nbtsearch.c

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/*-------------------------------------------------------------------------
 *
 * nbtsearch.c
 *    Search code for postgres btrees.
 *
 *
 * Portions Copyright (c) 1996-2023, 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 "miscadmin.h"
#include "pgstat.h"
#include "storage/predicate.h"
#include "utils/lsyscache.h"
#include "utils/rel.h"
 
 
static void _bt_drop_lock_and_maybe_pin(IndexScanDesc scan, BTScanPos sp);
static OffsetNumber _bt_binsrch(Relation rel, BTScanInsert key, Buffer buf);
static int  _bt_binsrch_posting(BTScanInsert key, Page page,
                                OffsetNumber offnum);
static bool _bt_readpage(IndexScanDesc scan, ScanDirection dir,
                         OffsetNumber offnum);
static void _bt_saveitem(BTScanOpaque so, int itemIndex,
                         OffsetNumber offnum, IndexTuple itup);
static int  _bt_setuppostingitems(BTScanOpaque so, int itemIndex,
                                  OffsetNumber offnum, ItemPointer heapTid,
                                  IndexTuple itup);
static inline void _bt_savepostingitem(BTScanOpaque so, int itemIndex,
                                       OffsetNumber offnum,
                                       ItemPointer heapTid, int tupleOffset);
static bool _bt_steppage(IndexScanDesc scan, ScanDirection dir);
static bool _bt_readnextpage(IndexScanDesc scan, BlockNumber blkno, ScanDirection dir);
static bool _bt_parallel_readpage(IndexScanDesc scan, BlockNumber blkno,
                                  ScanDirection dir);
static Buffer _bt_walk_left(Relation rel, Buffer buf);
static bool _bt_endpoint(IndexScanDesc scan, ScanDirection dir);
static inline void _bt_initialize_more_data(BTScanOpaque so, ScanDirection dir);
 
 
/*
 *  _bt_drop_lock_and_maybe_pin()
 *
 * Unlock the buffer; and if it is safe to release the pin, do that, too.
 * This will prevent vacuum from stalling in a blocked state trying to read a
 * page when a cursor is sitting on it.
 *
 * See nbtree/README section on making concurrent TID recycling safe.
 */
static void
_bt_drop_lock_and_maybe_pin(IndexScanDesc scan, BTScanPos sp)
{
    _bt_unlockbuf(scan->indexRelation, sp->buf);
 
    if (IsMVCCSnapshot(scan->xs_snapshot) &&
        RelationNeedsWAL(scan->indexRelation) &&
        !scan->xs_want_itup)
    {
        ReleaseBuffer(sp->buf);
        sp->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.
 *
 * Return value is a stack of parent-page pointers (i.e. there is no entry for
 * the leaf level/page).  *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)
{
    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.
         */
        new_stack = (BTStack) palloc(sizeof(BTStackData));
        new_stack->bts_blkno = BufferGetBlockNumber(*bufP);
        new_stack->bts_offset = offnum;
        new_stack->bts_parent = stack_in;
 
        /*
         * 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 */
        stack_in = new_stack;
    }
 
    /*
     * 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.
 */
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 a leaf page, _bt_binsrch() returns the OffsetNumber of the first
 * key >= given scankey, or > scankey if nextkey is true.  (NOTE: in
 * particular, this means it is possible to return a value 1 greater than the
 * number of keys on the page, if the scankey is > all keys on the 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.)  This key indicates the
 * right place to descend to be sure we find all leaf keys >= given scankey
 * (or leaf keys > given scankey when nextkey is true).
 *
 * 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 children).
     */
    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, but be careful: they could point
     * past the last slot on the page.
     *
     * On a leaf page, we always return the first key >= scan key (resp. >
     * scan key), which could be the last slot + 1.
     */
    if (P_ISLEAF(opaque))
        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.
     */
    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)
    {
        /*
         * Most searches 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.
         *
         * 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.
         *
         * However, some searches (pivotsearch searches) actually require that
         * we descend left when this happens.  -inf is treated as a possible
         * match for omitted scankey attribute(s).  This is needed by page
         * deletion, which must re-find leaf pages that are targets for
         * deletion using their high keys.
         *
         * Note: the heap TID part of the test ensures that scankey is being
         * compared to a pivot tuple with one or more truncated key
         * attributes.
         *
         * Note: pg_upgrade'd !heapkeyspace indexes must always descend to the
         * left here, since they have no heap TID attribute (and cannot have
         * any -inf key values in any case, since truncation can only remove
         * non-key attributes).  !heapkeyspace searches must always be
         * prepared to deal with matches on both sides of the pivot once the
         * leaf level is reached.
         */
        if (key->heapkeyspace && !key->pivotsearch &&
            key->keysz == ntupatts && heapTid == NULL)
            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, the page containing
 *      the current index tuple is pinned but not locked, and data about
 *      the matching tuple(s) on the page has been loaded into so->currPos.
 *      scan->xs_ctup.t_self is set to the heap TID of the current tuple,
 *      and if requested, scan->xs_itup points to a copy of the index tuple.
 *
 * If there are no matching items in the index, we return false, with no
 * pins or locks held.
 *
 * 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;
    Buffer      buf;
    BTStack     stack;
    OffsetNumber offnum;
    StrategyNumber strat;
    bool        nextkey;
    bool        goback;
    BTScanInsertData inskey;
    ScanKey     startKeys[INDEX_MAX_KEYS];
    ScanKeyData notnullkeys[INDEX_MAX_KEYS];
    int         keysCount = 0;
    int         i;
    bool        status;
    StrategyNumber strat_total;
    BTScanPosItem *currItem;
    BlockNumber blkno;
 
    Assert(!BTScanPosIsValid(so->currPos));
 
    pgstat_count_index_scan(rel);
 
    /*
     * 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)
    {
        /* Notify any other workers that we're done with this scan key. */
        _bt_parallel_done(scan);
        return false;
    }
 
    /*
     * For parallel scans, get the starting page from shared state. If the
     * scan has not started, proceed to find out first leaf page in the usual
     * way while keeping other participating processes waiting.  If the scan
     * has already begun, use the page number from the shared structure.
     */
    if (scan->parallel_scan != NULL)
    {
        status = _bt_parallel_seize(scan, &blkno);
        if (!status)
            return false;
        else if (blkno == P_NONE)
        {
            _bt_parallel_done(scan);
            return false;
        }
        else if (blkno != InvalidBlockNumber)
        {
            if (!_bt_parallel_readpage(scan, blkno, dir))
                return false;
            goto readcomplete;
        }
    }
 
