nbtreadpage.c

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/*-------------------------------------------------------------------------
 *
 * nbtreadpage.c
 *    Leaf page reading for btree index scans.
 *
 * NOTES
 *    This file contains code to return items that satisfy the scan's
 *    search-type scan keys within caller-supplied btree leaf page.
 *
 * Portions Copyright (c) 1996-2025, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * IDENTIFICATION
 *    src/backend/access/nbtree/nbtreadpage.c
 *
 *-------------------------------------------------------------------------
 */
 
#include "postgres.h"
 
#include "access/nbtree.h"
#include "access/relscan.h"
#include "storage/predicate.h"
#include "utils/datum.h"
#include "utils/rel.h"
 
 
/*
 * _bt_readpage state used across _bt_checkkeys calls for a page
 */
typedef struct BTReadPageState
{
    /* Input parameters, set by _bt_readpage for _bt_checkkeys */
    ScanDirection dir;          /* current scan direction */
    OffsetNumber minoff;        /* Lowest non-pivot tuple's offset */
    OffsetNumber maxoff;        /* Highest non-pivot tuple's offset */
    IndexTuple  finaltup;       /* Needed by scans with array keys */
    Page        page;           /* Page being read */
    bool        firstpage;      /* page is first for primitive scan? */
    bool        forcenonrequired;   /* treat all keys as nonrequired? */
    int         startikey;      /* start comparisons from this scan key */
 
    /* Per-tuple input parameters, set by _bt_readpage for _bt_checkkeys */
    OffsetNumber offnum;        /* current tuple's page offset number */
 
    /* Output parameters, set by _bt_checkkeys for _bt_readpage */
    OffsetNumber skip;          /* Array keys "look ahead" skip offnum */
    bool        continuescan;   /* Terminate ongoing (primitive) index scan? */
 
    /*
     * Private _bt_checkkeys state used to manage "look ahead" optimization
     * and primscan scheduling (only used during scans with array keys)
     */
    int16       rechecks;
    int16       targetdistance;
    int16       nskipadvances;
 
} BTReadPageState;
 
 
static void _bt_set_startikey(IndexScanDesc scan, BTReadPageState *pstate);
static bool _bt_scanbehind_checkkeys(IndexScanDesc scan, ScanDirection dir,
                                     IndexTuple finaltup);
static bool _bt_oppodir_checkkeys(IndexScanDesc scan, ScanDirection dir,
                                  IndexTuple finaltup);
static void _bt_saveitem(BTScanOpaque so, int itemIndex,
                         OffsetNumber offnum, IndexTuple itup);
static int  _bt_setuppostingitems(BTScanOpaque so, int itemIndex,
                                  OffsetNumber offnum, const ItemPointerData *heapTid,
                                  IndexTuple itup);
static inline void _bt_savepostingitem(BTScanOpaque so, int itemIndex,
                                       OffsetNumber offnum,
                                       ItemPointer heapTid, int tupleOffset);
static bool _bt_checkkeys(IndexScanDesc scan, BTReadPageState *pstate, bool arrayKeys,
                          IndexTuple tuple, int tupnatts);
static bool _bt_check_compare(IndexScanDesc scan, ScanDirection dir,
                              IndexTuple tuple, int tupnatts, TupleDesc tupdesc,
                              bool advancenonrequired, bool forcenonrequired,
                              bool *continuescan, int *ikey);
static bool _bt_check_rowcompare(ScanKey header,
                                 IndexTuple tuple, int tupnatts, TupleDesc tupdesc,
                                 ScanDirection dir, bool forcenonrequired, bool *continuescan);
static bool _bt_rowcompare_cmpresult(ScanKey subkey, int cmpresult);
static bool _bt_tuple_before_array_skeys(IndexScanDesc scan, ScanDirection dir,
                                         IndexTuple tuple, TupleDesc tupdesc, int tupnatts,
                                         bool readpagetup, int sktrig, bool *scanBehind);
static void _bt_checkkeys_look_ahead(IndexScanDesc scan, BTReadPageState *pstate,
                                     int tupnatts, TupleDesc tupdesc);
static bool _bt_advance_array_keys(IndexScanDesc scan, BTReadPageState *pstate,
                                   IndexTuple tuple, int tupnatts, TupleDesc tupdesc,
                                   int sktrig, bool sktrig_required);
static bool _bt_advance_array_keys_increment(IndexScanDesc scan, ScanDirection dir,
                                             bool *skip_array_set);
static bool _bt_array_increment(Relation rel, ScanKey skey, BTArrayKeyInfo *array);
static bool _bt_array_decrement(Relation rel, ScanKey skey, BTArrayKeyInfo *array);
static void _bt_array_set_low_or_high(Relation rel, ScanKey skey,
                                      BTArrayKeyInfo *array, bool low_not_high);
static void _bt_skiparray_set_element(Relation rel, ScanKey skey, BTArrayKeyInfo *array,
                                      int32 set_elem_result, Datum tupdatum, bool tupnull);
static void _bt_skiparray_set_isnull(Relation rel, ScanKey skey, BTArrayKeyInfo *array);
static inline int32 _bt_compare_array_skey(FmgrInfo *orderproc,
                                           Datum tupdatum, bool tupnull,
                                           Datum arrdatum, ScanKey cur);
static void _bt_binsrch_skiparray_skey(bool cur_elem_trig, ScanDirection dir,
                                       Datum tupdatum, bool tupnull,
                                       BTArrayKeyInfo *array, ScanKey cur,
                                       int32 *set_elem_result);
#ifdef USE_ASSERT_CHECKING
static bool _bt_verify_keys_with_arraykeys(IndexScanDesc scan);
#endif
 
 
/*
 *  _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
 * (could just be for the current primitive index scan when scan has arrays).
 *
 * 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.
 */
bool
_bt_readpage(IndexScanDesc scan, ScanDirection dir, OffsetNumber offnum,
             bool firstpage)
{
    Relation    rel = scan->indexRelation;
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    Page        page;
    BTPageOpaque opaque;
    OffsetNumber minoff;
    OffsetNumber maxoff;
    BTReadPageState pstate;
    bool        arrayKeys,
                ignore_killed_tuples = scan->ignore_killed_tuples;
    int         itemIndex,
                indnatts;
 
    /* save the page/buffer block number, along with its sibling links */
    page = BufferGetPage(so->currPos.buf);
    opaque = BTPageGetOpaque(page);
    so->currPos.currPage = BufferGetBlockNumber(so->currPos.buf);
    so->currPos.prevPage = opaque->btpo_prev;
    so->currPos.nextPage = opaque->btpo_next;
    /* delay setting so->currPos.lsn until _bt_drop_lock_and_maybe_pin */
    pstate.dir = so->currPos.dir = dir;
    so->currPos.nextTupleOffset = 0;
 
    /* either moreRight or moreLeft should be set now (may be unset later) */
    Assert(ScanDirectionIsForward(dir) ? so->currPos.moreRight :
           so->currPos.moreLeft);
    Assert(!P_IGNORE(opaque));
    Assert(BTScanPosIsPinned(so->currPos));
    Assert(!so->needPrimScan);
 
    /* initialize local variables */
    indnatts = IndexRelationGetNumberOfAttributes(rel);
    arrayKeys = so->numArrayKeys != 0;
    minoff = P_FIRSTDATAKEY(opaque);
    maxoff = PageGetMaxOffsetNumber(page);
 
    /* initialize page-level state that we'll pass to _bt_checkkeys */
    pstate.minoff = minoff;
    pstate.maxoff = maxoff;
    pstate.finaltup = NULL;
    pstate.page = page;
    pstate.firstpage = firstpage;
    pstate.forcenonrequired = false;
    pstate.startikey = 0;
    pstate.offnum = InvalidOffsetNumber;
    pstate.skip = InvalidOffsetNumber;
    pstate.continuescan = true; /* default assumption */
    pstate.rechecks = 0;
    pstate.targetdistance = 0;
    pstate.nskipadvances = 0;
 
    if (scan->parallel_scan)
    {
        /* allow next/prev page to be read by other worker without delay */
        if (ScanDirectionIsForward(dir))
            _bt_parallel_release(scan, so->currPos.nextPage,
                                 so->currPos.currPage);
        else
            _bt_parallel_release(scan, so->currPos.prevPage,
                                 so->currPos.currPage);
    }
 
    PredicateLockPage(rel, so->currPos.currPage, scan->xs_snapshot);
 
    if (ScanDirectionIsForward(dir))
    {
        /* SK_SEARCHARRAY forward scans must provide high key up front */
        if (arrayKeys)
        {
            if (!P_RIGHTMOST(opaque))
            {
                ItemId      iid = PageGetItemId(page, P_HIKEY);
 
                pstate.finaltup = (IndexTuple) PageGetItem(page, iid);
 
                if (unlikely(so->scanBehind) &&
                    !_bt_scanbehind_checkkeys(scan, dir, pstate.finaltup))
                {
                    /* Schedule another primitive index scan after all */
                    so->currPos.moreRight = false;
                    so->needPrimScan = true;
                    if (scan->parallel_scan)
                        _bt_parallel_primscan_schedule(scan,
                                                       so->currPos.currPage);
                    return false;
                }
            }
 
            so->scanBehind = so->oppositeDirCheck = false;  /* reset */
        }
 
        /*
         * Consider pstate.startikey optimization once the ongoing primitive
         * index scan has already read at least one page
         */
        if (!pstate.firstpage && minoff < maxoff)
            _bt_set_startikey(scan, &pstate);
 
        /* 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 (ignore_killed_tuples && ItemIdIsDead(iid))
            {
                offnum = OffsetNumberNext(offnum);
                continue;
            }
 
            itup = (IndexTuple) PageGetItem(page, iid);
            Assert(!BTreeTupleIsPivot(itup));
 
            pstate.offnum = offnum;
            passes_quals = _bt_checkkeys(scan, &pstate, arrayKeys,
                                         itup, indnatts);
 
            /*
             * Check if we need to skip ahead to a later tuple (only possible
             * when the scan uses array keys)
             */
            if (arrayKeys && OffsetNumberIsValid(pstate.skip))
            {
                Assert(!passes_quals && pstate.continuescan);
                Assert(offnum < pstate.skip);
                Assert(!pstate.forcenonrequired);
 
                offnum = pstate.skip;
                pstate.skip = InvalidOffsetNumber;
                continue;
            }
 
            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 posting list state (and remember first TID) */
                    tupleOffset =
                        _bt_setuppostingitems(so, itemIndex, offnum,
                                              BTreeTupleGetPostingN(itup, 0),
                                              itup);
                    itemIndex++;
 
                    /* Remember all later TIDs (must be at least one) */
                    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 (!pstate.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 (pstate.continuescan && !so->scanBehind && !P_RIGHTMOST(opaque))
        {
            ItemId      iid = PageGetItemId(page, P_HIKEY);
            IndexTuple  itup = (IndexTuple) PageGetItem(page, iid);
            int         truncatt;
 
            /* Reset arrays, per _bt_set_startikey contract */
            if (pstate.forcenonrequired)
                _bt_start_array_keys(scan, dir);
            pstate.forcenonrequired = false;
            pstate.startikey = 0;   /* _bt_set_startikey ignores P_HIKEY */
 
            truncatt = BTreeTupleGetNAtts(itup, rel);
            _bt_checkkeys(scan, &pstate, arrayKeys, itup, truncatt);
        }
 
        if (!pstate.continuescan)
            so->currPos.moreRight = false;
 
        Assert(itemIndex <= MaxTIDsPerBTreePage);
        so->currPos.firstItem = 0;
        so->currPos.lastItem = itemIndex - 1;
        so->currPos.itemIndex = 0;
    }
    else
    {
        /* SK_SEARCHARRAY backward scans must provide final tuple up front */
        if (arrayKeys)
        {
            if (minoff <= maxoff && !P_LEFTMOST(opaque))
            {
                ItemId      iid = PageGetItemId(page, minoff);
 
                pstate.finaltup = (IndexTuple) PageGetItem(page, iid);
 
                if (unlikely(so->scanBehind) &&
                    !_bt_scanbehind_checkkeys(scan, dir, pstate.finaltup))
                {
                    /* Schedule another primitive index scan after all */
                    so->currPos.moreLeft = false;
                    so->needPrimScan = true;
                    if (scan->parallel_scan)
                        _bt_parallel_primscan_schedule(scan,
                                                       so->currPos.currPage);
                    return false;
                }
            }
 
            so->scanBehind = so->oppositeDirCheck = false;  /* reset */
        }
 
        /*
         * Consider pstate.startikey optimization once the ongoing primitive
         * index scan has already read at least one page
         */
        if (!pstate.firstpage && minoff < maxoff)
            _bt_set_startikey(scan, &pstate);
 
        /* 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 (ignore_killed_tuples && ItemIdIsDead(iid))
            {
                if (offnum > minoff)
                {
                    offnum = OffsetNumberPrev(offnum);
                    continue;
                }
 
                tuple_alive = false;
            }
            else
                tuple_alive = true;
 
            itup = (IndexTuple) PageGetItem(page, iid);
            Assert(!BTreeTupleIsPivot(itup));
 
            pstate.offnum = offnum;
            if (arrayKeys && offnum == minoff && pstate.forcenonrequired)
            {
                /* Reset arrays, per _bt_set_startikey contract */
                pstate.forcenonrequired = false;
                pstate.startikey = 0;
                _bt_start_array_keys(scan, dir);
            }
            passes_quals = _bt_checkkeys(scan, &pstate, arrayKeys,
                                         itup, indnatts);
 
            if (arrayKeys && so->scanBehind)
            {
                /*
                 * Done scanning this page, but not done with the current
                 * primscan.
                 *
                 * Note: Forward scans don't check this explicitly, since they
                 * prefer to reuse pstate.skip for this instead.
                 */
                Assert(!passes_quals && pstate.continuescan);
                Assert(!pstate.forcenonrequired);
 
                break;
            }
 
            /*
             * Check if we need to skip ahead to a later tuple (only possible
             * when the scan uses array keys)
             */
            if (arrayKeys && OffsetNumberIsValid(pstate.skip))
            {
                Assert(!passes_quals && pstate.continuescan);
                Assert(offnum > pstate.skip);
                Assert(!pstate.forcenonrequired);
 
                offnum = pstate.skip;
                pstate.skip = InvalidOffsetNumber;
                continue;
            }
 
            if (passes_quals && tuple_alive)
            {
                /* tuple passes all scan key conditions */
                if (!BTreeTupleIsPosting(itup))
                {
                    /* Remember it */
                    itemIndex--;
                    _bt_saveitem(so, itemIndex, offnum, itup);
                }
                else
                {
                    uint16      nitems = BTreeTupleGetNPosting(itup);
                    int         tupleOffset;
 
                    /* Set up posting list state (and remember last TID) */
                    itemIndex--;
                    tupleOffset =
                        _bt_setuppostingitems(so, itemIndex, offnum,
                                              BTreeTupleGetPostingN(itup, nitems - 1),
                                              itup);
 
