIsValid(so->currPos.buf))
    {
        /*
         * Empty index. Lock the whole relation, as nothing finer to lock
         * exists.
         */
        PredicateLockRelation(rel, scan->xs_snapshot);
        _bt_parallel_done(scan);
        return false;
    }
 
    page = BufferGetPage(so->currPos.buf);
    opaque = BTPageGetOpaque(page);
    Assert(P_ISLEAF(opaque));
 
    if (ScanDirectionIsForward(dir))
    {
        /* There could be dead pages to the left, so not this: */
        /* Assert(P_LEFTMOST(opaque)); */
 
        start = P_FIRSTDATAKEY(opaque);
    }
    else if (ScanDirectionIsBackward(dir))
    {
        Assert(P_RIGHTMOST(opaque));
 
        start = PageGetMaxOffsetNumber(page);
    }
    else
    {
        elog(ERROR, "invalid scan direction: %d", (int) dir);
        start = 0;              /* keep compiler quiet */
    }
 
    /*
     * Now load data from the first page of the scan.
     */
    if (!_bt_readfirstpage(scan, start, dir))
        return false;
 
    _bt_returnitem(scan, so);
    return true;
}