    /*----------
     * Examine the scan keys to discover where we need to start the scan.
     *
     * We want to identify the keys that can be used as starting boundaries;
     * these are =, >, 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.  Once we accept
     * a > or < boundary or find an attribute with no boundary (which can be
     * thought of as the same as "> -infinity"), we can't use keys for any
     * attributes to its right, because it would break our simplistic notion
     * of what initial positioning strategy to use.
     *
     * When the scan keys include cross-type operators, _bt_preprocess_keys
     * may not be able to eliminate redundant keys; in such cases we will
     * arbitrarily pick a usable one for each attribute.  This is correct
     * but possibly not optimal behavior.  (For example, with keys like
     * "x >= 4 AND x >= 5" we would elect to scan starting at x=4 when
     * x=5 would be more efficient.)  Since the situation only arises given
     * a poorly-worded query plus an incomplete opfamily, live with it.
     *
     * When both equality and inequality keys appear for a single attribute
     * (again, only possible when cross-type operators appear), we *must*
     * select one of the equality keys for the starting point, because
     * _bt_checkkeys() will stop the scan as soon as an equality qual fails.
     * For example, if we have keys like "x >= 4 AND x = 10" and we elect to
     * start at x=4, we will fail and stop before reaching x=10.  If multiple
     * equality quals survive preprocessing, however, it doesn't matter which
     * one we use --- by definition, they are either redundant or
     * contradictory.
     *
     * Any regular (not SK_SEARCHNULL) key implies 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 on lower-order columns of the row
     * comparison below, if possible.
     *
     * The selected scan keys (at most one per index column) are remembered by
     * storing their addresses into the local startKeys[] array.
     *----------
     */
    strat_total = BTEqualStrategyNumber;
    if (so->numberOfKeys > 0)
    {
        AttrNumber  curattr;
        ScanKey     chosen;
        ScanKey     impliesNN;
        ScanKey     cur;
 
        /*
         * chosen is the so-far-chosen key for the current attribute, if any.
         * We don't cast the decision in stone until we reach keys for the
         * next attribute.
         */
        curattr = 1;
        chosen = 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 (cur = so->keyData, i = 0;; cur++, i++)
        {
            if (i >= so->numberOfKeys || cur->sk_attno != curattr)
            {
                /*
                 * Done looking at keys for curattr.  If we didn't find a
                 * usable boundary key, see if we can deduce a NOT NULL key.
                 */
                if (chosen == NULL && impliesNN != NULL &&
                    ((impliesNN->sk_flags & SK_BT_NULLS_FIRST) ?
                     ScanDirectionIsForward(dir) :
                     ScanDirectionIsBackward(dir)))
                {
                    /* Yes, so build the key in notnullkeys[keysCount] */
                    chosen = &notnullkeys[keysCount];
                    ScanKeyEntryInitialize(chosen,
                                           (SK_SEARCHNOTNULL | SK_ISNULL |
                                            (impliesNN->sk_flags &
                                             (SK_BT_DESC | SK_BT_NULLS_FIRST))),
                                           curattr,
                                           ((impliesNN->sk_flags & SK_BT_NULLS_FIRST) ?
                                            BTGreaterStrategyNumber :
                                            BTLessStrategyNumber),
                                           InvalidOid,
                                           InvalidOid,
                                           InvalidOid,
                                           (Datum) 0);
                }
 
                /*
                 * If we still didn't find a usable boundary key, quit; else
                 * save the boundary key pointer in startKeys.
                 */
                if (chosen == NULL)
                    break;
                startKeys[keysCount++] = chosen;
 
                /*
                 * Adjust strat_total, and quit if we have stored a > or <
                 * key.
                 */
                strat = chosen->sk_strategy;
                if (strat != BTEqualStrategyNumber)
                {
                    strat_total = strat;
                    if (strat == BTGreaterStrategyNumber ||
                        strat == BTLessStrategyNumber)
                        break;
                }
 
                /*
                 * Done if that was the last attribute, or if next key is not
                 * in sequence (implying no boundary key is available for the
                 * next attribute).
                 */
                if (i >= so->numberOfKeys ||
                    cur->sk_attno != curattr + 1)
                    break;
 
                /*
                 * Reset for next attr.
                 */
                curattr = cur->sk_attno;
                chosen = NULL;
                impliesNN = NULL;
            }
 
            /*
             * Can we use this key as a starting boundary for this attr?
             *
             * 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 (chosen == NULL)
                    {
                        if (ScanDirectionIsBackward(dir))
                            chosen = cur;
                        else
                            impliesNN = cur;
                    }
                    break;
                case BTEqualStrategyNumber:
                    /* override any non-equality choice */
                    chosen = cur;
                    break;
                case BTGreaterEqualStrategyNumber:
                case BTGreaterStrategyNumber:
                    if (chosen == NULL)
                    {
                        if (ScanDirectionIsForward(dir))
                            chosen = cur;
                        else
                            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.
     */
    if (keysCount == 0)
    {
        bool        match;
 
        match = _bt_endpoint(scan, dir);
 
        if (!match)
        {
            /* No match, so mark (parallel) scan finished */
            _bt_parallel_done(scan);
        }
 
        return match;
    }
 
    /*
     * 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 strategy is finalized.)
     */
    Assert(keysCount <= INDEX_MAX_KEYS);
    for (i = 0; i < keysCount; i++)
    {
        ScanKey     cur = startKeys[i];
 
        Assert(cur->sk_attno == i + 1);
 
        if (cur->sk_flags & SK_ROW_HEADER)
        {
            /*
             * Row comparison header: look to the first row member instead.
             *
             * The member scankeys are already in insertion format (ie, they
             * have sk_func = 3-way-comparison function), but we have to watch
             * out for nulls, which _bt_preprocess_keys didn't check. A null
             * in the first row member makes the condition unmatchable, just
             * like qual_ok = false.
             */
            ScanKey     subkey = (ScanKey) DatumGetPointer(cur->sk_argument);
 