                    /* Remember all prior TIDs (must be at least one) */
                    for (int i = nitems - 2; i >= 0; i--)
                    {
                        itemIndex--;
                        _bt_savepostingitem(so, itemIndex, offnum,
                                            BTreeTupleGetPostingN(itup, i),
                                            tupleOffset);
                    }
                }
            }
            /* When !continuescan, there can't be any more matches, so stop */
            if (!pstate.continuescan)
                break;
 
            offnum = OffsetNumberPrev(offnum);
        }
 
        /*
         * We don't need to visit page to the left when no more matches will
         * be found there
         */
        if (!pstate.continuescan)
            so->currPos.moreLeft = false;
 
        Assert(itemIndex >= 0);
        so->currPos.firstItem = itemIndex;
        so->currPos.lastItem = MaxTIDsPerBTreePage - 1;
        so->currPos.itemIndex = MaxTIDsPerBTreePage - 1;
    }
 
    /*
     * If _bt_set_startikey told us to temporarily treat the scan's keys as
     * nonrequired (possible only during scans with array keys), there must be
     * no lasting consequences for the scan's array keys.  The scan's arrays
     * should now have exactly the same elements as they would have had if the
     * nonrequired behavior had never been used.  (In general, a scan's arrays
     * are expected to track its progress through the index's key space.)
     *
     * We are required (by _bt_set_startikey) to call _bt_checkkeys against
     * pstate.finaltup with pstate.forcenonrequired=false to allow the scan's
     * arrays to recover.  Assert that that step hasn't been missed.
     */
    Assert(!pstate.forcenonrequired);
 
    return (so->currPos.firstItem <= so->currPos.lastItem);
}
 
/*
 * _bt_start_array_keys() -- Initialize array keys at start of a scan
 *
 * Set up the cur_elem counters and fill in the first sk_argument value for
 * each array scankey.
 */
void
_bt_start_array_keys(IndexScanDesc scan, ScanDirection dir)
{
    Relation    rel = scan->indexRelation;
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
 
    Assert(so->numArrayKeys);
    Assert(so->qual_ok);
 
    for (int i = 0; i < so->numArrayKeys; i++)
    {
        BTArrayKeyInfo *array = &so->arrayKeys[i];
        ScanKey     skey = &so->keyData[array->scan_key];
 
        Assert(skey->sk_flags & SK_SEARCHARRAY);
 
        _bt_array_set_low_or_high(rel, skey, array,
                                  ScanDirectionIsForward(dir));
    }
    so->scanBehind = so->oppositeDirCheck = false;  /* reset */
}
 
/*
 * Determines an offset to the first scan key (an so->keyData[]-wise offset)
 * that is _not_ guaranteed to be satisfied by every tuple from pstate.page,
 * which is set in pstate.startikey for _bt_checkkeys calls for the page.
 * This allows caller to save cycles on comparisons of a prefix of keys while
 * reading pstate.page.
 *
 * Also determines if later calls to _bt_checkkeys (for pstate.page) should be
 * forced to treat all required scan keys >= pstate.startikey as nonrequired
 * (that is, if they're to be treated as if any SK_BT_REQFWD/SK_BT_REQBKWD
 * markings that were set by preprocessing were not set at all, for the
 * duration of _bt_checkkeys calls prior to the call for pstate.finaltup).
 * This is indicated to caller by setting pstate.forcenonrequired.
 *
 * Call here at the start of reading a leaf page beyond the first one for the
 * primitive index scan.  We consider all non-pivot tuples, so it doesn't make
 * sense to call here when only a subset of those tuples can ever be read.
 * This is also a good idea on performance grounds; not calling here when on
 * the first page (first for the current primitive scan) avoids wasting cycles
 * during selective point queries.  They typically don't stand to gain as much
 * when we can set pstate.startikey, and are likely to notice the overhead of
 * calling here.  (Also, allowing pstate.forcenonrequired to be set on a
 * primscan's first page would mislead _bt_advance_array_keys, which expects
 * pstate.nskipadvances to be representative of every first page's key space.)
 *
 * Caller must call _bt_start_array_keys and reset startikey/forcenonrequired
 * ahead of the finaltup _bt_checkkeys call when we set forcenonrequired=true.
 * This will give _bt_checkkeys the opportunity to call _bt_advance_array_keys
 * with sktrig_required=true, restoring the invariant that the scan's required
 * arrays always track the scan's progress through the index's key space.
 * Caller won't need to do this on the rightmost/leftmost page in the index
 * (where pstate.finaltup isn't ever set), since forcenonrequired will never
 * be set here in the first place.
 */
static void
_bt_set_startikey(IndexScanDesc scan, BTReadPageState *pstate)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    Relation    rel = scan->indexRelation;
    TupleDesc   tupdesc = RelationGetDescr(rel);
    ItemId      iid;
    IndexTuple  firsttup,
                lasttup;
    int         startikey = 0,
                arrayidx = 0,
                firstchangingattnum;
    bool        start_past_saop_eq = false;
 
    Assert(!so->scanBehind);
    Assert(pstate->minoff < pstate->maxoff);
    Assert(!pstate->firstpage);
    Assert(pstate->startikey == 0);
    Assert(!so->numArrayKeys || pstate->finaltup ||
           P_RIGHTMOST(BTPageGetOpaque(pstate->page)) ||
           P_LEFTMOST(BTPageGetOpaque(pstate->page)));
 
    if (so->numberOfKeys == 0)
        return;
 
    /* minoff is an offset to the lowest non-pivot tuple on the page */
    iid = PageGetItemId(pstate->page, pstate->minoff);
    firsttup = (IndexTuple) PageGetItem(pstate->page, iid);
 
    /* maxoff is an offset to the highest non-pivot tuple on the page */
    iid = PageGetItemId(pstate->page, pstate->maxoff);
    lasttup = (IndexTuple) PageGetItem(pstate->page, iid);
 
    /* Determine the first attribute whose values change on caller's page */
    firstchangingattnum = _bt_keep_natts_fast(rel, firsttup, lasttup);
 
    for (; startikey < so->numberOfKeys; startikey++)
    {
        ScanKey     key = so->keyData + startikey;
        BTArrayKeyInfo *array;
        Datum       firstdatum,
                    lastdatum;
        bool        firstnull,
                    lastnull;
        int32       result;
 
        /*
         * Determine if it's safe to set pstate.startikey to an offset to a
         * key that comes after this key, by examining this key
         */
        if (key->sk_flags & SK_ROW_HEADER)
        {
            /* RowCompare inequality (header key) */
            ScanKey     subkey = (ScanKey) DatumGetPointer(key->sk_argument);
            bool        satisfied = false;
 
            for (;;)
            {
                int         cmpresult;
                bool        firstsatisfies = false;
 
                if (subkey->sk_attno > firstchangingattnum) /* >, not >= */
                    break;      /* unsafe, preceding attr has multiple
                                 * distinct values */
 
                if (subkey->sk_flags & SK_ISNULL)
                    break;      /* unsafe, unsatisfiable NULL subkey arg */
 
                firstdatum = index_getattr(firsttup, subkey->sk_attno,
                                           tupdesc, &firstnull);
                lastdatum = index_getattr(lasttup, subkey->sk_attno,
                                          tupdesc, &lastnull);
 
                if (firstnull || lastnull)
                    break;      /* unsafe, NULL value won't satisfy subkey */
 
                /*
                 * Compare the first tuple's datum for this row compare member
                 */
                cmpresult = DatumGetInt32(FunctionCall2Coll(&subkey->sk_func,
                                                            subkey->sk_collation,
                                                            firstdatum,
                                                            subkey->sk_argument));
                if (subkey->sk_flags & SK_BT_DESC)
                    INVERT_COMPARE_RESULT(cmpresult);
 
                if (cmpresult != 0 || (subkey->sk_flags & SK_ROW_END))
                {
                    firstsatisfies = _bt_rowcompare_cmpresult(subkey,
                                                              cmpresult);
                    if (!firstsatisfies)
                    {
                        /* Unsafe, firstdatum does not satisfy subkey */
                        break;
                    }
                }
 
                /*
                 * Compare the last tuple's datum for this row compare member
                 */
                cmpresult = DatumGetInt32(FunctionCall2Coll(&subkey->sk_func,
                                                            subkey->sk_collation,
                                                            lastdatum,
                                                            subkey->sk_argument));
                if (subkey->sk_flags & SK_BT_DESC)
                    INVERT_COMPARE_RESULT(cmpresult);
 
                if (cmpresult != 0 || (subkey->sk_flags & SK_ROW_END))
                {
                    if (!firstsatisfies)
                    {
                        /*
                         * It's only safe to set startikey beyond the row
                         * compare header key when both firsttup and lasttup
                         * satisfy the key as a whole based on the same
                         * deciding subkey/attribute.  That can't happen now.
                         */
                        break;  /* unsafe */
                    }
 
                    satisfied = _bt_rowcompare_cmpresult(subkey, cmpresult);
                    break;      /* safe iff 'satisfied' is true */
                }
 
                /* Move on to next row member/subkey */
                if (subkey->sk_flags & SK_ROW_END)
                    break;      /* defensive */
                subkey++;
 
                /*
                 * We deliberately don't check if the next subkey has the same
                 * strategy as this iteration's subkey (which happens when
                 * subkeys for both ASC and DESC columns are used together),
                 * nor if any subkey is marked required.  This is safe because
                 * in general all prior index attributes must have only one
                 * distinct value (across all of the tuples on the page) in
                 * order for us to even consider any subkey's attribute.
                 */
            }
 
            if (satisfied)
            {
                /* Safe, row compare satisfied by every tuple on page */
                continue;
            }
 
            break;              /* unsafe */
        }
        if (key->sk_strategy != BTEqualStrategyNumber)
        {
            /*
             * Scalar inequality key.
             *
             * It's definitely safe for _bt_checkkeys to avoid assessing this
             * inequality when the page's first and last non-pivot tuples both
             * satisfy the inequality (since the same must also be true of all
             * the tuples in between these two).
             *
             * Unlike the "=" case, it doesn't matter if this attribute has
             * more than one distinct value (though it _is_ necessary for any
             * and all _prior_ attributes to contain no more than one distinct
             * value amongst all of the tuples from pstate.page).
             */
            if (key->sk_attno > firstchangingattnum)    /* >, not >= */
                break;          /* unsafe, preceding attr has multiple
                                 * distinct values */
 
            firstdatum = index_getattr(firsttup, key->sk_attno, tupdesc, &firstnull);
            lastdatum = index_getattr(lasttup, key->sk_attno, tupdesc, &lastnull);
 
            if (key->sk_flags & SK_ISNULL)
            {
                /* IS NOT NULL key */
                Assert(key->sk_flags & SK_SEARCHNOTNULL);
 
                if (firstnull || lastnull)
                    break;      /* unsafe */
 
                /* Safe, IS NOT NULL key satisfied by every tuple */
                continue;
            }
 
            /* Test firsttup */
            if (firstnull ||
                !DatumGetBool(FunctionCall2Coll(&key->sk_func,
                                                key->sk_collation, firstdatum,
                                                key->sk_argument)))
                break;          /* unsafe */
 
            /* Test lasttup */
            if (lastnull ||
                !DatumGetBool(FunctionCall2Coll(&key->sk_func,
                                                key->sk_collation, lastdatum,
                                                key->sk_argument)))
                break;          /* unsafe */
 
            /* Safe, scalar inequality satisfied by every tuple */
            continue;
        }
 
        /* Some = key (could be a scalar = key, could be an array = key) */
        Assert(key->sk_strategy == BTEqualStrategyNumber);
 
        if (!(key->sk_flags & SK_SEARCHARRAY))
        {
            /*
             * Scalar = key (possibly an IS NULL key).
             *
             * It is unsafe to set pstate.startikey to an ikey beyond this
             * key, unless the = key is satisfied by every possible tuple on
             * the page (possible only when attribute has just one distinct
             * value among all tuples on the page).
             */
            if (key->sk_attno >= firstchangingattnum)
                break;          /* unsafe, multiple distinct attr values */
 
            firstdatum = index_getattr(firsttup, key->sk_attno, tupdesc,
                                       &firstnull);
            if (key->sk_flags & SK_ISNULL)
            {
                /* IS NULL key */
                Assert(key->sk_flags & SK_SEARCHNULL);
 
                if (!firstnull)
                    break;      /* unsafe */
 
                /* Safe, IS NULL key satisfied by every tuple */
                continue;
            }
            if (firstnull ||
                !DatumGetBool(FunctionCall2Coll(&key->sk_func,
                                                key->sk_collation, firstdatum,
                                                key->sk_argument)))
                break;          /* unsafe */
 
            /* Safe, scalar = key satisfied by every tuple */
            continue;
        }
 
        /* = array key (could be a SAOP array, could be a skip array) */
        array = &so->arrayKeys[arrayidx++];
        Assert(array->scan_key == startikey);
        if (array->num_elems != -1)
        {
            /*
             * SAOP array = key.
             *
             * Handle this like we handle scalar = keys (though binary search
             * for a matching element, to avoid relying on key's sk_argument).
             */
            if (key->sk_attno >= firstchangingattnum)
                break;          /* unsafe, multiple distinct attr values */
 
            firstdatum = index_getattr(firsttup, key->sk_attno, tupdesc,
                                       &firstnull);
            _bt_binsrch_array_skey(&so->orderProcs[startikey],
                                   false, NoMovementScanDirection,
                                   firstdatum, firstnull, array, key,
                                   &result);
            if (result != 0)
                break;          /* unsafe */
 
            /* Safe, SAOP = key satisfied by every tuple */
            start_past_saop_eq = true;
            continue;
        }
 
        /*
         * Skip array = key
         */
        Assert(key->sk_flags & SK_BT_SKIP);
        if (array->null_elem)
        {
            /*
             * Non-range skip array = key.
             *
             * Safe, non-range skip array "satisfied" by every tuple on page
             * (safe even when "key->sk_attno > firstchangingattnum").
             */
            continue;
        }
 
        /*
         * Range skip array = key.
         *
         * Handle this like we handle scalar inequality keys (but avoid using
         * key's sk_argument directly, as in the SAOP array case).
         */
        if (key->sk_attno > firstchangingattnum)    /* >, not >= */
            break;              /* unsafe, preceding attr has multiple
                                 * distinct values */
 
        firstdatum = index_getattr(firsttup, key->sk_attno, tupdesc, &firstnull);
        lastdatum = index_getattr(lasttup, key->sk_attno, tupdesc, &lastnull);
 
        /* Test firsttup */
        _bt_binsrch_skiparray_skey(false, ForwardScanDirection,
                                   firstdatum, firstnull, array, key,
                                   &result);
        if (result != 0)
            break;              /* unsafe */
 
        /* Test lasttup */
        _bt_binsrch_skiparray_skey(false, ForwardScanDirection,
                                   lastdatum, lastnull, array, key,
                                   &result);
        if (result != 0)
            break;              /* unsafe */
 