            Assert(subkey->sk_flags & SK_ROW_MEMBER);
            if (subkey->sk_flags & SK_ISNULL)
            {
                _bt_parallel_done(scan);
                return false;
            }
            memcpy(inskey.scankeys + i, subkey, sizeof(ScanKeyData));
 
            /*
             * If the row comparison is the last positioning key we accepted,
             * try to add additional keys from the lower-order row members.
             * (If we accepted independent conditions on additional index
             * columns, we use those instead --- doesn't seem worth trying to
             * determine which is more restrictive.)  Note that this is OK
             * even if the row comparison is of ">" or "<" type, because the
             * condition applied to all but the last row member is effectively
             * ">=" or "<=", and so the extra keys don't break the positioning
             * scheme.  But, by the same token, if we aren't able to use all
             * the row members, then the part of the row comparison that we
             * did use has to be treated as just a ">=" or "<=" condition, and
             * so we'd better adjust strat_total accordingly.
             */
            if (i == keysCount - 1)
            {
                bool        used_all_subkeys = false;
 
                Assert(!(subkey->sk_flags & SK_ROW_END));
                for (;;)
                {
                    subkey++;
                    Assert(subkey->sk_flags & SK_ROW_MEMBER);
                    if (subkey->sk_attno != keysCount + 1)
                        break;  /* out-of-sequence, can't use it */
                    if (subkey->sk_strategy != cur->sk_strategy)
                        break;  /* wrong direction, can't use it */
                    if (subkey->sk_flags & SK_ISNULL)
                        break;  /* can't use null keys */
                    Assert(keysCount < INDEX_MAX_KEYS);
                    memcpy(inskey.scankeys + keysCount, subkey,
                           sizeof(ScanKeyData));
                    keysCount++;
                    if (subkey->sk_flags & SK_ROW_END)
                    {
                        used_all_subkeys = true;
                        break;
                    }
                }
                if (!used_all_subkeys)
                {
                    switch (strat_total)
                    {
                        case BTLessStrategyNumber:
                            strat_total = BTLessEqualStrategyNumber;
                            break;
                        case BTGreaterStrategyNumber:
                            strat_total = BTGreaterEqualStrategyNumber;
                            break;
                    }
                }
                break;          /* done with outer loop */
            }
        }
        else
        {
            /*
             * Ordinary comparison key.  Transform the search-style scan key
             * to an insertion scan key by replacing the sk_func with the
             * appropriate btree 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 is a hack to simplify life for
             * ScanKeyInit().
             */
            if (cur->sk_subtype == rel->rd_opcintype[i] ||
                cur->sk_subtype == InvalidOid)
            {
                FmgrInfo   *procinfo;
 
                procinfo = index_getprocinfo(rel, cur->sk_attno, BTORDER_PROC);
                ScanKeyEntryInitializeWithInfo(inskey.scankeys + i,
                                               cur->sk_flags,
                                               cur->sk_attno,
                                               InvalidStrategy,
                                               cur->sk_subtype,
                                               cur->sk_collation,
                                               procinfo,
                                               cur->sk_argument);
            }
            else
            {
                RegProcedure cmp_proc;
 
                cmp_proc = get_opfamily_proc(rel->rd_opfamily[i],
                                             rel->rd_opcintype[i],
                                             cur->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], cur->sk_subtype,
                         cur->sk_attno, RelationGetRelationName(rel));
                ScanKeyEntryInitialize(inskey.scankeys + i,
                                       cur->sk_flags,
                                       cur->sk_attno,
                                       InvalidStrategy,
                                       cur->sk_subtype,
                                       cur->sk_collation,
                                       cmp_proc,
                                       cur->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
     * code below.
     *
     * If nextkey = false, _bt_search and _bt_binsrch will locate the first
     * item >= scan key.  If nextkey = true, they will locate the first
     * item > scan key.
     *
     * If goback = true, we will then step back one item, while if
     * goback = false, we will start the scan on the located item.
     *----------
     */
    switch (strat_total)
    {
        case BTLessStrategyNumber:
 
            /*
             * Find first item >= scankey, then back up one to arrive at last
             * item < scankey.  (Note: this positioning strategy is only used
             * for a backward scan, so that is always the correct starting
             * position.)
             */
            nextkey = false;
            goback = true;
            break;
 
        case BTLessEqualStrategyNumber:
 
            /*
             * Find first item > scankey, then back up one to arrive at last
             * item <= scankey.  (Note: this positioning strategy is only used
             * for a backward scan, so that is always the correct starting
             * position.)
             */
            nextkey = true;
            goback = 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.  We will check at the
                 * end whether the found item is actually =.
                 */
                nextkey = true;
                goback = true;
            }
            else
            {
                /*
                 * This is the same as the >= strategy.  We will check at the
                 * end whether the found item is actually =.
                 */
                nextkey = false;
                goback = false;
            }
            break;
 
        case BTGreaterEqualStrategyNumber:
 
            /*
             * Find first item >= scankey.  (This is only used for forward
             * scans.)
             */
            nextkey = false;
            goback = false;
            break;
 
        case BTGreaterStrategyNumber:
 
            /*
             * Find first item > scankey.  (This is only used for forward
             * scans.)
             */
            nextkey = true;
            goback = false;
            break;
 
        default:
            /* can't get here, but keep compiler quiet */
            elog(ERROR, "unrecognized strat_total: %d", (int) strat_total);
            return false;
    }
 
    /* Initialize remaining insertion scan key fields */
    _bt_metaversion(rel, &inskey.heapkeyspace, &inskey.allequalimage);
    inskey.anynullkeys = false; /* unused */
    inskey.nextkey = nextkey;
    inskey.pivotsearch = false;
    inskey.scantid = NULL;
    inskey.keysz = keysCount;
 
    /*
     * Use the manufactured insertion scan key to descend the tree and
     * position ourselves on the target leaf page.
     */
    stack = _bt_search(rel, NULL, &inskey, &buf, BT_READ);
 
    /* don't need to keep the stack around... */
    _bt_freestack(stack);
 
    if (!BufferIsValid(buf))
    {
        /*
         * 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);
            stack = _bt_search(rel, NULL, &inskey, &buf, BT_READ);
            _bt_freestack(stack);
        }
 
        if (!BufferIsValid(buf))
        {
            /*
             * Mark parallel scan as done, so that all the workers can finish
             * their scan.
             */
            _bt_parallel_done(scan);
            BTScanPosInvalidate(so->currPos);
            return false;
        }
    }
 
    PredicateLockPage(rel, BufferGetBlockNumber(buf), scan->xs_snapshot);
 
    _bt_initialize_more_data(so, dir);
 
    /* position to the precise item on the page */
    offnum = _bt_binsrch(rel, &inskey, buf);
 
    /*
     * If nextkey = false, we are positioned at the first item >= scan key, or
     * possibly at the end of a page on which all the existing items are less
     * than the scan key and we know that everything on later pages is greater
     * than or equal to scan key.
     *
     * If nextkey = true, we are positioned at the first item > scan key, or
     * possibly at the end of a page on which all the existing items are less
     * than or equal to the scan key and we know that everything on later
     * pages is greater than scan key.
     *
     * The actually desired starting point is either this item or the prior
     * one, or in the end-of-page case it's the first item on the next page or
     * the last item on this page.  Adjust the starting offset if needed. (If
     * this results in an offset before the first item or after the last one,
     * _bt_readpage will report no items found, and then we'll step to the
     * next page as needed.)
     */
    if (goback)
        offnum = OffsetNumberPrev(offnum);
 
    /* remember which buffer we have pinned, if any */
    Assert(!BTScanPosIsValid(so->currPos));
    so->currPos.buf = buf;
    so->firstPage = true;
 
    /*
     * Now load data from the first page of the scan.
     */
    if (!_bt_readpage(scan, dir, offnum))
    {
        /*
         * There's no actually-matching data on this page.  Try to advance to
         * the next page.  Return false if there's no matching data at all.
         */
        _bt_unlockbuf(scan->indexRelation, so->currPos.buf);
        if (!_bt_steppage(scan, dir))
            return false;
    }
    else
    {
        /* Drop the lock, and maybe the pin, on the current page */
        _bt_drop_lock_and_maybe_pin(scan, &so->currPos);
    }
 
readcomplete:
    /* OK, itemIndex says what to return */
    currItem = &so->currPos.items[so->currPos.itemIndex];
    scan->xs_heaptid = currItem->heapTid;
    if (scan->xs_want_itup)
        scan->xs_itup = (IndexTuple) (so->currTuples + currItem->tupleOffset);
 
    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 successful exit, scan->xs_ctup.t_self is set to the TID of the
 *      next heap tuple, and if requested, scan->xs_itup points to a copy of
 *      the index tuple.  so->currPos is updated as needed.
 *
 *      On failure exit (no more tuples), we release pin and set
 *      so->currPos.buf to InvalidBuffer.
 */
bool
_bt_next(IndexScanDesc scan, ScanDirection dir)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    BTScanPosItem *currItem;
 
    /*
     * 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;
        }
    }
 
    /* OK, itemIndex says what to return */
    currItem = &so->currPos.items[so->currPos.itemIndex];
    scan->xs_heaptid = currItem->heapTid;
    if (scan->xs_want_itup)
        scan->xs_itup = (IndexTuple) (so->currTuples + currItem->tupleOffset);
 
    return true;
}
 
/*
 *  _bt_readpage() -- Load data from current index page into so->currPos
 *
 * Caller must have pinned and read-locked so->currPos.buf; the buffer's state
 * is not changed here.  Also, currPos.moreLeft and moreRight must be valid;
 * they are updated as appropriate.  All other fields of so->currPos are
 * initialized from scratch here.
 *
 * We scan the current page starting at offnum and moving in the indicated
 * direction.  All items matching the scan keys are loaded into currPos.items.
 * moreLeft or moreRight (as appropriate) is cleared if _bt_checkkeys reports
 * that there can be no more matching tuples in the current scan direction.
 *
 * In the case of a parallel scan, caller must have called _bt_parallel_seize
 * prior to calling this function; this function will invoke
 * _bt_parallel_release before returning.
 *
 * Returns true if any matching items found on the page, false if none.
 */
static bool
_bt_readpage(IndexScanDesc scan, ScanDirection dir, OffsetNumber offnum)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    Page        page;
    BTPageOpaque opaque;
    OffsetNumber minoff;
    OffsetNumber maxoff;
    int         itemIndex;
    bool        continuescan;
    int         indnatts;
    bool        requiredMatchedByPrecheck;
 
    /*
     * We must have the buffer pinned and locked, but the usual macro can't be
     * used here; this function is what makes it good for currPos.
     */
    Assert(BufferIsValid(so->currPos.buf));
 
    page = BufferGetPage(so->currPos.buf);
    opaque = BTPageGetOpaque(page);
 
    /* allow next page be processed by parallel worker */
    if (scan->parallel_scan)
    {
        if (ScanDirectionIsForward(dir))
            _bt_parallel_release(scan, opaque->btpo_next);
        else
            _bt_parallel_release(scan, BufferGetBlockNumber(so->currPos.buf));
    }
 
    continuescan = true;        /* default assumption */
    indnatts = IndexRelationGetNumberOfAttributes(scan->indexRelation);
    minoff = P_FIRSTDATAKEY(opaque);
    maxoff = PageGetMaxOffsetNumber(page);
 
    /*
     * We note the buffer's block number so that we can release the pin later.
     * This allows us to re-read the buffer if it is needed again for hinting.
     */
    so->currPos.currPage = BufferGetBlockNumber(so->currPos.buf);
 
    /*
     * We save the LSN of the page as we read it, so that we know whether it
     * safe to apply LP_DEAD hints to the page later.  This allows us to drop
     * the pin for MVCC scans, which allows vacuum to avoid blocking.
     */
    so->currPos.lsn = BufferGetLSNAtomic(so->currPos.buf);
 
    /*
     * we must save the page's right-link while scanning it; this tells us
     * where to step right to after we're done with these items.  There is no
     * corresponding need for the left-link, since splits always go right.
     */
    so->currPos.nextPage = opaque->btpo_next;
 
    /* initialize tuple workspace to empty */
    so->currPos.nextTupleOffset = 0;
 
    /*
     * Now that the current page has been made consistent, the macro should be
     * good.
     */
    Assert(BTScanPosIsPinned(so->currPos));
 