        /* Safe, range skip array satisfied by every tuple on page */
    }
 
    /*
     * Use of forcenonrequired is typically undesirable, since it'll force
     * _bt_readpage caller to read every tuple on the page -- even though, in
     * general, it might well be possible to end the scan on an earlier tuple.
     * However, caller must use forcenonrequired when start_past_saop_eq=true,
     * since the usual required array behavior might fail to roll over to the
     * SAOP array.
     *
     * We always prefer forcenonrequired=true during scans with skip arrays
     * (except on the first page of each primitive index scan), though -- even
     * when "startikey == 0".  That way, _bt_advance_array_keys's low-order
     * key precheck optimization can always be used (unless on the first page
     * of the scan).  It seems slightly preferable to check more tuples when
     * that allows us to do significantly less skip array maintenance.
     */
    pstate->forcenonrequired = (start_past_saop_eq || so->skipScan);
    pstate->startikey = startikey;
 
    /*
     * _bt_readpage caller is required to call _bt_checkkeys against page's
     * finaltup with forcenonrequired=false whenever we initially set
     * forcenonrequired=true.  That way the scan's arrays will reliably track
     * its progress through the index's key space.
     *
     * We don't expect this when _bt_readpage caller has no finaltup due to
     * its page being the rightmost (or the leftmost, during backwards scans).
     * When we see that _bt_readpage has no finaltup, back out of everything.
     */
    Assert(!pstate->forcenonrequired || so->numArrayKeys);
    if (pstate->forcenonrequired && !pstate->finaltup)
    {
        pstate->forcenonrequired = false;
        pstate->startikey = 0;
    }
}
 
/*
 * Test whether caller's finaltup tuple is still before the start of matches
 * for the current array keys.
 *
 * Called at the start of reading a page during a scan with array keys, though
 * only when the so->scanBehind flag was set on the scan's prior page.
 *
 * Returns false if the tuple is still before the start of matches.  When that
 * happens, caller should cut its losses and start a new primitive index scan.
 * Otherwise returns true.
 */
static bool
_bt_scanbehind_checkkeys(IndexScanDesc scan, ScanDirection dir,
                         IndexTuple finaltup)
{
    Relation    rel = scan->indexRelation;
    TupleDesc   tupdesc = RelationGetDescr(rel);
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    int         nfinaltupatts = BTreeTupleGetNAtts(finaltup, rel);
    bool        scanBehind;
 
    Assert(so->numArrayKeys);
 
    if (_bt_tuple_before_array_skeys(scan, dir, finaltup, tupdesc,
                                     nfinaltupatts, false, 0, &scanBehind))
        return false;
 
    /*
     * If scanBehind was set, all of the untruncated attribute values from
     * finaltup that correspond to an array match the array's current element,
     * but there are other keys associated with truncated suffix attributes.
     * Array advancement must have incremented the scan's arrays on the
     * previous page, resulting in a set of array keys that happen to be an
     * exact match for the current page high key's untruncated prefix values.
     *
     * This page definitely doesn't contain tuples that the scan will need to
     * return.  The next page may or may not contain relevant tuples.  Handle
     * this by cutting our losses and starting a new primscan.
     */
    if (scanBehind)
        return false;
 
    if (!so->oppositeDirCheck)
        return true;
 
    return _bt_oppodir_checkkeys(scan, dir, finaltup);
}
 
/*
 * Test whether an indextuple fails to satisfy an inequality required in the
 * opposite direction only.
 *
 * Caller's finaltup tuple is the page high key (for forwards scans), or the
 * first non-pivot tuple (for backwards scans).  Called during scans with
 * required array keys and required opposite-direction inequalities.
 *
 * Returns false if an inequality scan key required in the opposite direction
 * only isn't satisfied (and any earlier required scan keys are satisfied).
 * Otherwise returns true.
 *
 * An unsatisfied inequality required in the opposite direction only might
 * well enable skipping over many leaf pages, provided another _bt_first call
 * takes place.  This type of unsatisfied inequality won't usually cause
 * _bt_checkkeys to stop the scan to consider array advancement/starting a new
 * primitive index scan.
 */
static bool
_bt_oppodir_checkkeys(IndexScanDesc scan, ScanDirection dir,
                      IndexTuple finaltup)
{
    Relation    rel = scan->indexRelation;
    TupleDesc   tupdesc = RelationGetDescr(rel);
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    int         nfinaltupatts = BTreeTupleGetNAtts(finaltup, rel);
    bool        continuescan;
    ScanDirection flipped = -dir;
    int         ikey = 0;
 
    Assert(so->numArrayKeys);
 
    _bt_check_compare(scan, flipped, finaltup, nfinaltupatts, tupdesc, false,
                      false, &continuescan,
                      &ikey);
 
    if (!continuescan && so->keyData[ikey].sk_strategy != BTEqualStrategyNumber)
        return false;
 
    return true;
}
 
/* 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,
                      const ItemPointerData *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;
}
 
#define LOOK_AHEAD_REQUIRED_RECHECKS    3
#define LOOK_AHEAD_DEFAULT_DISTANCE     5
#define NSKIPADVANCES_THRESHOLD         3
 
/*
 * Test whether an indextuple satisfies all the scankey conditions.
 *
 * Return true if so, false if not.  If the tuple fails to pass the qual,
 * we also determine whether there's any need to continue the scan beyond
 * this tuple, and set pstate.continuescan accordingly.  See comments for
 * _bt_preprocess_keys() about how this is done.
 *
 * Forward scan callers can pass a high key tuple in the hopes of having
 * us set *continuescan to false, and avoiding an unnecessary visit to
 * the page to the right.
 *
 * Advances the scan's array keys when necessary for arrayKeys=true callers.
 * Scans without any array keys must always pass arrayKeys=false.
 *
 * Also stops and starts primitive index scans for arrayKeys=true callers.
 * Scans with array keys are required to set up page state that helps us with
 * this.  The page's finaltup tuple (the page high key for a forward scan, or
 * the page's first non-pivot tuple for a backward scan) must be set in
 * pstate.finaltup ahead of the first call here for the page.  Set this to
 * NULL for rightmost page (or the leftmost page for backwards scans).
 *
 * scan: index scan descriptor (containing a search-type scankey)
 * pstate: page level input and output parameters
 * arrayKeys: should we advance the scan's array keys if necessary?
 * tuple: index tuple to test
 * tupnatts: number of attributes in tupnatts (high key may be truncated)
 */
static bool
_bt_checkkeys(IndexScanDesc scan, BTReadPageState *pstate, bool arrayKeys,
              IndexTuple tuple, int tupnatts)
{
    TupleDesc   tupdesc = RelationGetDescr(scan->indexRelation);
    BTScanOpaque so PG_USED_FOR_ASSERTS_ONLY = (BTScanOpaque) scan->opaque;
    ScanDirection dir = pstate->dir;
    int         ikey = pstate->startikey;
    bool        res;
 
    Assert(BTreeTupleGetNAtts(tuple, scan->indexRelation) == tupnatts);
    Assert(!so->needPrimScan && !so->scanBehind && !so->oppositeDirCheck);
    Assert(arrayKeys || so->numArrayKeys == 0);
 
    res = _bt_check_compare(scan, dir, tuple, tupnatts, tupdesc, arrayKeys,
                            pstate->forcenonrequired, &pstate->continuescan,
                            &ikey);
 
    /*
     * If _bt_check_compare relied on the pstate.startikey optimization, call
     * again (in assert-enabled builds) to verify it didn't affect our answer.
     *
     * Note: we can't do this when !pstate.forcenonrequired, since any arrays
     * before pstate.startikey won't have advanced on this page at all.
     */
    Assert(!pstate->forcenonrequired || arrayKeys);
#ifdef USE_ASSERT_CHECKING
    if (pstate->startikey > 0 && !pstate->forcenonrequired)
    {
        bool        dres,
                    dcontinuescan;
        int         dikey = 0;
 
        /* Pass arrayKeys=false to avoid array side-effects */
        dres = _bt_check_compare(scan, dir, tuple, tupnatts, tupdesc, false,
                                 pstate->forcenonrequired, &dcontinuescan,
                                 &dikey);
        Assert(res == dres);
        Assert(pstate->continuescan == dcontinuescan);
 
        /*
         * Should also get the same ikey result.  We need a slightly weaker
         * assertion during arrayKeys calls, since they might be using an
         * array that couldn't be marked required during preprocessing.
         */
        Assert(arrayKeys || ikey == dikey);
        Assert(ikey <= dikey);
    }
#endif
 
    /*
     * Only one _bt_check_compare call is required in the common case where
     * there are no equality strategy array scan keys.  Otherwise we can only
     * accept _bt_check_compare's answer unreservedly when it didn't set
     * pstate.continuescan=false.
     */
    if (!arrayKeys || pstate->continuescan)
        return res;
 
    /*
     * _bt_check_compare call set continuescan=false in the presence of
     * equality type array keys.  This could mean that the tuple is just past
     * the end of matches for the current array keys.
     *
     * It's also possible that the scan is still _before_ the _start_ of
     * tuples matching the current set of array keys.  Check for that first.
     */
    Assert(!pstate->forcenonrequired);
    if (_bt_tuple_before_array_skeys(scan, dir, tuple, tupdesc, tupnatts, true,
                                     ikey, NULL))
    {
        /* Override _bt_check_compare, continue primitive scan */
        pstate->continuescan = true;
 
        /*
         * We will end up here repeatedly given a group of tuples > the
         * previous array keys and < the now-current keys (for a backwards
         * scan it's just the same, though the operators swap positions).
         *
         * We must avoid allowing this linear search process to scan very many
         * tuples from well before the start of tuples matching the current
         * array keys (or from well before the point where we'll once again
         * have to advance the scan's array keys).
         *
         * We keep the overhead under control by speculatively "looking ahead"
         * to later still-unscanned items from this same leaf page.  We'll
         * only attempt this once the number of tuples that the linear search
         * process has examined starts to get out of hand.
         */
        pstate->rechecks++;
        if (pstate->rechecks >= LOOK_AHEAD_REQUIRED_RECHECKS)
        {
            /* See if we should skip ahead within the current leaf page */
            _bt_checkkeys_look_ahead(scan, pstate, tupnatts, tupdesc);
 
            /*
             * Might have set pstate.skip to a later page offset.  When that
             * happens then _bt_readpage caller will inexpensively skip ahead
             * to a later tuple from the same page (the one just after the
             * tuple we successfully "looked ahead" to).
             */
        }
 
        /* This indextuple doesn't match the current qual, in any case */
        return false;
    }
 
    /*
     * Caller's tuple is >= the current set of array keys and other equality
     * constraint scan keys (or <= if this is a backwards scan).  It's now
     * clear that we _must_ advance any required array keys in lockstep with
     * the scan.
     */
    return _bt_advance_array_keys(scan, pstate, tuple, tupnatts, tupdesc,
                                  ikey, true);
}
 
/*
 * Test whether an indextuple satisfies current scan condition.
 *
 * Return true if so, false if not.  If not, also sets *continuescan to false
 * when it's also not possible for any later tuples to pass the current qual
 * (with the scan's current set of array keys, in the current scan direction),
 * in addition to setting *ikey to the so->keyData[] subscript/offset for the
 * unsatisfied scan key (needed when caller must consider advancing the scan's
 * array keys).
 *
 * This is a subroutine for _bt_checkkeys.  We provisionally assume that
 * reaching the end of the current set of required keys (in particular the
 * current required array keys) ends the ongoing (primitive) index scan.
 * Callers without array keys should just end the scan right away when they
 * find that continuescan has been set to false here by us.  Things are more
 * complicated for callers with array keys.
 *
 * Callers with array keys must first consider advancing the arrays when
 * continuescan has been set to false here by us.  They must then consider if
 * it really does make sense to end the current (primitive) index scan, in
 * light of everything that is known at that point.  (In general when we set
 * continuescan=false for these callers it must be treated as provisional.)
 *
 * We deal with advancing unsatisfied non-required arrays directly, though.
 * This is safe, since by definition non-required keys can't end the scan.
 * This is just how we determine if non-required arrays are just unsatisfied
 * by the current array key, or if they're truly unsatisfied (that is, if
 * they're unsatisfied by every possible array key).
 *
 * Pass advancenonrequired=false to avoid all array related side effects.
 * This allows _bt_advance_array_keys caller to avoid infinite recursion.
 *
 * Pass forcenonrequired=true to instruct us to treat all keys as nonrequired.
 * This is used to make it safe to temporarily stop properly maintaining the
 * scan's required arrays.  _bt_checkkeys caller (_bt_readpage, actually)
 * determines a prefix of keys that must satisfy every possible corresponding
 * index attribute value from its page, which is passed to us via *ikey arg
 * (this is the first key that might be unsatisfied by tuples on the page).
 * Obviously, we won't maintain any array keys from before *ikey, so it's
 * quite possible for such arrays to "fall behind" the index's keyspace.
 * Caller will need to "catch up" by passing forcenonrequired=true (alongside
 * an *ikey=0) once the page's finaltup is reached.
 *
 * Note: it's safe to pass an *ikey > 0 with forcenonrequired=false, but only
 * when caller determines that it won't affect array maintenance.
 */
static bool
_bt_check_compare(IndexScanDesc scan, ScanDirection dir,
                  IndexTuple tuple, int tupnatts, TupleDesc tupdesc,
                  bool advancenonrequired, bool forcenonrequired,
                  bool *continuescan, int *ikey)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
 
    *continuescan = true;       /* default assumption */
 
    for (; *ikey < so->numberOfKeys; (*ikey)++)
    {
        ScanKey     key = so->keyData + *ikey;
        Datum       datum;
        bool        isNull;
        bool        requiredSameDir = false,
                    requiredOppositeDirOnly = false;
 
        /*
         * Check if the key is required in the current scan direction, in the
         * opposite scan direction _only_, or in neither direction (except
         * when we're forced to treat all scan keys as nonrequired)
         */
        if (forcenonrequired)
        {
            /* treating scan's keys as non-required */
        }
        else if (((key->sk_flags & SK_BT_REQFWD) && ScanDirectionIsForward(dir)) ||
                 ((key->sk_flags & SK_BT_REQBKWD) && ScanDirectionIsBackward(dir)))
            requiredSameDir = true;
        else if (((key->sk_flags & SK_BT_REQFWD) && ScanDirectionIsBackward(dir)) ||
                 ((key->sk_flags & SK_BT_REQBKWD) && ScanDirectionIsForward(dir)))
            requiredOppositeDirOnly = true;
 
        if (key->sk_attno > tupnatts)
        {
            /*
             * This attribute is truncated (must be high key).  The value for
             * this attribute in the first non-pivot tuple on the page to the
             * right could be any possible value.  Assume that truncated
             * attribute passes the qual.
             */
            Assert(BTreeTupleIsPivot(tuple));
            continue;
        }
 
        /*
         * A skip array scan key uses one of several sentinel values.  We just
         * fall back on _bt_tuple_before_array_skeys when we see such a value.
         */
        if (key->sk_flags & (SK_BT_MINVAL | SK_BT_MAXVAL |
                             SK_BT_NEXT | SK_BT_PRIOR))
        {
            Assert(key->sk_flags & SK_SEARCHARRAY);
            Assert(key->sk_flags & SK_BT_SKIP);
            Assert(requiredSameDir || forcenonrequired);
 