    /*
     * Prechecking the page with scan keys required for direction scan.  We
     * check these keys with the last item on the page (according to our scan
     * direction).  If these keys are matched, we can skip checking them with
     * every item on the page.  Scan keys for our scan direction would
     * necessarily match the previous items.  Scan keys required for opposite
     * direction scan are already matched by the _bt_first() call.
     *
     * With the forward scan, we do this check for the last item on the page
     * instead of the high key.  It's relatively likely that the most
     * significant column in the high key will be different from the
     * corresponding value from the last item on the page.  So checking with
     * the last item on the page would give a more precise answer.
     *
     * We skip this for the first page in the scan to evade the possible
     * slowdown of the point queries.
     */
    if (!so->firstPage && minoff < maxoff)
    {
        ItemId      iid;
        IndexTuple  itup;
 
        iid = PageGetItemId(page, ScanDirectionIsForward(dir) ? maxoff : minoff);
        itup = (IndexTuple) PageGetItem(page, iid);
 
        /*
         * Do the precheck.  Note that we pass the pointer to
         * 'requiredMatchedByPrecheck' to 'continuescan' argument.  That will
         * set flag to true if all required keys are satisfied and false
         * otherwise.
         */
        (void) _bt_checkkeys(scan, itup, indnatts, dir,
                             &requiredMatchedByPrecheck, false);
    }
    else
    {
        so->firstPage = false;
        requiredMatchedByPrecheck = false;
    }
 
    if (ScanDirectionIsForward(dir))
    {
        /* load items[] in ascending order */
        itemIndex = 0;
 
        offnum = Max(offnum, minoff);
 
        while (offnum <= maxoff)
        {
            ItemId      iid = PageGetItemId(page, offnum);
            IndexTuple  itup;
            bool        passes_quals;
 
            /*
             * If the scan specifies not to return killed tuples, then we
             * treat a killed tuple as not passing the qual
             */
            if (scan->ignore_killed_tuples && ItemIdIsDead(iid))
            {
                offnum = OffsetNumberNext(offnum);
                continue;
            }
 
            itup = (IndexTuple) PageGetItem(page, iid);
 
            passes_quals = _bt_checkkeys(scan, itup, indnatts, dir,
                                         &continuescan, requiredMatchedByPrecheck);
 
            /*
             * If the result of prechecking required keys was true, then in
             * assert-enabled builds we also recheck that the _bt_checkkeys()
             * result is the same.
             */
            Assert(!requiredMatchedByPrecheck ||
                   passes_quals == _bt_checkkeys(scan, itup, indnatts, dir,
                                                 &continuescan, false));
            if (passes_quals)
            {
                /* tuple passes all scan key conditions */
                if (!BTreeTupleIsPosting(itup))
                {
                    /* Remember it */
                    _bt_saveitem(so, itemIndex, offnum, itup);
                    itemIndex++;
                }
                else
                {
                    int         tupleOffset;
 
                    /*
                     * Set up state to return posting list, and remember first
                     * TID
                     */
                    tupleOffset =
                        _bt_setuppostingitems(so, itemIndex, offnum,
                                              BTreeTupleGetPostingN(itup, 0),
                                              itup);
                    itemIndex++;
                    /* Remember additional TIDs */
                    for (int i = 1; i < BTreeTupleGetNPosting(itup); i++)
                    {
                        _bt_savepostingitem(so, itemIndex, offnum,
                                            BTreeTupleGetPostingN(itup, i),
                                            tupleOffset);
                        itemIndex++;
                    }
                }
            }
            /* When !continuescan, there can't be any more matches, so stop */
            if (!continuescan)
                break;
 
            offnum = OffsetNumberNext(offnum);
        }
 
        /*
         * We don't need to visit page to the right when the high key
         * indicates that no more matches will be found there.
         *
         * Checking the high key like this works out more often than you might
         * think.  Leaf page splits pick a split point between the two most
         * dissimilar tuples (this is weighed against the need to evenly share
         * free space).  Leaf pages with high key attribute values that can
         * only appear on non-pivot tuples on the right sibling page are
         * common.
         */
        if (continuescan && !P_RIGHTMOST(opaque))
        {
            ItemId      iid = PageGetItemId(page, P_HIKEY);
            IndexTuple  itup = (IndexTuple) PageGetItem(page, iid);
            int         truncatt;
 
            truncatt = BTreeTupleGetNAtts(itup, scan->indexRelation);
            _bt_checkkeys(scan, itup, truncatt, dir, &continuescan, false);
        }
 
        if (!continuescan)
            so->currPos.moreRight = false;
 
        Assert(itemIndex <= MaxTIDsPerBTreePage);
        so->currPos.firstItem = 0;
        so->currPos.lastItem = itemIndex - 1;
        so->currPos.itemIndex = 0;
    }
    else
    {
        /* load items[] in descending order */
        itemIndex = MaxTIDsPerBTreePage;
 
        offnum = Min(offnum, maxoff);
 
        while (offnum >= minoff)
        {
            ItemId      iid = PageGetItemId(page, offnum);
            IndexTuple  itup;
            bool        tuple_alive;
            bool        passes_quals;
 
            /*
             * If the scan specifies not to return killed tuples, then we
             * treat a killed tuple as not passing the qual.  Most of the
             * time, it's a win to not bother examining the tuple's index
             * keys, but just skip to the next tuple (previous, actually,
             * since we're scanning backwards).  However, if this is the first
             * tuple on the page, we do check the index keys, to prevent
             * uselessly advancing to the page to the left.  This is similar
             * to the high key optimization used by forward scans.
             */
            if (scan->ignore_killed_tuples && ItemIdIsDead(iid))
            {
                Assert(offnum >= P_FIRSTDATAKEY(opaque));
                if (offnum > P_FIRSTDATAKEY(opaque))
                {
                    offnum = OffsetNumberPrev(offnum);
                    continue;
                }
 
                tuple_alive = false;
            }
            else
                tuple_alive = true;
 
            itup = (IndexTuple) PageGetItem(page, iid);
 
            passes_quals = _bt_checkkeys(scan, itup, indnatts, dir,
                                         &continuescan, requiredMatchedByPrecheck);
 
            /*
             * If the result of prechecking required keys was true, then in
             * assert-enabled builds we also recheck that the _bt_checkkeys()
             * result is the same.
             */
            Assert(!requiredMatchedByPrecheck ||
                   passes_quals == _bt_checkkeys(scan, itup, indnatts, dir,
                                                 &continuescan, false));
            if (passes_quals && tuple_alive)
            {
                /* tuple passes all scan key conditions */
                if (!BTreeTupleIsPosting(itup))
                {
                    /* Remember it */
                    itemIndex--;
                    _bt_saveitem(so, itemIndex, offnum, itup);
                }
                else
                {
                    int         tupleOffset;
 
                    /*
                     * Set up state to return posting list, and remember first
                     * TID.
                     *
                     * Note that we deliberately save/return items from
                     * posting lists in ascending heap TID order for backwards
                     * scans.  This allows _bt_killitems() to make a
                     * consistent assumption about the order of items
                     * associated with the same posting list tuple.
                     */
                    itemIndex--;
                    tupleOffset =
                        _bt_setuppostingitems(so, itemIndex, offnum,
                                              BTreeTupleGetPostingN(itup, 0),
                                              itup);
                    /* Remember additional TIDs */
                    for (int i = 1; i < BTreeTupleGetNPosting(itup); i++)
                    {
                        itemIndex--;
                        _bt_savepostingitem(so, itemIndex, offnum,
                                            BTreeTupleGetPostingN(itup, i),
                                            tupleOffset);
                    }
                }
            }
            if (!continuescan)
            {
                /* there can't be any more matches, so stop */
                so->currPos.moreLeft = false;
                break;
            }
 
            offnum = OffsetNumberPrev(offnum);
        }
 
        Assert(itemIndex >= 0);
        so->currPos.firstItem = itemIndex;
        so->currPos.lastItem = MaxTIDsPerBTreePage - 1;
        so->currPos.itemIndex = MaxTIDsPerBTreePage - 1;
    }
 
    return (so->currPos.firstItem <= so->currPos.lastItem);
}
 
/* Save an index item into so->currPos.items[itemIndex] */
static void
_bt_saveitem(BTScanOpaque so, int itemIndex,
             OffsetNumber offnum, IndexTuple itup)
{
    BTScanPosItem *currItem = &so->currPos.items[itemIndex];
 
    Assert(!BTreeTupleIsPivot(itup) && !BTreeTupleIsPosting(itup));
 
    currItem->heapTid = itup->t_tid;
    currItem->indexOffset = offnum;
    if (so->currTuples)
    {
        Size        itupsz = IndexTupleSize(itup);
 
        currItem->tupleOffset = so->currPos.nextTupleOffset;
        memcpy(so->currTuples + so->currPos.nextTupleOffset, itup, itupsz);
        so->currPos.nextTupleOffset += MAXALIGN(itupsz);
    }
}
 
/*
 * Setup state to save TIDs/items from a single posting list tuple.
 *
 * Saves an index item into so->currPos.items[itemIndex] for TID that is
 * returned to scan first.  Second or subsequent TIDs for posting list should
 * be saved by calling _bt_savepostingitem().
 *
 * Returns an offset into tuple storage space that main tuple is stored at if
 * needed.
 */
static int
_bt_setuppostingitems(BTScanOpaque so, int itemIndex, OffsetNumber offnum,
                      ItemPointer heapTid, IndexTuple itup)
{
    BTScanPosItem *currItem = &so->currPos.items[itemIndex];
 
    Assert(BTreeTupleIsPosting(itup));
 
    currItem->heapTid = *heapTid;
    currItem->indexOffset = offnum;
    if (so->currTuples)
    {
        /* Save base IndexTuple (truncate posting list) */
        IndexTuple  base;
        Size        itupsz = BTreeTupleGetPostingOffset(itup);
 
        itupsz = MAXALIGN(itupsz);
        currItem->tupleOffset = so->currPos.nextTupleOffset;
        base = (IndexTuple) (so->currTuples + so->currPos.nextTupleOffset);
        memcpy(base, itup, itupsz);
        /* Defensively reduce work area index tuple header size */
        base->t_info &= ~INDEX_SIZE_MASK;
        base->t_info |= itupsz;
        so->currPos.nextTupleOffset += itupsz;
 
        return currItem->tupleOffset;
    }
 
    return 0;
}
 
/*
 * Save an index item into so->currPos.items[itemIndex] for current posting
 * tuple.
 *
 * Assumes that _bt_setuppostingitems() has already been called for current
 * posting list tuple.  Caller passes its return value as tupleOffset.
 */
static inline void
_bt_savepostingitem(BTScanOpaque so, int itemIndex, OffsetNumber offnum,
                    ItemPointer heapTid, int tupleOffset)
{
    BTScanPosItem *currItem = &so->currPos.items[itemIndex];
 
    currItem->heapTid = *heapTid;
    currItem->indexOffset = offnum;
 
    /*
     * Have index-only scans return the same base IndexTuple for every TID
     * that originates from the same posting list
     */
    if (so->currTuples)
        currItem->tupleOffset = tupleOffset;
}
 
/*
 *  _bt_steppage() -- Step to next page containing valid data for scan
 *
 * On entry, if so->currPos.buf is valid the buffer is pinned but not locked;
 * if pinned, we'll drop the pin before moving to next page.  The buffer is
 * not locked on entry.
 *
 * For success on a scan using a non-MVCC snapshot we hold a pin, but not a
 * read lock, on that page.  If we do not hold the pin, we set so->currPos.buf
 * to InvalidBuffer.  We return true to indicate success.
 */
static bool
_bt_steppage(IndexScanDesc scan, ScanDirection dir)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    BlockNumber blkno = InvalidBlockNumber;
    bool        status;
 
    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 (ScanDirectionIsForward(dir))
    {
        /* Walk right to the next page with data */
        if (scan->parallel_scan != NULL)
        {
            /*
             * Seize the scan to get the next block number; if the scan has
             * ended already, bail out.
             */
            status = _bt_parallel_seize(scan, &blkno);
            if (!status)
            {
                /* release the previous buffer, if pinned */
                BTScanPosUnpinIfPinned(so->currPos);
                BTScanPosInvalidate(so->currPos);
                return false;
            }
        }
        else
        {
            /* Not parallel, so use the previously-saved nextPage link. */
            blkno = so->currPos.nextPage;
        }
 
        /* Remember we left a page with data */
        so->currPos.moreLeft = true;
 