            /*
             * Cannot fall back on _bt_tuple_before_array_skeys when we're
             * treating the scan's keys as nonrequired, though.  Just handle
             * this like any other non-required equality-type array key.
             */
            if (forcenonrequired)
                return _bt_advance_array_keys(scan, NULL, tuple, tupnatts,
                                              tupdesc, *ikey, false);
 
            *continuescan = false;
            return false;
        }
 
        /* row-comparison keys need special processing */
        if (key->sk_flags & SK_ROW_HEADER)
        {
            if (_bt_check_rowcompare(key, tuple, tupnatts, tupdesc, dir,
                                     forcenonrequired, continuescan))
                continue;
            return false;
        }
 
        datum = index_getattr(tuple,
                              key->sk_attno,
                              tupdesc,
                              &isNull);
 
        if (key->sk_flags & SK_ISNULL)
        {
            /* Handle IS NULL/NOT NULL tests */
            if (key->sk_flags & SK_SEARCHNULL)
            {
                if (isNull)
                    continue;   /* tuple satisfies this qual */
            }
            else
            {
                Assert(key->sk_flags & SK_SEARCHNOTNULL);
                Assert(!(key->sk_flags & SK_BT_SKIP));
                if (!isNull)
                    continue;   /* tuple satisfies this qual */
            }
 
            /*
             * Tuple fails this qual.  If it's a required qual for the current
             * scan direction, then we can conclude no further tuples will
             * pass, either.
             */
            if (requiredSameDir)
                *continuescan = false;
            else if (unlikely(key->sk_flags & SK_BT_SKIP))
            {
                /*
                 * If we're treating scan keys as nonrequired, and encounter a
                 * skip array scan key whose current element is NULL, then it
                 * must be a non-range skip array.  It must be satisfied, so
                 * there's no need to call _bt_advance_array_keys to check.
                 */
                Assert(forcenonrequired && *ikey > 0);
                continue;
            }
 
            /*
             * This indextuple doesn't match the qual.
             */
            return false;
        }
 
        if (isNull)
        {
            /*
             * Scalar scan key isn't satisfied by NULL tuple value.
             *
             * If we're treating scan keys as nonrequired, and key is for a
             * skip array, then we must attempt to advance the array to NULL
             * (if we're successful then the tuple might match the qual).
             */
            if (unlikely(forcenonrequired && key->sk_flags & SK_BT_SKIP))
                return _bt_advance_array_keys(scan, NULL, tuple, tupnatts,
                                              tupdesc, *ikey, false);
 
            if (key->sk_flags & SK_BT_NULLS_FIRST)
            {
                /*
                 * Since NULLs are sorted before non-NULLs, we know we have
                 * reached the lower limit of the range of values for this
                 * index attr.  On a backward scan, we can stop if this qual
                 * is one of the "must match" subset.  We can stop regardless
                 * of whether the qual is > or <, so long as it's required,
                 * because it's not possible for any future tuples to pass. On
                 * a forward scan, however, we must keep going, because we may
                 * have initially positioned to the start of the index.
                 * (_bt_advance_array_keys also relies on this behavior during
                 * forward scans.)
                 */
                if ((requiredSameDir || requiredOppositeDirOnly) &&
                    ScanDirectionIsBackward(dir))
                    *continuescan = false;
            }
            else
            {
                /*
                 * Since NULLs are sorted after non-NULLs, we know we have
                 * reached the upper limit of the range of values for this
                 * index attr.  On a forward scan, we can stop if this qual is
                 * one of the "must match" subset.  We can stop regardless of
                 * whether the qual is > or <, so long as it's required,
                 * because it's not possible for any future tuples to pass. On
                 * a backward scan, however, we must keep going, because we
                 * may have initially positioned to the end of the index.
                 * (_bt_advance_array_keys also relies on this behavior during
                 * backward scans.)
                 */
                if ((requiredSameDir || requiredOppositeDirOnly) &&
                    ScanDirectionIsForward(dir))
                    *continuescan = false;
            }
 
            /*
             * This indextuple doesn't match the qual.
             */
            return false;
        }
 
        if (!DatumGetBool(FunctionCall2Coll(&key->sk_func, key->sk_collation,
                                            datum, key->sk_argument)))
        {
            /*
             * Tuple fails this qual.  If it's a required qual for the current
             * scan direction, then we can conclude no further tuples will
             * pass, either.
             */
            if (requiredSameDir)
                *continuescan = false;
 
            /*
             * If this is a non-required equality-type array key, the tuple
             * needs to be checked against every possible array key.  Handle
             * this by "advancing" the scan key's array to a matching value
             * (if we're successful then the tuple might match the qual).
             */
            else if (advancenonrequired &&
                     key->sk_strategy == BTEqualStrategyNumber &&
                     (key->sk_flags & SK_SEARCHARRAY))
                return _bt_advance_array_keys(scan, NULL, tuple, tupnatts,
                                              tupdesc, *ikey, false);
 
            /*
             * This indextuple doesn't match the qual.
             */
            return false;
        }
    }
 
    /* If we get here, the tuple passes all index quals. */
    return true;
}
 
/*
 * Test whether an indextuple satisfies a row-comparison scan condition.
 *
 * Return true if so, false if not.  If not, also clear *continuescan if
 * it's not possible for any future tuples in the current scan direction
 * to pass the qual.
 *
 * This is a subroutine for _bt_checkkeys/_bt_check_compare.  Caller passes us
 * a row compare header key taken from so->keyData[].
 *
 * Row value comparisons can be described in terms of logical expansions that
 * use only scalar operators.  Consider the following example row comparison:
 *
 * "(a, b, c) > (7, 'bar', 62)"
 *
 * This can be evaluated as:
 *
 * "(a = 7 AND b = 'bar' AND c > 62) OR (a = 7 AND b > 'bar') OR (a > 7)".
 *
 * Notice that this condition is satisfied by _all_ rows that satisfy "a > 7",
 * and by a subset of all rows that satisfy "a >= 7" (possibly all such rows).
 * It _can't_ be satisfied by other rows (where "a < 7" or where "a IS NULL").
 * A row comparison header key can therefore often be treated as if it was a
 * simple scalar inequality on the row compare's most significant column.
 * (For example, _bt_advance_array_keys and most preprocessing routines treat
 * row compares like any other same-strategy inequality on the same column.)
 *
 * Things get more complicated for our row compare given a row where "a = 7".
 * Note that a row compare isn't necessarily satisfied by _every_ tuple that
 * appears between the first and last satisfied tuple returned by the scan,
 * due to the way that its lower-order subkeys are only conditionally applied.
 * A forwards scan that uses our example qual might initially return a tuple
 * "(a, b, c) = (7, 'zebra', 54)".  But it won't subsequently return a tuple
 * "(a, b, c) = (7, NULL, 1)" located to the right of the first matching tuple
 * (assume that "b" was declared NULLS LAST here).  The scan will only return
 * additional matches upon reaching tuples where "a > 7".  If you rereview our
 * example row comparison's logical expansion, you'll understand why this is.
 * (Here we assume that all subkeys could be marked required, guaranteeing
 * that row comparison order matches index order.  This is the common case.)
 *
 * Note that a row comparison header key behaves _exactly_ the same as a
 * similar scalar inequality key on the row's most significant column once the
 * scan reaches the point where it no longer needs to evaluate lower-order
 * subkeys (or before the point where it starts needing to evaluate them).
 * For example, once a forwards scan that uses our example qual reaches the
 * first tuple "a > 7", we'll behave in just the same way as our caller would
 * behave with a similar scalar inequality "a > 7" for the remainder of the
 * scan (assuming that the scan never changes direction/never goes backwards).
 * We'll even set continuescan=false according to exactly the same rules as
 * the ones our caller applies with simple scalar inequalities, including the
 * rules it applies when NULL tuple values don't satisfy an inequality qual.
 */
static bool
_bt_check_rowcompare(ScanKey header, IndexTuple tuple, int tupnatts,
                     TupleDesc tupdesc, ScanDirection dir,
                     bool forcenonrequired, bool *continuescan)
{
    ScanKey     subkey = (ScanKey) DatumGetPointer(header->sk_argument);
    int32       cmpresult = 0;
    bool        result;
 
    /* First subkey should be same as the header says */
    Assert(header->sk_flags & SK_ROW_HEADER);
    Assert(subkey->sk_attno == header->sk_attno);
    Assert(subkey->sk_strategy == header->sk_strategy);
 
    /* Loop over columns of the row condition */
    for (;;)
    {
        Datum       datum;
        bool        isNull;
 
        Assert(subkey->sk_flags & SK_ROW_MEMBER);
 
        /* When a NULL row member is compared, the row never matches */
        if (subkey->sk_flags & SK_ISNULL)
        {
            /*
             * Unlike the simple-scankey case, this isn't a disallowed case
             * (except when it's the first row element that has the NULL arg).
             * But it can never match.  If all the earlier row comparison
             * columns are required for the scan direction, we can stop the
             * scan, because there can't be another tuple that will succeed.
             */
            Assert(subkey != (ScanKey) DatumGetPointer(header->sk_argument));
            subkey--;
            if (forcenonrequired)
            {
                /* treating scan's keys as non-required */
            }
            else if ((subkey->sk_flags & SK_BT_REQFWD) &&
                     ScanDirectionIsForward(dir))
                *continuescan = false;
            else if ((subkey->sk_flags & SK_BT_REQBKWD) &&
                     ScanDirectionIsBackward(dir))
                *continuescan = false;
            return false;
        }
 
        if (subkey->sk_attno > tupnatts)
        {
            /*
             * This attribute is truncated (must be high key).  The value for
             * this attribute in the first non-pivot tuple on the page to the
             * right could be any possible value.  Assume that truncated
             * attribute passes the qual.
             */
            Assert(BTreeTupleIsPivot(tuple));
            return true;
        }
 
        datum = index_getattr(tuple,
                              subkey->sk_attno,
                              tupdesc,
                              &isNull);
 
        if (isNull)
        {
            int         reqflags;
 
            if (forcenonrequired)
            {
                /* treating scan's keys as non-required */
            }
            else if (subkey->sk_flags & SK_BT_NULLS_FIRST)
            {
                /*
                 * Since NULLs are sorted before non-NULLs, we know we have
                 * reached the lower limit of the range of values for this
                 * index attr.  On a backward scan, we can stop if this qual
                 * is one of the "must match" subset.  However, on a forwards
                 * scan, we must keep going, because we may have initially
                 * positioned to the start of the index.
                 *
                 * All required NULLS FIRST > row members can use NULL tuple
                 * values to end backwards scans, just like with other values.
                 * A qual "WHERE (a, b, c) > (9, 42, 'foo')" can terminate a
                 * backwards scan upon reaching the index's rightmost "a = 9"
                 * tuple whose "b" column contains a NULL (if not sooner).
                 * Since "b" is NULLS FIRST, we can treat its NULLs as "<" 42.
                 */
                reqflags = SK_BT_REQBKWD;
 
                /*
                 * When a most significant required NULLS FIRST < row compare
                 * member sees NULL tuple values during a backwards scan, it
                 * signals the end of matches for the whole row compare/scan.
                 * A qual "WHERE (a, b, c) < (9, 42, 'foo')" will terminate a
                 * backwards scan upon reaching the rightmost tuple whose "a"
                 * column has a NULL.  The "a" NULL value is "<" 9, and yet
                 * our < row compare will still end the scan.  (This isn't
                 * safe with later/lower-order row members.  Notice that it
                 * can only happen with an "a" NULL some time after the scan
                 * completely stops needing to use its "b" and "c" members.)
                 */
                if (subkey == (ScanKey) DatumGetPointer(header->sk_argument))
                    reqflags |= SK_BT_REQFWD;   /* safe, first row member */
 
                if ((subkey->sk_flags & reqflags) &&
                    ScanDirectionIsBackward(dir))
                    *continuescan = false;
            }
            else
            {
                /*
                 * Since NULLs are sorted after non-NULLs, we know we have
                 * reached the upper limit of the range of values for this
                 * index attr.  On a forward scan, we can stop if this qual is
                 * one of the "must match" subset.  However, on a backward
                 * scan, we must keep going, because we may have initially
                 * positioned to the end of the index.
                 *
                 * All required NULLS LAST < row members can use NULL tuple
                 * values to end forwards scans, just like with other values.
                 * A qual "WHERE (a, b, c) < (9, 42, 'foo')" can terminate a
                 * forwards scan upon reaching the index's leftmost "a = 9"
                 * tuple whose "b" column contains a NULL (if not sooner).
                 * Since "b" is NULLS LAST, we can treat its NULLs as ">" 42.
                 */
                reqflags = SK_BT_REQFWD;
 
                /*
                 * When a most significant required NULLS LAST > row compare
                 * member sees NULL tuple values during a forwards scan, it
                 * signals the end of matches for the whole row compare/scan.
                 * A qual "WHERE (a, b, c) > (9, 42, 'foo')" will terminate a
                 * forwards scan upon reaching the leftmost tuple whose "a"
                 * column has a NULL.  The "a" NULL value is ">" 9, and yet
                 * our > row compare will end the scan.  (This isn't safe with
                 * later/lower-order row members.  Notice that it can only
                 * happen with an "a" NULL some time after the scan completely
                 * stops needing to use its "b" and "c" members.)
                 */
                if (subkey == (ScanKey) DatumGetPointer(header->sk_argument))
                    reqflags |= SK_BT_REQBKWD;  /* safe, first row member */
 
                if ((subkey->sk_flags & reqflags) &&
                    ScanDirectionIsForward(dir))
                    *continuescan = false;
            }
 
            /*
             * In any case, this indextuple doesn't match the qual.
             */
            return false;
        }
 
        /* Perform the test --- three-way comparison not bool operator */
        cmpresult = DatumGetInt32(FunctionCall2Coll(&subkey->sk_func,
                                                    subkey->sk_collation,
                                                    datum,
                                                    subkey->sk_argument));
 
        if (subkey->sk_flags & SK_BT_DESC)
            INVERT_COMPARE_RESULT(cmpresult);
 
        /* Done comparing if unequal, else advance to next column */
        if (cmpresult != 0)
            break;
 
        if (subkey->sk_flags & SK_ROW_END)
            break;
        subkey++;
    }
 
    /* Final subkey/column determines if row compare is satisfied */
    result = _bt_rowcompare_cmpresult(subkey, cmpresult);
 
    if (!result && !forcenonrequired)
    {
        /*
         * Tuple fails this qual.  If it's a required qual for the current
         * scan direction, then we can conclude no further tuples will pass,
         * either.  Note we have to look at the deciding column, not
         * necessarily the first or last column of the row condition.
         */
        if ((subkey->sk_flags & SK_BT_REQFWD) &&
            ScanDirectionIsForward(dir))
            *continuescan = false;
        else if ((subkey->sk_flags & SK_BT_REQBKWD) &&
                 ScanDirectionIsBackward(dir))
            *continuescan = false;
    }
 
    return result;
}
 
/*
 * Call here when a row compare member returns a non-zero result, or with the
 * result for the final ROW_END row compare member (no matter the cmpresult).
 *
 * cmpresult indicates the overall result of the row comparison (must already
 * be commuted for DESC subkeys), and subkey is the deciding row member.
 */
static bool
_bt_rowcompare_cmpresult(ScanKey subkey, int cmpresult)
{
    bool        satisfied;
 