        /* release the previous buffer, if pinned */
        BTScanPosUnpinIfPinned(so->currPos);
    }
    else
    {
        /* Remember we left a page with data */
        so->currPos.moreRight = true;
 
        if (scan->parallel_scan != NULL)
        {
            /*
             * Seize the scan to get the current block number; if the scan has
             * ended already, bail out.
             */
            status = _bt_parallel_seize(scan, &blkno);
            BTScanPosUnpinIfPinned(so->currPos);
            if (!status)
            {
                BTScanPosInvalidate(so->currPos);
                return false;
            }
        }
        else
        {
            /* Not parallel, so just use our own notion of the current page */
            blkno = so->currPos.currPage;
        }
    }
 
    if (!_bt_readnextpage(scan, blkno, dir))
        return false;
 
    /* Drop the lock, and maybe the pin, on the current page */
    _bt_drop_lock_and_maybe_pin(scan, &so->currPos);
 
    return true;
}
 
/*
 *  _bt_readnextpage() -- Read next page containing valid data for scan
 *
 * On success exit, so->currPos is updated to contain data from the next
 * interesting page.  Caller is responsible to release lock and pin on
 * buffer on success.  We return true to indicate success.
 *
 * If there are no more matching records in the given direction, we drop all
 * locks and pins, set so->currPos.buf to InvalidBuffer, and return false.
 */
static bool
_bt_readnextpage(IndexScanDesc scan, BlockNumber blkno, ScanDirection dir)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    Relation    rel;
    Page        page;
    BTPageOpaque opaque;
    bool        status;
 
    rel = scan->indexRelation;
 
    if (ScanDirectionIsForward(dir))
    {
        for (;;)
        {
            /*
             * if we're at end of scan, give up and mark parallel scan as
             * done, so that all the workers can finish their scan
             */
            if (blkno == P_NONE || !so->currPos.moreRight)
            {
                _bt_parallel_done(scan);
                BTScanPosInvalidate(so->currPos);
                return false;
            }
            /* check for interrupts while we're not holding any buffer lock */
            CHECK_FOR_INTERRUPTS();
            /* step right one page */
            so->currPos.buf = _bt_getbuf(rel, blkno, BT_READ);
            page = BufferGetPage(so->currPos.buf);
            opaque = BTPageGetOpaque(page);
            /* check for deleted page */
            if (!P_IGNORE(opaque))
            {
                PredicateLockPage(rel, blkno, scan->xs_snapshot);
                /* see if there are any matches on this page */
                /* note that this will clear moreRight if we can stop */
                if (_bt_readpage(scan, dir, P_FIRSTDATAKEY(opaque)))
                    break;
            }
            else if (scan->parallel_scan != NULL)
            {
                /* allow next page be processed by parallel worker */
                _bt_parallel_release(scan, opaque->btpo_next);
            }
 
            /* nope, keep going */
            if (scan->parallel_scan != NULL)
            {
                _bt_relbuf(rel, so->currPos.buf);
                status = _bt_parallel_seize(scan, &blkno);
                if (!status)
                {
                    BTScanPosInvalidate(so->currPos);
                    return false;
                }
            }
            else
            {
                blkno = opaque->btpo_next;
                _bt_relbuf(rel, so->currPos.buf);
            }
        }
    }
    else
    {
        /*
         * Should only happen in parallel cases, when some other backend
         * advanced the scan.
         */
        if (so->currPos.currPage != blkno)
        {
            BTScanPosUnpinIfPinned(so->currPos);
            so->currPos.currPage = blkno;
        }
 
        /*
         * Walk left to the next page with data.  This is much more complex
         * than the walk-right case because of the possibility that the page
         * to our left splits while we are in flight to it, plus the
         * possibility that the page we were on gets deleted after we leave
         * it.  See nbtree/README for details.
         *
         * It might be possible to rearrange this code to have less overhead
         * in pinning and locking, but that would require capturing the left
         * pointer when the page is initially read, and using it here, along
         * with big changes to _bt_walk_left() and the code below.  It is not
         * clear whether this would be a win, since if the page immediately to
         * the left splits after we read this page and before we step left, we
         * would need to visit more pages than with the current code.
         *
         * Note that if we change the code so that we drop the pin for a scan
         * which uses a non-MVCC snapshot, we will need to modify the code for
         * walking left, to allow for the possibility that a referenced page
         * has been deleted.  As long as the buffer is pinned or the snapshot
         * is MVCC the page cannot move past the half-dead state to fully
         * deleted.
         */
        if (BTScanPosIsPinned(so->currPos))
            _bt_lockbuf(rel, so->currPos.buf, BT_READ);
        else
            so->currPos.buf = _bt_getbuf(rel, so->currPos.currPage, BT_READ);
 
        for (;;)
        {
            /* Done if we know there are no matching keys to the left */
            if (!so->currPos.moreLeft)
            {
                _bt_relbuf(rel, so->currPos.buf);
                _bt_parallel_done(scan);
                BTScanPosInvalidate(so->currPos);
                return false;
            }
 
            /* Step to next physical page */
            so->currPos.buf = _bt_walk_left(rel, so->currPos.buf);
 
            /* if we're physically at end of index, return failure */
            if (so->currPos.buf == InvalidBuffer)
            {
                _bt_parallel_done(scan);
                BTScanPosInvalidate(so->currPos);
                return false;
            }
 
            /*
             * Okay, we managed to move left to a non-deleted page. Done if
             * it's not half-dead and contains matching tuples. Else loop back
             * and do it all again.
             */
            page = BufferGetPage(so->currPos.buf);
            opaque = BTPageGetOpaque(page);
            if (!P_IGNORE(opaque))
            {
                PredicateLockPage(rel, BufferGetBlockNumber(so->currPos.buf), scan->xs_snapshot);
                /* see if there are any matches on this page */
                /* note that this will clear moreLeft if we can stop */
                if (_bt_readpage(scan, dir, PageGetMaxOffsetNumber(page)))
                    break;
            }
            else if (scan->parallel_scan != NULL)
            {
                /* allow next page be processed by parallel worker */
                _bt_parallel_release(scan, BufferGetBlockNumber(so->currPos.buf));
            }
 