    Assert(subkey->sk_flags & SK_ROW_MEMBER);
 
    switch (subkey->sk_strategy)
    {
        case BTLessStrategyNumber:
            satisfied = (cmpresult < 0);
            break;
        case BTLessEqualStrategyNumber:
            satisfied = (cmpresult <= 0);
            break;
        case BTGreaterEqualStrategyNumber:
            satisfied = (cmpresult >= 0);
            break;
        case BTGreaterStrategyNumber:
            satisfied = (cmpresult > 0);
            break;
        default:
            /* EQ and NE cases aren't allowed here */
            elog(ERROR, "unexpected strategy number %d", subkey->sk_strategy);
            satisfied = false;  /* keep compiler quiet */
            break;
    }
 
    return satisfied;
}
 
/*
 * _bt_tuple_before_array_skeys() -- too early to advance required arrays?
 *
 * We always compare the tuple using the current array keys (which we assume
 * are already set in so->keyData[]).  readpagetup indicates if tuple is the
 * scan's current _bt_readpage-wise tuple.
 *
 * readpagetup callers must only call here when _bt_check_compare already set
 * continuescan=false.  We help these callers deal with _bt_check_compare's
 * inability to distinguish between the < and > cases (it uses equality
 * operator scan keys, whereas we use 3-way ORDER procs).  These callers pass
 * a _bt_check_compare-set sktrig value that indicates which scan key
 * triggered the call (!readpagetup callers just pass us sktrig=0 instead).
 * This information allows us to avoid wastefully checking earlier scan keys
 * that were already deemed to have been satisfied inside _bt_check_compare.
 *
 * Returns false when caller's tuple is >= the current required equality scan
 * keys (or <=, in the case of backwards scans).  This happens to readpagetup
 * callers when the scan has reached the point of needing its array keys
 * advanced; caller will need to advance required and non-required arrays at
 * scan key offsets >= sktrig, plus scan keys < sktrig iff sktrig rolls over.
 * (When we return false to readpagetup callers, tuple can only be == current
 * required equality scan keys when caller's sktrig indicates that the arrays
 * need to be advanced due to an unsatisfied required inequality key trigger.)
 *
 * Returns true when caller passes a tuple that is < the current set of
 * equality keys for the most significant non-equal required scan key/column
 * (or > the keys, during backwards scans).  This happens to readpagetup
 * callers when tuple is still before the start of matches for the scan's
 * required equality strategy scan keys.  (sktrig can't have indicated that an
 * inequality strategy scan key wasn't satisfied in _bt_check_compare when we
 * return true.  In fact, we automatically return false when passed such an
 * inequality sktrig by readpagetup callers -- _bt_check_compare's initial
 * continuescan=false doesn't really need to be confirmed here by us.)
 *
 * !readpagetup callers optionally pass us *scanBehind, which tracks whether
 * any missing truncated attributes might have affected array advancement
 * (compared to what would happen if it was shown the first non-pivot tuple on
 * the page to the right of caller's finaltup/high key tuple instead).  It's
 * only possible that we'll set *scanBehind to true when caller passes us a
 * pivot tuple (with truncated -inf attributes) that we return false for.
 */
static bool
_bt_tuple_before_array_skeys(IndexScanDesc scan, ScanDirection dir,
                             IndexTuple tuple, TupleDesc tupdesc, int tupnatts,
                             bool readpagetup, int sktrig, bool *scanBehind)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
 
    Assert(so->numArrayKeys);
    Assert(so->numberOfKeys);
    Assert(sktrig == 0 || readpagetup);
    Assert(!readpagetup || scanBehind == NULL);
 
    if (scanBehind)
        *scanBehind = false;
 
    for (int ikey = sktrig; ikey < so->numberOfKeys; ikey++)
    {
        ScanKey     cur = so->keyData + ikey;
        Datum       tupdatum;
        bool        tupnull;
        int32       result;
 
        /* readpagetup calls require one ORDER proc comparison (at most) */
        Assert(!readpagetup || ikey == sktrig);
 
        /*
         * Once we reach a non-required scan key, we're completely done.
         *
         * Note: we deliberately don't consider the scan direction here.
         * _bt_advance_array_keys caller requires that we track *scanBehind
         * without concern for scan direction.
         */
        if ((cur->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD)) == 0)
        {
            Assert(!readpagetup);
            Assert(ikey > sktrig || ikey == 0);
            return false;
        }
 
        if (cur->sk_attno > tupnatts)
        {
            Assert(!readpagetup);
 
            /*
             * When we reach a high key's truncated attribute, assume that the
             * tuple attribute's value is >= the scan's equality constraint
             * scan keys (but set *scanBehind to let interested callers know
             * that a truncated attribute might have affected our answer).
             */
            if (scanBehind)
                *scanBehind = true;
 
            return false;
        }
 
        /*
         * Deal with inequality strategy scan keys that _bt_check_compare set
         * continuescan=false for
         */
        if (cur->sk_strategy != BTEqualStrategyNumber)
        {
            /*
             * When _bt_check_compare indicated that a required inequality
             * scan key wasn't satisfied, there's no need to verify anything;
             * caller always calls _bt_advance_array_keys with this sktrig.
             */
            if (readpagetup)
                return false;
 
            /*
             * Otherwise we can't give up, since we must check all required
             * scan keys (required in either direction) in order to correctly
             * track *scanBehind for caller
             */
            continue;
        }
 
        tupdatum = index_getattr(tuple, cur->sk_attno, tupdesc, &tupnull);
 
        if (likely(!(cur->sk_flags & (SK_BT_MINVAL | SK_BT_MAXVAL))))
        {
            /* Scankey has a valid/comparable sk_argument value */
            result = _bt_compare_array_skey(&so->orderProcs[ikey],
                                            tupdatum, tupnull,
                                            cur->sk_argument, cur);
 
            if (result == 0)
            {
                /*
                 * Interpret result in a way that takes NEXT/PRIOR into
                 * account
                 */
                if (cur->sk_flags & SK_BT_NEXT)
                    result = -1;
                else if (cur->sk_flags & SK_BT_PRIOR)
                    result = 1;
 
                Assert(result == 0 || (cur->sk_flags & SK_BT_SKIP));
            }
        }
        else
        {
            BTArrayKeyInfo *array = NULL;
 
            /*
             * Current array element/array = scan key value is a sentinel
             * value that represents the lowest (or highest) possible value
             * that's still within the range of the array.
             *
             * Like _bt_first, we only see MINVAL keys during forwards scans
             * (and similarly only see MAXVAL keys during backwards scans).
             * Even if the scan's direction changes, we'll stop at some higher
             * order key before we can ever reach any MAXVAL (or MINVAL) keys.
             * (However, unlike _bt_first we _can_ get to keys marked either
             * NEXT or PRIOR, regardless of the scan's current direction.)
             */
            Assert(ScanDirectionIsForward(dir) ?
                   !(cur->sk_flags & SK_BT_MAXVAL) :
                   !(cur->sk_flags & SK_BT_MINVAL));
 
            /*
             * There are no valid sk_argument values in MINVAL/MAXVAL keys.
             * Check if tupdatum is within the range of skip array instead.
             */
            for (int arrayidx = 0; arrayidx < so->numArrayKeys; arrayidx++)
            {
                array = &so->arrayKeys[arrayidx];
                if (array->scan_key == ikey)
                    break;
            }
 
            _bt_binsrch_skiparray_skey(false, dir, tupdatum, tupnull,
                                       array, cur, &result);
 
            if (result == 0)
            {
                /*
                 * tupdatum satisfies both low_compare and high_compare, so
                 * it's time to advance the array keys.
                 *
                 * Note: It's possible that the skip array will "advance" from
                 * its MINVAL (or MAXVAL) representation to an alternative,
                 * logically equivalent representation of the same value: a
                 * representation where the = key gets a valid datum in its
                 * sk_argument.  This is only possible when low_compare uses
                 * the >= strategy (or high_compare uses the <= strategy).
                 */
                return false;
            }
        }
 
        /*
         * Does this comparison indicate that caller must _not_ advance the
         * scan's arrays just yet?
         */
        if ((ScanDirectionIsForward(dir) && result < 0) ||
            (ScanDirectionIsBackward(dir) && result > 0))
            return true;
 
        /*
         * Does this comparison indicate that caller should now advance the
         * scan's arrays?  (Must be if we get here during a readpagetup call.)
         */
        if (readpagetup || result != 0)
        {
            Assert(result != 0);
            return false;
        }
 
        /*
         * Inconclusive -- need to check later scan keys, too.
         *
         * This must be a finaltup precheck, or a call made from an assertion.
         */
        Assert(result == 0);
    }
 
    Assert(!readpagetup);
 
    return false;
}
 
/*
 * Determine if a scan with array keys should skip over uninteresting tuples.
 *
 * This is a subroutine for _bt_checkkeys.  Called when _bt_readpage's linear
 * search process (started after it finishes reading an initial group of
 * matching tuples, used to locate the start of the next group of tuples
 * matching the next set of required array keys) has already scanned an
 * excessive number of tuples whose key space is "between arrays".
 *
 * When we perform look ahead successfully, we'll sets pstate.skip, which
 * instructs _bt_readpage to skip ahead to that tuple next (could be past the
 * end of the scan's leaf page).  Pages where the optimization is effective
 * will generally still need to skip several times.  Each call here performs
 * only a single "look ahead" comparison of a later tuple, whose distance from
 * the current tuple's offset number is determined by applying heuristics.
 */
static void
_bt_checkkeys_look_ahead(IndexScanDesc scan, BTReadPageState *pstate,
                         int tupnatts, TupleDesc tupdesc)
{
    ScanDirection dir = pstate->dir;
    OffsetNumber aheadoffnum;
    IndexTuple  ahead;
 
    Assert(!pstate->forcenonrequired);
 
    /* Avoid looking ahead when comparing the page high key */
    if (pstate->offnum < pstate->minoff)
        return;
 
    /*
     * Don't look ahead when there aren't enough tuples remaining on the page
     * (in the current scan direction) for it to be worth our while
     */
    if (ScanDirectionIsForward(dir) &&
        pstate->offnum >= pstate->maxoff - LOOK_AHEAD_DEFAULT_DISTANCE)
        return;
    else if (ScanDirectionIsBackward(dir) &&
             pstate->offnum <= pstate->minoff + LOOK_AHEAD_DEFAULT_DISTANCE)
        return;
 
    /*
     * The look ahead distance starts small, and ramps up as each call here
     * allows _bt_readpage to skip over more tuples
     */
    if (!pstate->targetdistance)
        pstate->targetdistance = LOOK_AHEAD_DEFAULT_DISTANCE;
    else if (pstate->targetdistance < MaxIndexTuplesPerPage / 2)
        pstate->targetdistance *= 2;
 
    /* Don't read past the end (or before the start) of the page, though */
    if (ScanDirectionIsForward(dir))
        aheadoffnum = Min((int) pstate->maxoff,
                          (int) pstate->offnum + pstate->targetdistance);
    else
        aheadoffnum = Max((int) pstate->minoff,
                          (int) pstate->offnum - pstate->targetdistance);
 
    ahead = (IndexTuple) PageGetItem(pstate->page,
                                     PageGetItemId(pstate->page, aheadoffnum));
    if (_bt_tuple_before_array_skeys(scan, dir, ahead, tupdesc, tupnatts,
                                     false, 0, NULL))
    {
        /*
         * Success -- instruct _bt_readpage to skip ahead to very next tuple
         * after the one we determined was still before the current array keys
         */
        if (ScanDirectionIsForward(dir))
            pstate->skip = aheadoffnum + 1;
        else
            pstate->skip = aheadoffnum - 1;
    }
    else
    {
        /*
         * Failure -- "ahead" tuple is too far ahead (we were too aggressive).
         *
         * Reset the number of rechecks, and aggressively reduce the target
         * distance (we're much more aggressive here than we were when the
         * distance was initially ramped up).
         */
        pstate->rechecks = 0;
        pstate->targetdistance = Max(pstate->targetdistance / 8, 1);
    }
}
 
/*
 * _bt_advance_array_keys() -- Advance array elements using a tuple
 *
 * The scan always gets a new qual as a consequence of calling here (except
 * when we determine that the top-level scan has run out of matching tuples).
 * All later _bt_check_compare calls also use the same new qual that was first
 * used here (at least until the next call here advances the keys once again).
 * It's convenient to structure _bt_check_compare rechecks of caller's tuple
 * (using the new qual) as one the steps of advancing the scan's array keys,
 * so this function works as a wrapper around _bt_check_compare.
 *
 * Like _bt_check_compare, we'll set pstate.continuescan on behalf of the
 * caller, and return a boolean indicating if caller's tuple satisfies the
 * scan's new qual.  But unlike _bt_check_compare, we set so->needPrimScan
 * when we set continuescan=false, indicating if a new primitive index scan
 * has been scheduled (otherwise, the top-level scan has run out of tuples in
 * the current scan direction).
 *
 * Caller must use _bt_tuple_before_array_skeys to determine if the current
 * place in the scan is >= the current array keys _before_ calling here.
 * We're responsible for ensuring that caller's tuple is <= the newly advanced
 * required array keys once we return.  We try to find an exact match, but
 * failing that we'll advance the array keys to whatever set of array elements
 * comes next in the key space for the current scan direction.  Required array
 * keys "ratchet forwards" (or backwards).  They can only advance as the scan
 * itself advances through the index/key space.
 *
 * (The rules are the same for backwards scans, except that the operators are
 * flipped: just replace the precondition's >= operator with a <=, and the
 * postcondition's <= operator with a >=.  In other words, just swap the
 * precondition with the postcondition.)
 *
 * We also deal with "advancing" non-required arrays here (or arrays that are
 * treated as non-required for the duration of a _bt_readpage call).  Callers
 * whose sktrig scan key is non-required specify sktrig_required=false.  These
 * calls are the only exception to the general rule about always advancing the
 * required array keys (the scan may not even have a required array).  These
 * callers should just pass a NULL pstate (since there is never any question
 * of stopping the scan).  No call to _bt_tuple_before_array_skeys is required
 * ahead of these calls (it's already clear that any required scan keys must
 * be satisfied by caller's tuple).
 *
 * Note that we deal with non-array required equality strategy scan keys as
 * degenerate single element arrays here.  Obviously, they can never really
 * advance in the way that real arrays can, but they must still affect how we
 * advance real array scan keys (exactly like true array equality scan keys).
 * We have to keep around a 3-way ORDER proc for these (using the "=" operator
 * won't do), since in general whether the tuple is < or > _any_ unsatisfied
 * required equality key influences how the scan's real arrays must advance.
 *
 * Note also that we may sometimes need to advance the array keys when the
 * existing required array keys (and other required equality keys) are already
 * an exact match for every corresponding value from caller's tuple.  We must
 * do this for inequalities that _bt_check_compare set continuescan=false for.
 * They'll advance the array keys here, just like any other scan key that
 * _bt_check_compare stops on.  (This can even happen _after_ we advance the
 * array keys, in which case we'll advance the array keys a second time.  That
 * way _bt_checkkeys caller always has its required arrays advance to the
 * maximum possible extent that its tuple will allow.)
 */
static bool
_bt_advance_array_keys(IndexScanDesc scan, BTReadPageState *pstate,
                       IndexTuple tuple, int tupnatts, TupleDesc tupdesc,
                       int sktrig, bool sktrig_required)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    Relation    rel = scan->indexRelation;
    ScanDirection dir = pstate ? pstate->dir : ForwardScanDirection;
    int         arrayidx = 0;
    bool        beyond_end_advance = false,
                skip_array_advanced = false,
                has_required_opposite_direction_only = false,
                all_required_satisfied = true,
                all_satisfied = true;
 
    Assert(!so->needPrimScan && !so->scanBehind && !so->oppositeDirCheck);
    Assert(_bt_verify_keys_with_arraykeys(scan));
 
    if (sktrig_required)
    {
        /*
         * Precondition array state assertion
         */
        Assert(!_bt_tuple_before_array_skeys(scan, dir, tuple, tupdesc,
                                             tupnatts, false, 0, NULL));
 
        /*
         * Once we return we'll have a new set of required array keys, so
         * reset state used by "look ahead" optimization
         */
        pstate->rechecks = 0;
        pstate->targetdistance = 0;
    }
    else if (sktrig < so->numberOfKeys - 1 &&
             !(so->keyData[so->numberOfKeys - 1].sk_flags & SK_SEARCHARRAY))
    {
        int         least_sign_ikey = so->numberOfKeys - 1;
        bool        continuescan;
 
        /*
         * Optimization: perform a precheck of the least significant key
         * during !sktrig_required calls when it isn't already our sktrig
         * (provided the precheck key is not itself an array).
         *
         * When the precheck works out we'll avoid an expensive binary search
         * of sktrig's array (plus any other arrays before least_sign_ikey).
         */
        Assert(so->keyData[sktrig].sk_flags & SK_SEARCHARRAY);
        if (!_bt_check_compare(scan, dir, tuple, tupnatts, tupdesc, false,
                               false, &continuescan,
                               &least_sign_ikey))
            return false;
    }
 
    for (int ikey = 0; ikey < so->numberOfKeys; ikey++)
    {
        ScanKey     cur = so->keyData + ikey;
        BTArrayKeyInfo *array = NULL;
        Datum       tupdatum;
        bool        required = false,
                    tupnull;
        int32       result;
        int         set_elem = 0;
 
        if (cur->sk_strategy == BTEqualStrategyNumber)
        {
            /* Manage array state */
            if (cur->sk_flags & SK_SEARCHARRAY)
            {
                array = &so->arrayKeys[arrayidx++];
                Assert(array->scan_key == ikey);
            }
        }
        else
        {
            /*
             * Are any inequalities required in the opposite direction only
             * present here?
             */
            if (((ScanDirectionIsForward(dir) &&
                  (cur->sk_flags & (SK_BT_REQBKWD))) ||
                 (ScanDirectionIsBackward(dir) &&
                  (cur->sk_flags & (SK_BT_REQFWD)))))
                has_required_opposite_direction_only = true;
        }
 
        /* Optimization: skip over known-satisfied scan keys */
        if (ikey < sktrig)
            continue;
 
        if (cur->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD))
        {
            required = true;
 
            if (cur->sk_attno > tupnatts)
            {
                /* Set this just like _bt_tuple_before_array_skeys */
                Assert(sktrig < ikey);
                so->scanBehind = true;
            }
        }
 
        /*
         * Handle a required non-array scan key that the initial call to
         * _bt_check_compare indicated triggered array advancement, if any.
         *
         * The non-array scan key's strategy will be <, <=, or = during a
         * forwards scan (or any one of =, >=, or > during a backwards scan).
         * It follows that the corresponding tuple attribute's value must now
         * be either > or >= the scan key value (for backwards scans it must
         * be either < or <= that value).
         *
         * If this is a required equality strategy scan key, this is just an
         * optimization; _bt_tuple_before_array_skeys already confirmed that
         * this scan key places us ahead of caller's tuple.  There's no need
         * to repeat that work now.  (The same underlying principle also gets
         * applied by the cur_elem_trig optimization used to speed up searches
         * for the next array element.)
         *
         * If this is a required inequality strategy scan key, we _must_ rely
         * on _bt_check_compare like this; we aren't capable of directly
         * evaluating required inequality strategy scan keys here, on our own.
         */
        if (ikey == sktrig && !array)
        {
            Assert(sktrig_required && required && all_required_satisfied);
 
            /* Use "beyond end" advancement.  See below for an explanation. */
            beyond_end_advance = true;
            all_satisfied = all_required_satisfied = false;
 
            continue;
        }
 
        /*
         * Nothing more for us to do with an inequality strategy scan key that
         * wasn't the one that _bt_check_compare stopped on, though.
         *
         * Note: if our later call to _bt_check_compare (to recheck caller's
         * tuple) sets continuescan=false due to finding this same inequality
         * unsatisfied (possible when it's required in the scan direction),
         * we'll deal with it via a recursive "second pass" call.
         */
        else if (cur->sk_strategy != BTEqualStrategyNumber)
            continue;
 
        /*
         * Nothing for us to do with an equality strategy scan key that isn't
         * marked required, either -- unless it's a non-required array
         */
        else if (!required && !array)
            continue;
 
        /*
         * Here we perform steps for all array scan keys after a required
         * array scan key whose binary search triggered "beyond end of array
         * element" array advancement due to encountering a tuple attribute
         * value > the closest matching array key (or < for backwards scans).
         */
        if (beyond_end_advance)
        {
            if (array)
                _bt_array_set_low_or_high(rel, cur, array,
                                          ScanDirectionIsBackward(dir));
 
            continue;
        }
 
        /*
         * Here we perform steps for all array scan keys after a required
         * array scan key whose tuple attribute was < the closest matching
         * array key when we dealt with it (or > for backwards scans).
         *
         * This earlier required array key already puts us ahead of caller's
         * tuple in the key space (for the current scan direction).  We must
         * make sure that subsequent lower-order array keys do not put us too
         * far ahead (ahead of tuples that have yet to be seen by our caller).
         * For example, when a tuple "(a, b) = (42, 5)" advances the array
         * keys on "a" from 40 to 45, we must also set "b" to whatever the
         * first array element for "b" is.  It would be wrong to allow "b" to
         * be set based on the tuple value.
         *
         * Perform the same steps with truncated high key attributes.  You can
         * think of this as a "binary search" for the element closest to the
         * value -inf.  Again, the arrays must never get ahead of the scan.
         */
        if (!all_required_satisfied || cur->sk_attno > tupnatts)
        {
            if (array)
                _bt_array_set_low_or_high(rel, cur, array,
                                          ScanDirectionIsForward(dir));
 
            continue;
        }
 
        /*
         * Search in scankey's array for the corresponding tuple attribute
         * value from caller's tuple
         */
        tupdatum = index_getattr(tuple, cur->sk_attno, tupdesc, &tupnull);
 
        if (array)
        {
            bool        cur_elem_trig = (sktrig_required && ikey == sktrig);
 
            /*
             * "Binary search" by checking if tupdatum/tupnull are within the
             * range of the skip array
             */
            if (array->num_elems == -1)
                _bt_binsrch_skiparray_skey(cur_elem_trig, dir,
                                           tupdatum, tupnull, array, cur,
                                           &result);
 
            /*
             * Binary search for the closest match from the SAOP array
             */
            else
                set_elem = _bt_binsrch_array_skey(&so->orderProcs[ikey],
                                                  cur_elem_trig, dir,
                                                  tupdatum, tupnull, array, cur,
                                                  &result);
        }
        else
        {
            Assert(required);
 
            /*
             * This is a required non-array equality strategy scan key, which
             * we'll treat as a degenerate single element array.
             *
             * This scan key's imaginary "array" can't really advance, but it
             * can still roll over like any other array.  (Actually, this is
             * no different to real single value arrays, which never advance
             * without rolling over -- they can never truly advance, either.)
             */
            result = _bt_compare_array_skey(&so->orderProcs[ikey],
                                            tupdatum, tupnull,
                                            cur->sk_argument, cur);
        }
 
        /*
         * Consider "beyond end of array element" array advancement.
         *
         * When the tuple attribute value is > the closest matching array key
         * (or < in the backwards scan case), we need to ratchet this array
         * forward (backward) by one increment, so that caller's tuple ends up
         * being < final array value instead (or > final array value instead).
         * This process has to work for all of the arrays, not just this one:
         * it must "carry" to higher-order arrays when the set_elem that we
         * just found happens to be the final one for the scan's direction.
         * Incrementing (decrementing) set_elem itself isn't good enough.
         *
         * Our approach is to provisionally use set_elem as if it was an exact
         * match now, then set each later/less significant array to whatever
         * its final element is.  Once outside the loop we'll then "increment
         * this array's set_elem" by calling _bt_advance_array_keys_increment.
         * That way the process rolls over to higher order arrays as needed.
         *
         * Under this scheme any required arrays only ever ratchet forwards
         * (or backwards), and always do so to the maximum possible extent
         * that we can know will be safe without seeing the scan's next tuple.
         * We don't need any special handling for required scan keys that lack
         * a real array to advance, nor for redundant scan keys that couldn't
         * be eliminated by _bt_preprocess_keys.  It won't matter if some of
         * our "true" array scan keys (or even all of them) are non-required.
         */
        if (sktrig_required && required &&
            ((ScanDirectionIsForward(dir) && result > 0) ||
             (ScanDirectionIsBackward(dir) && result < 0)))
            beyond_end_advance = true;
 
        Assert(all_required_satisfied && all_satisfied);
        if (result != 0)
        {
            /*
             * Track whether caller's tuple satisfies our new post-advancement
             * qual, for required scan keys, as well as for the entire set of
             * interesting scan keys (all required scan keys plus non-required
             * array scan keys are considered interesting.)
             */
            all_satisfied = false;
            if (sktrig_required && required)
                all_required_satisfied = false;
            else
            {
                /*
                 * There's no need to advance the arrays using the best
                 * available match for a non-required array.  Give up now.
                 * (Though note that sktrig_required calls still have to do
                 * all the usual post-advancement steps, including the recheck
                 * call to _bt_check_compare.)
                 */
                break;
            }
        }
 
        /* Advance array keys, even when we don't have an exact match */
        if (array)
        {
            if (array->num_elems == -1)
            {
                /* Skip array's new element is tupdatum (or MINVAL/MAXVAL) */
                _bt_skiparray_set_element(rel, cur, array, result,
                                          tupdatum, tupnull);
                skip_array_advanced = true;
            }
            else if (array->cur_elem != set_elem)
            {
                /* SAOP array's new element is set_elem datum */
                array->cur_elem = set_elem;
                cur->sk_argument = array->elem_values[set_elem];
            }
        }
    }
 
    /*
     * Advance the array keys incrementally whenever "beyond end of array
     * element" array advancement happens, so that advancement will carry to
     * higher-order arrays (might exhaust all the scan's arrays instead, which
     * ends the top-level scan).
     */
    if (beyond_end_advance &&
        !_bt_advance_array_keys_increment(scan, dir, &skip_array_advanced))
        goto end_toplevel_scan;
 
    Assert(_bt_verify_keys_with_arraykeys(scan));
 
    /*
     * Maintain a page-level count of the number of times the scan's array
     * keys advanced in a way that affected at least one skip array
     */
    if (sktrig_required && skip_array_advanced)
        pstate->nskipadvances++;
 
    /*
     * Does tuple now satisfy our new qual?  Recheck with _bt_check_compare.
     *
     * Calls triggered by an unsatisfied required scan key, whose tuple now
     * satisfies all required scan keys, but not all nonrequired array keys,
     * will still require a recheck call to _bt_check_compare.  They'll still
     * need its "second pass" handling of required inequality scan keys.
     * (Might have missed a still-unsatisfied required inequality scan key
     * that caller didn't detect as the sktrig scan key during its initial
     * _bt_check_compare call that used the old/original qual.)
     *
     * Calls triggered by an unsatisfied nonrequired array scan key never need
     * "second pass" handling of required inequalities (nor any other handling
     * of any required scan key).  All that matters is whether caller's tuple
     * satisfies the new qual, so it's safe to just skip the _bt_check_compare
     * recheck when we've already determined that it can only return 'false'.
     *
     * Note: In practice most scan keys are marked required by preprocessing,
     * if necessary by generating a preceding skip array.  We nevertheless
     * often handle array keys marked required as if they were nonrequired.
     * This behavior is requested by our _bt_check_compare caller, though only
     * when it is passed "forcenonrequired=true" by _bt_checkkeys.
     */
    if ((sktrig_required && all_required_satisfied) ||
        (!sktrig_required && all_satisfied))
    {
        int         nsktrig = sktrig + 1;
        bool        continuescan;
 
        Assert(all_required_satisfied);
 
        /* Recheck _bt_check_compare on behalf of caller */
        if (_bt_check_compare(scan, dir, tuple, tupnatts, tupdesc, false,
                              !sktrig_required, &continuescan,
                              &nsktrig) &&
            !so->scanBehind)
        {
            /* This tuple satisfies the new qual */
            Assert(all_satisfied && continuescan);
 
            if (pstate)
                pstate->continuescan = true;
 
            return true;
        }
 
        /*
         * Consider "second pass" handling of required inequalities.
         *
         * It's possible that our _bt_check_compare call indicated that the
         * scan should end due to some unsatisfied inequality that wasn't
         * initially recognized as such by us.  Handle this by calling
         * ourselves recursively, this time indicating that the trigger is the
         * inequality that we missed first time around (and using a set of
         * required array/equality keys that are now exact matches for tuple).
         *
         * We make a strong, general guarantee that every _bt_checkkeys call
         * here will advance the array keys to the maximum possible extent
         * that we can know to be safe based on caller's tuple alone.  If we
         * didn't perform this step, then that guarantee wouldn't quite hold.
         */
        if (unlikely(!continuescan))
        {
            bool        satisfied PG_USED_FOR_ASSERTS_ONLY;
 
            Assert(sktrig_required);
            Assert(so->keyData[nsktrig].sk_strategy != BTEqualStrategyNumber);
 
            /*
             * The tuple must use "beyond end" advancement during the
             * recursive call, so we cannot possibly end up back here when
             * recursing.  We'll consume a small, fixed amount of stack space.
             */
            Assert(!beyond_end_advance);
 
            /* Advance the array keys a second time using same tuple */
            satisfied = _bt_advance_array_keys(scan, pstate, tuple, tupnatts,
                                               tupdesc, nsktrig, true);
 