            /*
             * For parallel scans, get the last page scanned as it is quite
             * possible that by the time we try to seize the scan, some other
             * worker has already advanced the scan to a different page.  We
             * must continue based on the latest page scanned by any worker.
             */
            if (scan->parallel_scan != NULL)
            {
                _bt_relbuf(rel, so->currPos.buf);
                status = _bt_parallel_seize(scan, &blkno);
                if (!status)
                {
                    BTScanPosInvalidate(so->currPos);
                    return false;
                }
                so->currPos.buf = _bt_getbuf(rel, blkno, BT_READ);
            }
        }
    }
 
    return true;
}
 
/*
 *  _bt_parallel_readpage() -- Read current page containing valid data for scan
 *
 * On success, release lock and maybe pin on buffer.  We return true to
 * indicate success.
 */
static bool
_bt_parallel_readpage(IndexScanDesc scan, BlockNumber blkno, ScanDirection dir)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
 
    _bt_initialize_more_data(so, dir);
 
    if (!_bt_readnextpage(scan, blkno, dir))
        return false;
 
    /* Drop the lock, and maybe the pin, on the current page */
    _bt_drop_lock_and_maybe_pin(scan, &so->currPos);
 
    return true;
}
 
/*
 * _bt_walk_left() -- step left one page, if possible
 *
 * The given buffer must be pinned and read-locked.  This will be dropped
 * before stepping left.  On return, we have pin and read lock on the
 * returned page, instead.
 *
 * Returns InvalidBuffer if there is no page to the left (no lock is held
 * in that case).
 *
 * When working on a non-leaf level, it is possible for the returned page
 * to be half-dead; the caller should check that condition and step left
 * again if it's important.
 */
static Buffer
_bt_walk_left(Relation rel, Buffer buf)
{
    Page        page;
    BTPageOpaque opaque;
 
    page = BufferGetPage(buf);
    opaque = BTPageGetOpaque(page);
 
    for (;;)
    {
        BlockNumber obknum;
        BlockNumber lblkno;
        BlockNumber blkno;
        int         tries;
 
        /* if we're at end of tree, release buf and return failure */
        if (P_LEFTMOST(opaque))
        {
            _bt_relbuf(rel, buf);
            break;
        }
        /* remember original page we are stepping left from */
        obknum = BufferGetBlockNumber(buf);
        /* step left */
        blkno = lblkno = opaque->btpo_prev;
        _bt_relbuf(rel, buf);
        /* 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
         * the original page 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.  Caller
         * must reject half-dead pages if wanted.
         */
        tries = 0;
        for (;;)
        {
            if (!P_ISDELETED(opaque) && opaque->btpo_next == obknum)
            {
                /* Found desired page, return it */
                return buf;
            }
            if (P_RIGHTMOST(opaque) || ++tries > 4)
                break;
            blkno = opaque->btpo_next;
            buf = _bt_relandgetbuf(rel, buf, blkno, BT_READ);
            page = BufferGetPage(buf);
            opaque = BTPageGetOpaque(page);
        }
 
        /* Return to the original page to see what's up */
        buf = _bt_relandgetbuf(rel, buf, obknum, 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));
                blkno = opaque->btpo_next;
                buf = _bt_relandgetbuf(rel, buf, blkno, BT_READ);
                page = BufferGetPage(buf);
                opaque = BTPageGetOpaque(page);
                if (!P_ISDELETED(opaque))
                    break;
            }
 
            /*
             * Now return to top of loop, resetting obknum to point to this
             * nondeleted page, and try again.
             */
        }
        else
        {
            /*
             * It wasn't deleted; the explanation had better be that the page
             * to the left got split or deleted. Without this check, we'd go
             * into an infinite loop if there's anything wrong.
             */
            if (opaque->btpo_prev == lblkno)
                elog(ERROR, "could not find left sibling of block %u in index \"%s\"",
                     obknum, RelationGetRelationName(rel));
            /* Okay to try again with new lblkno value */
        }
    }
 
    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);
 
        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).  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;
    Buffer      buf;
    Page        page;
    BTPageOpaque opaque;
    OffsetNumber start;
    BTScanPosItem *currItem;
 
    /*
     * Scan down to the leftmost or rightmost leaf page.  This is a simplified
     * version of _bt_search().  We don't maintain a stack since we know we
     * won't need it.
     */
    buf = _bt_get_endpoint(rel, 0, ScanDirectionIsBackward(dir));
 
    if (!BufferIsValid(buf))
    {
        /*
         * Empty index. Lock the whole relation, as nothing finer to lock
         * exists.
         */
        PredicateLockRelation(rel, scan->xs_snapshot);
        BTScanPosInvalidate(so->currPos);
        return false;
    }
 
    PredicateLockPage(rel, BufferGetBlockNumber(buf), scan->xs_snapshot);
    page = BufferGetPage(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 */
    }
 
    /* remember which buffer we have pinned */
    so->currPos.buf = buf;
    so->firstPage = true;
 
    _bt_initialize_more_data(so, dir);
 
    /*
     * Now load data from the first page of the scan.
     */
    if (!_bt_readpage(scan, dir, start))
    {
        /*
         * There's no actually-matching data on this page.  Try to advance to
         * the next page.  Return false if there's no matching data at all.
         */
        _bt_unlockbuf(scan->indexRelation, so->currPos.buf);
        if (!_bt_steppage(scan, dir))
            return false;
    }
    else
    {
        /* Drop the lock, and maybe the pin, on the current page */
        _bt_drop_lock_and_maybe_pin(scan, &so->currPos);
    }
 
    /* OK, itemIndex says what to return */
    currItem = &so->currPos.items[so->currPos.itemIndex];
    scan->xs_heaptid = currItem->heapTid;
    if (scan->xs_want_itup)
        scan->xs_itup = (IndexTuple) (so->currTuples + currItem->tupleOffset);
 
    return true;
}
 
/*
 * _bt_initialize_more_data() -- initialize moreLeft/moreRight appropriately
 * for scan direction
 */
static inline void
_bt_initialize_more_data(BTScanOpaque so, ScanDirection dir)
{
    /* initialize moreLeft/moreRight appropriately for scan direction */
    if (ScanDirectionIsForward(dir))
    {
        so->currPos.moreLeft = false;
        so->currPos.moreRight = true;
    }
    else
    {
        so->currPos.moreLeft = true;
        so->currPos.moreRight = false;
    }
    so->numKilled = 0;          /* just paranoia */
    so->markItemIndex = -1;     /* ditto */
}