            /* This tuple doesn't satisfy the inequality */
            Assert(!satisfied);
            return false;
        }
 
        /*
         * Some non-required scan key (from new qual) still not satisfied.
         *
         * All scan keys required in the current scan direction must still be
         * satisfied, though, so we can trust all_required_satisfied below.
         */
    }
 
    /*
     * When we were called just to deal with "advancing" non-required arrays,
     * this is as far as we can go (cannot stop the scan for these callers)
     */
    if (!sktrig_required)
    {
        /* Caller's tuple doesn't match any qual */
        return false;
    }
 
    /*
     * Postcondition array state assertion (for still-unsatisfied tuples).
     *
     * By here we have established that the scan's required arrays (scan must
     * have at least one required array) advanced, without becoming exhausted.
     *
     * Caller's tuple is now < the newly advanced array keys (or > when this
     * is a backwards scan), except in the case where we only got this far due
     * to an unsatisfied non-required scan key.  Verify that with an assert.
     *
     * Note: we don't just quit at this point when all required scan keys were
     * found to be satisfied because we need to consider edge-cases involving
     * scan keys required in the opposite direction only; those aren't tracked
     * by all_required_satisfied.
     */
    Assert(_bt_tuple_before_array_skeys(scan, dir, tuple, tupdesc, tupnatts,
                                        false, 0, NULL) ==
           !all_required_satisfied);
 
    /*
     * We generally permit primitive index scans to continue onto the next
     * sibling page when the page's finaltup satisfies all required scan keys
     * at the point where we're between pages.
     *
     * If caller's tuple is also the page's finaltup, and we see that required
     * scan keys still aren't satisfied, start a new primitive index scan.
     */
    if (!all_required_satisfied && pstate->finaltup == tuple)
        goto new_prim_scan;
 
    /*
     * Proactively check finaltup (don't wait until finaltup is reached by the
     * scan) when it might well turn out to not be satisfied later on.
     *
     * Note: if so->scanBehind hasn't already been set for finaltup by us,
     * it'll be set during this call to _bt_tuple_before_array_skeys.  Either
     * way, it'll be set correctly (for the whole page) after this point.
     */
    if (!all_required_satisfied && pstate->finaltup &&
        _bt_tuple_before_array_skeys(scan, dir, pstate->finaltup, tupdesc,
                                     BTreeTupleGetNAtts(pstate->finaltup, rel),
                                     false, 0, &so->scanBehind))
        goto new_prim_scan;
 
    /*
     * When we encounter a truncated finaltup high key attribute, we're
     * optimistic about the chances of its corresponding required scan key
     * being satisfied when we go on to recheck it against tuples from this
     * page's right sibling leaf page.  We consider truncated attributes to be
     * satisfied by required scan keys, which allows the primitive index scan
     * to continue to the next leaf page.  We must set so->scanBehind to true
     * to remember that the last page's finaltup had "satisfied" required scan
     * keys for one or more truncated attribute values (scan keys required in
     * _either_ scan direction).
     *
     * There is a chance that _bt_readpage (which checks so->scanBehind) will
     * find that even the sibling leaf page's finaltup is < the new array
     * keys.  When that happens, our optimistic policy will have incurred a
     * single extra leaf page access that could have been avoided.
     *
     * A pessimistic policy would give backward scans a gratuitous advantage
     * over forward scans.  We'd punish forward scans for applying more
     * accurate information from the high key, rather than just using the
     * final non-pivot tuple as finaltup, in the style of backward scans.
     * Being pessimistic would also give some scans with non-required arrays a
     * perverse advantage over similar scans that use required arrays instead.
     *
     * This is similar to our scan-level heuristics, below.  They also set
     * scanBehind to speculatively continue the primscan onto the next page.
     */
    if (so->scanBehind)
    {
        /* Truncated high key -- _bt_scanbehind_checkkeys recheck scheduled */
    }
 
    /*
     * Handle inequalities marked required in the opposite scan direction.
     * They can also signal that we should start a new primitive index scan.
     *
     * It's possible that the scan is now positioned where "matching" tuples
     * begin, and that caller's tuple satisfies all scan keys required in the
     * current scan direction.  But if caller's tuple still doesn't satisfy
     * other scan keys that are required in the opposite scan direction only
     * (e.g., a required >= strategy scan key when scan direction is forward),
     * it's still possible that there are many leaf pages before the page that
     * _bt_first could skip straight to.  Groveling through all those pages
     * will always give correct answers, but it can be very inefficient.  We
     * must avoid needlessly scanning extra pages.
     *
     * Separately, it's possible that _bt_check_compare set continuescan=false
     * for a scan key that's required in the opposite direction only.  This is
     * a special case, that happens only when _bt_check_compare sees that the
     * inequality encountered a NULL value.  This signals the end of non-NULL
     * values in the current scan direction, which is reason enough to end the
     * (primitive) scan.  If this happens at the start of a large group of
     * NULL values, then we shouldn't expect to be called again until after
     * the scan has already read indefinitely-many leaf pages full of tuples
     * with NULL suffix values.  (_bt_first is expected to skip over the group
     * of NULLs by applying a similar "deduce NOT NULL" rule of its own, which
     * involves consing up an explicit SK_SEARCHNOTNULL key.)
     *
     * Apply a test against finaltup to detect and recover from the problem:
     * if even finaltup doesn't satisfy such an inequality, we just skip by
     * starting a new primitive index scan.  When we skip, we know for sure
     * that all of the tuples on the current page following caller's tuple are
     * also before the _bt_first-wise start of tuples for our new qual.  That
     * at least suggests many more skippable pages beyond the current page.
     * (when so->scanBehind and so->oppositeDirCheck are set, this'll happen
     * when we test the next page's finaltup/high key instead.)
     */
    else if (has_required_opposite_direction_only && pstate->finaltup &&
             unlikely(!_bt_oppodir_checkkeys(scan, dir, pstate->finaltup)))
        goto new_prim_scan;
 
continue_scan:
 
    /*
     * Stick with the ongoing primitive index scan for now.
     *
     * It's possible that later tuples will also turn out to have values that
     * are still < the now-current array keys (or > the current array keys).
     * Our caller will handle this by performing what amounts to a linear
     * search of the page, implemented by calling _bt_check_compare and then
     * _bt_tuple_before_array_skeys for each tuple.
     *
     * This approach has various advantages over a binary search of the page.
     * Repeated binary searches of the page (one binary search for every array
     * advancement) won't outperform a continuous linear search.  While there
     * are workloads that a naive linear search won't handle well, our caller
     * has a "look ahead" fallback mechanism to deal with that problem.
     */
    pstate->continuescan = true;    /* Override _bt_check_compare */
    so->needPrimScan = false;   /* _bt_readpage has more tuples to check */
 
    if (so->scanBehind)
    {
        /*
         * Remember if recheck needs to call _bt_oppodir_checkkeys for next
         * page's finaltup (see above comments about "Handle inequalities
         * marked required in the opposite scan direction" for why).
         */
        so->oppositeDirCheck = has_required_opposite_direction_only;
 
        /*
         * skip by setting "look ahead" mechanism's offnum for forwards scans
         * (backwards scans check scanBehind flag directly instead)
         */
        if (ScanDirectionIsForward(dir))
            pstate->skip = pstate->maxoff + 1;
    }
 
    /* Caller's tuple doesn't match the new qual */
    return false;
 
new_prim_scan:
 
    Assert(pstate->finaltup);   /* not on rightmost/leftmost page */
 
    /*
     * Looks like another primitive index scan is required.  But consider
     * continuing the current primscan based on scan-level heuristics.
     *
     * Continue the ongoing primitive scan (and schedule a recheck for when
     * the scan arrives on the next sibling leaf page) when it has already
     * read at least one leaf page before the one we're reading now.  This
     * makes primscan scheduling more efficient when scanning subsets of an
     * index with many distinct attribute values matching many array elements.
     * It encourages fewer, larger primitive scans where that makes sense.
     * This will in turn encourage _bt_readpage to apply the pstate.startikey
     * optimization more often.
     *
     * Also continue the ongoing primitive index scan when it is still on the
     * first page if there have been more than NSKIPADVANCES_THRESHOLD calls
     * here that each advanced at least one of the scan's skip arrays
     * (deliberately ignore advancements that only affected SAOP arrays here).
     * A page that cycles through this many skip array elements is quite
     * likely to neighbor similar pages, that we'll also need to read.
     *
     * Note: These heuristics aren't as aggressive as you might think.  We're
     * conservative about allowing a primitive scan to step from the first
     * leaf page it reads to the page's sibling page (we only allow it on
     * first pages whose finaltup strongly suggests that it'll work out, as
     * well as first pages that have a large number of skip array advances).
     * Clearing this first page finaltup hurdle is a strong signal in itself.
     *
     * Note: The NSKIPADVANCES_THRESHOLD heuristic exists only to avoid
     * pathological cases.  Specifically, cases where a skip scan should just
     * behave like a traditional full index scan, but ends up "skipping" again
     * and again, descending to the prior leaf page's direct sibling leaf page
     * each time.  This misbehavior would otherwise be possible during scans
     * that never quite manage to "clear the first page finaltup hurdle".
     */
    if (!pstate->firstpage || pstate->nskipadvances > NSKIPADVANCES_THRESHOLD)
    {
        /* Schedule a recheck once on the next (or previous) page */
        so->scanBehind = true;
 
        /* Continue the current primitive scan after all */
        goto continue_scan;
    }
 
    /*
     * End this primitive index scan, but schedule another.
     *
     * Note: We make a soft assumption that the current scan direction will
     * also be used within _bt_next, when it is asked to step off this page.
     * It is up to _bt_next to cancel this scheduled primitive index scan
     * whenever it steps to a page in the direction opposite currPos.dir.
     */
    pstate->continuescan = false;   /* Tell _bt_readpage we're done... */
    so->needPrimScan = true;    /* ...but call _bt_first again */
 
    if (scan->parallel_scan)
        _bt_parallel_primscan_schedule(scan, so->currPos.currPage);
 
    /* Caller's tuple doesn't match the new qual */
    return false;
 
end_toplevel_scan:
 
    /*
     * End the current primitive index scan, but don't schedule another.
     *
     * This ends the entire top-level scan in the current scan direction.
     *
     * Note: The scan's arrays (including any non-required arrays) are now in
     * their final positions for the current scan direction.  If the scan
     * direction happens to change, then the arrays will already be in their
     * first positions for what will then be the current scan direction.
     */
    pstate->continuescan = false;   /* Tell _bt_readpage we're done... */
    so->needPrimScan = false;   /* ...and don't call _bt_first again */
 
    /* Caller's tuple doesn't match any qual */
    return false;
}
 
/*
 * _bt_advance_array_keys_increment() -- Advance to next set of array elements
 *
 * Advances the array keys by a single increment in the current scan
 * direction.  When there are multiple array keys this can roll over from the
 * lowest order array to higher order arrays.
 *
 * Returns true if there is another set of values to consider, false if not.
 * On true result, the scankeys are initialized with the next set of values.
 * On false result, the scankeys stay the same, and the array keys are not
 * advanced (every array remains at its final element for scan direction).
 */
static bool
_bt_advance_array_keys_increment(IndexScanDesc scan, ScanDirection dir,
                                 bool *skip_array_set)
{
    Relation    rel = scan->indexRelation;
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
 
    /*
     * We must advance the last array key most quickly, since it will
     * correspond to the lowest-order index column among the available
     * qualifications
     */
    for (int i = so->numArrayKeys - 1; i >= 0; i--)
    {
        BTArrayKeyInfo *array = &so->arrayKeys[i];
        ScanKey     skey = &so->keyData[array->scan_key];
 
        if (array->num_elems == -1)
            *skip_array_set = true;
 
        if (ScanDirectionIsForward(dir))
        {
            if (_bt_array_increment(rel, skey, array))
                return true;
        }
        else
        {
            if (_bt_array_decrement(rel, skey, array))
                return true;
        }
 
        /*
         * Couldn't increment (or decrement) array.  Handle array roll over.
         *
         * Start over at the array's lowest sorting value (or its highest
         * value, for backward scans)...
         */
        _bt_array_set_low_or_high(rel, skey, array,
                                  ScanDirectionIsForward(dir));
 
        /* ...then increment (or decrement) next most significant array */
    }
 
    /*
     * The array keys are now exhausted.
     *
     * Restore the array keys to the state they were in immediately before we
     * were called.  This ensures that the arrays only ever ratchet in the
     * current scan direction.
     *
     * Without this, scans could overlook matching tuples when the scan
     * direction gets reversed just before btgettuple runs out of items to
     * return, but just after _bt_readpage prepares all the items from the
     * scan's final page in so->currPos.  When we're on the final page it is
     * typical for so->currPos to get invalidated once btgettuple finally
     * returns false, which'll effectively invalidate the scan's array keys.
     * That hasn't happened yet, though -- and in general it may never happen.
     */
    _bt_start_array_keys(scan, -dir);
 
    return false;
}
 
/*
 * _bt_array_increment() -- increment array scan key's sk_argument
 *
 * Return value indicates whether caller's array was successfully incremented.
 * Cannot increment an array whose current element is already the final one.
 */
static bool
_bt_array_increment(Relation rel, ScanKey skey, BTArrayKeyInfo *array)
{
    bool        oflow = false;
    Datum       inc_sk_argument;
 
    Assert(skey->sk_flags & SK_SEARCHARRAY);
    Assert(!(skey->sk_flags & (SK_BT_MINVAL | SK_BT_NEXT | SK_BT_PRIOR)));
 
    /* SAOP array? */
    if (array->num_elems != -1)
    {
        Assert(!(skey->sk_flags & (SK_BT_SKIP | SK_BT_MINVAL | SK_BT_MAXVAL)));
        if (array->cur_elem < array->num_elems - 1)
        {
            /*
             * Just increment current element, and assign its datum to skey
             * (only skip arrays need us to free existing sk_argument memory)
             */
            array->cur_elem++;
            skey->sk_argument = array->elem_values[array->cur_elem];
 
            /* Successfully incremented array */
            return true;
        }
 
        /* Cannot increment past final array element */
        return false;
    }
 
    /* Nope, this is a skip array */
    Assert(skey->sk_flags & SK_BT_SKIP);
 
    /*
     * The sentinel value that represents the maximum value within the range
     * of a skip array (often just +inf) is never incrementable
     */
    if (skey->sk_flags & SK_BT_MAXVAL)
        return false;
 
    /*
     * When the current array element is NULL, and the highest sorting value
     * in the index is also NULL, we cannot increment past the final element
     */
    if ((skey->sk_flags & SK_ISNULL) && !(skey->sk_flags & SK_BT_NULLS_FIRST))
        return false;
 
    /*
     * Opclasses without skip support "increment" the scan key's current
     * element by setting the NEXT flag.  The true next value is determined by
     * repositioning to the first index tuple > existing sk_argument/current
     * array element.  Note that this works in the usual way when the scan key
     * is already marked ISNULL (i.e. when the current element is NULL).
     */
    if (!array->sksup)
    {
        /* Successfully "incremented" array */
        skey->sk_flags |= SK_BT_NEXT;
        return true;
    }
 
    /*
     * Opclasses with skip support directly increment sk_argument
     */
    if (skey->sk_flags & SK_ISNULL)
    {
        Assert(skey->sk_flags & SK_BT_NULLS_FIRST);
 
        /*
         * Existing sk_argument/array element is NULL (for an IS NULL qual).
         *
         * "Increment" from NULL to the low_elem value provided by opclass
         * skip support routine.
         */
        skey->sk_flags &= ~(SK_SEARCHNULL | SK_ISNULL);
        skey->sk_argument = datumCopy(array->sksup->low_elem,
                                      array->attbyval, array->attlen);
        return true;
    }
 
    /*
     * Ask opclass support routine to provide incremented copy of existing
     * non-NULL sk_argument
     */
    inc_sk_argument = array->sksup->increment(rel, skey->sk_argument, &oflow);
    if (unlikely(oflow))
    {
        /* inc_sk_argument has undefined value (so no pfree) */
        if (array->null_elem && !(skey->sk_flags & SK_BT_NULLS_FIRST))
        {
            _bt_skiparray_set_isnull(rel, skey, array);
 
            /* Successfully "incremented" array to NULL */
            return true;
        }
 
        /* Cannot increment past final array element */
        return false;
    }
 
    /*
     * Successfully incremented sk_argument to a non-NULL value.  Make sure
     * that the incremented value is still within the range of the array.
     */
    if (array->high_compare &&
        !DatumGetBool(FunctionCall2Coll(&array->high_compare->sk_func,
                                        array->high_compare->sk_collation,
                                        inc_sk_argument,
                                        array->high_compare->sk_argument)))
    {
        /* Keep existing sk_argument after all */
        if (!array->attbyval)
            pfree(DatumGetPointer(inc_sk_argument));
 
        /* Cannot increment past final array element */
        return false;
    }
 
    /* Accept value returned by opclass increment callback */
    if (!array->attbyval && skey->sk_argument)
        pfree(DatumGetPointer(skey->sk_argument));
    skey->sk_argument = inc_sk_argument;
 
    /* Successfully incremented array */
    return true;
}
 
/*
 * _bt_array_decrement() -- decrement array scan key's sk_argument
 *
 * Return value indicates whether caller's array was successfully decremented.
 * Cannot decrement an array whose current element is already the first one.
 */
static bool
_bt_array_decrement(Relation rel, ScanKey skey, BTArrayKeyInfo *array)
{
    bool        uflow = false;
    Datum       dec_sk_argument;
 
    Assert(skey->sk_flags & SK_SEARCHARRAY);
    Assert(!(skey->sk_flags & (SK_BT_MAXVAL | SK_BT_NEXT | SK_BT_PRIOR)));
 
    /* SAOP array? */
    if (array->num_elems != -1)
    {
        Assert(!(skey->sk_flags & (SK_BT_SKIP | SK_BT_MINVAL | SK_BT_MAXVAL)));
        if (array->cur_elem > 0)
        {
            /*
             * Just decrement current element, and assign its datum to skey
             * (only skip arrays need us to free existing sk_argument memory)
             */
            array->cur_elem--;
            skey->sk_argument = array->elem_values[array->cur_elem];
 
            /* Successfully decremented array */
            return true;
        }
 
        /* Cannot decrement to before first array element */
        return false;
    }
 
    /* Nope, this is a skip array */
    Assert(skey->sk_flags & SK_BT_SKIP);
 
    /*
     * The sentinel value that represents the minimum value within the range
     * of a skip array (often just -inf) is never decrementable
     */
    if (skey->sk_flags & SK_BT_MINVAL)
        return false;
 
    /*
     * When the current array element is NULL, and the lowest sorting value in
     * the index is also NULL, we cannot decrement before first array element
     */
    if ((skey->sk_flags & SK_ISNULL) && (skey->sk_flags & SK_BT_NULLS_FIRST))
        return false;
 
    /*
     * Opclasses without skip support "decrement" the scan key's current
     * element by setting the PRIOR flag.  The true prior value is determined
     * by repositioning to the last index tuple < existing sk_argument/current
     * array element.  Note that this works in the usual way when the scan key
     * is already marked ISNULL (i.e. when the current element is NULL).
     */
    if (!array->sksup)
    {
        /* Successfully "decremented" array */
        skey->sk_flags |= SK_BT_PRIOR;
        return true;
    }
 
    /*
     * Opclasses with skip support directly decrement sk_argument
     */
    if (skey->sk_flags & SK_ISNULL)
    {
        Assert(!(skey->sk_flags & SK_BT_NULLS_FIRST));
 
        /*
         * Existing sk_argument/array element is NULL (for an IS NULL qual).
         *
         * "Decrement" from NULL to the high_elem value provided by opclass
         * skip support routine.
         */
        skey->sk_flags &= ~(SK_SEARCHNULL | SK_ISNULL);
        skey->sk_argument = datumCopy(array->sksup->high_elem,
                                      array->attbyval, array->attlen);
        return true;
    }
 
    /*
     * Ask opclass support routine to provide decremented copy of existing
     * non-NULL sk_argument
     */
    dec_sk_argument = array->sksup->decrement(rel, skey->sk_argument, &uflow);
    if (unlikely(uflow))
    {
        /* dec_sk_argument has undefined value (so no pfree) */
        if (array->null_elem && (skey->sk_flags & SK_BT_NULLS_FIRST))
        {
            _bt_skiparray_set_isnull(rel, skey, array);
 
            /* Successfully "decremented" array to NULL */
            return true;
        }
 
        /* Cannot decrement to before first array element */
        return false;
    }
 
    /*
     * Successfully decremented sk_argument to a non-NULL value.  Make sure
     * that the decremented value is still within the range of the array.
     */
    if (array->low_compare &&
        !DatumGetBool(FunctionCall2Coll(&array->low_compare->sk_func,
                                        array->low_compare->sk_collation,
                                        dec_sk_argument,
                                        array->low_compare->sk_argument)))
    {
        /* Keep existing sk_argument after all */
        if (!array->attbyval)
            pfree(DatumGetPointer(dec_sk_argument));
 
        /* Cannot decrement to before first array element */
        return false;
    }
 
    /* Accept value returned by opclass decrement callback */
    if (!array->attbyval && skey->sk_argument)
        pfree(DatumGetPointer(skey->sk_argument));
    skey->sk_argument = dec_sk_argument;
 
    /* Successfully decremented array */
    return true;
}
 
/*
 * _bt_array_set_low_or_high() -- Set array scan key to lowest/highest element
 *
 * Caller also passes associated scan key, which will have its argument set to
 * the lowest/highest array value in passing.
 */
static void
_bt_array_set_low_or_high(Relation rel, ScanKey skey, BTArrayKeyInfo *array,
                          bool low_not_high)
{
    Assert(skey->sk_flags & SK_SEARCHARRAY);
 
    if (array->num_elems != -1)
    {
        /* set low or high element for SAOP array */
        int         set_elem = 0;
 
        Assert(!(skey->sk_flags & SK_BT_SKIP));
 
        if (!low_not_high)
            set_elem = array->num_elems - 1;
 
        /*
         * Just copy over array datum (only skip arrays require freeing and
         * allocating memory for sk_argument)
         */
        array->cur_elem = set_elem;
        skey->sk_argument = array->elem_values[set_elem];
 
        return;
    }
 
    /* set low or high element for skip array */
    Assert(skey->sk_flags & SK_BT_SKIP);
    Assert(array->num_elems == -1);
 
    /* Free memory previously allocated for sk_argument if needed */
    if (!array->attbyval && skey->sk_argument)
        pfree(DatumGetPointer(skey->sk_argument));
 
    /* Reset flags */
    skey->sk_argument = (Datum) 0;
    skey->sk_flags &= ~(SK_SEARCHNULL | SK_ISNULL |
                        SK_BT_MINVAL | SK_BT_MAXVAL |
                        SK_BT_NEXT | SK_BT_PRIOR);
 
    if (array->null_elem &&
        (low_not_high == ((skey->sk_flags & SK_BT_NULLS_FIRST) != 0)))
    {
        /* Requested element (either lowest or highest) has the value NULL */
        skey->sk_flags |= (SK_SEARCHNULL | SK_ISNULL);
    }
    else if (low_not_high)
    {
        /* Setting array to lowest element (according to low_compare) */
        skey->sk_flags |= SK_BT_MINVAL;
    }
    else
    {
        /* Setting array to highest element (according to high_compare) */
        skey->sk_flags |= SK_BT_MAXVAL;
    }
}
 
/*
 * _bt_skiparray_set_element() -- Set skip array scan key's sk_argument
 *
 * Caller passes set_elem_result returned by _bt_binsrch_skiparray_skey for
 * caller's tupdatum/tupnull.
 *
 * We copy tupdatum/tupnull into skey's sk_argument iff set_elem_result == 0.
 * Otherwise, we set skey to either the lowest or highest value that's within
 * the range of caller's skip array (whichever is the best available match to
 * tupdatum/tupnull that is still within the range of the skip array according
 * to _bt_binsrch_skiparray_skey/set_elem_result).
 */
static void
_bt_skiparray_set_element(Relation rel, ScanKey skey, BTArrayKeyInfo *array,
                          int32 set_elem_result, Datum tupdatum, bool tupnull)
{
    Assert(skey->sk_flags & SK_BT_SKIP);
    Assert(skey->sk_flags & SK_SEARCHARRAY);
 
    if (set_elem_result)
    {
        /* tupdatum/tupnull is out of the range of the skip array */
        Assert(!array->null_elem);
 
        _bt_array_set_low_or_high(rel, skey, array, set_elem_result < 0);
        return;
    }
 
    /* Advance skip array to tupdatum (or tupnull) value */
    if (unlikely(tupnull))
    {
        _bt_skiparray_set_isnull(rel, skey, array);
        return;
    }
 
    /* Free memory previously allocated for sk_argument if needed */
    if (!array->attbyval && skey->sk_argument)
        pfree(DatumGetPointer(skey->sk_argument));
 
    /* tupdatum becomes new sk_argument/new current element */
    skey->sk_flags &= ~(SK_SEARCHNULL | SK_ISNULL |
                        SK_BT_MINVAL | SK_BT_MAXVAL |
                        SK_BT_NEXT | SK_BT_PRIOR);
    skey->sk_argument = datumCopy(tupdatum, array->attbyval, array->attlen);
}
 
/*
 * _bt_skiparray_set_isnull() -- set skip array scan key to NULL
 */
static void
_bt_skiparray_set_isnull(Relation rel, ScanKey skey, BTArrayKeyInfo *array)
{
    Assert(skey->sk_flags & SK_BT_SKIP);
    Assert(skey->sk_flags & SK_SEARCHARRAY);
    Assert(array->null_elem && !array->low_compare && !array->high_compare);
 
    /* Free memory previously allocated for sk_argument if needed */
    if (!array->attbyval && skey->sk_argument)
        pfree(DatumGetPointer(skey->sk_argument));
 
    /* NULL becomes new sk_argument/new current element */
    skey->sk_argument = (Datum) 0;
    skey->sk_flags &= ~(SK_BT_MINVAL | SK_BT_MAXVAL |
                        SK_BT_NEXT | SK_BT_PRIOR);
    skey->sk_flags |= (SK_SEARCHNULL | SK_ISNULL);
}
 
/*
 * _bt_compare_array_skey() -- apply array comparison function
 *
 * Compares caller's tuple attribute value to a scan key/array element.
 * Helper function used during binary searches of SK_SEARCHARRAY arrays.
 *
 *      This routine returns:
 *          <0 if tupdatum < arrdatum;
 *           0 if tupdatum == arrdatum;
 *          >0 if tupdatum > arrdatum.
 *
 * This is essentially the same interface as _bt_compare: both functions
 * compare the value that they're searching for to a binary search pivot.
 * However, unlike _bt_compare, this function's "tuple argument" comes first,
 * while its "array/scankey argument" comes second.
*/
static inline int32
_bt_compare_array_skey(FmgrInfo *orderproc,
                       Datum tupdatum, bool tupnull,
                       Datum arrdatum, ScanKey cur)
{
    int32       result = 0;
 
    Assert(cur->sk_strategy == BTEqualStrategyNumber);
    Assert(!(cur->sk_flags & (SK_BT_MINVAL | SK_BT_MAXVAL)));
 
    if (tupnull)                /* NULL tupdatum */
    {
        if (cur->sk_flags & SK_ISNULL)
            result = 0;         /* NULL "=" NULL */
        else if (cur->sk_flags & SK_BT_NULLS_FIRST)
            result = -1;        /* NULL "<" NOT_NULL */
        else
            result = 1;         /* NULL ">" NOT_NULL */
    }
    else if (cur->sk_flags & SK_ISNULL) /* NOT_NULL tupdatum, NULL arrdatum */
    {
        if (cur->sk_flags & SK_BT_NULLS_FIRST)
            result = 1;         /* NOT_NULL ">" NULL */
        else
            result = -1;        /* NOT_NULL "<" NULL */
    }
    else
    {
        /*
         * Like _bt_compare, we need to be careful of cross-type comparisons,
         * so the left value has to be the value that came from an index tuple
         */
        result = DatumGetInt32(FunctionCall2Coll(orderproc, cur->sk_collation,
                                                 tupdatum, arrdatum));
 
        /*
         * We flip the sign by following the obvious rule: flip whenever the
         * column is a DESC column.
         *
         * _bt_compare does it the wrong way around (flip when *ASC*) in order
         * to compensate for passing its orderproc arguments backwards.  We
         * don't need to play these games because we find it natural to pass
         * tupdatum as the left value (and arrdatum as the right value).
         */
        if (cur->sk_flags & SK_BT_DESC)
            INVERT_COMPARE_RESULT(result);
    }
 
    return result;
}
 
/*
 * _bt_binsrch_array_skey() -- Binary search for next matching array key
 *
 * Returns an index to the first array element >= caller's tupdatum argument.
 * This convention is more natural for forwards scan callers, but that can't
 * really matter to backwards scan callers.  Both callers require handling for
 * the case where the match we return is < tupdatum, and symmetric handling
 * for the case where our best match is > tupdatum.
 *
 * Also sets *set_elem_result to the result _bt_compare_array_skey returned
 * when we used it to compare the matching array element to tupdatum/tupnull.
 *
 * cur_elem_trig indicates if array advancement was triggered by this array's
 * scan key, and that the array is for a required scan key.  We can apply this
 * information to find the next matching array element in the current scan
 * direction using far fewer comparisons (fewer on average, compared to naive
 * binary search).  This scheme takes advantage of an important property of
 * required arrays: required arrays always advance in lockstep with the index
 * scan's progress through the index's key space.
 */
int
_bt_binsrch_array_skey(FmgrInfo *orderproc,
                       bool cur_elem_trig, ScanDirection dir,
                       Datum tupdatum, bool tupnull,
                       BTArrayKeyInfo *array, ScanKey cur,
                       int32 *set_elem_result)
{
    int         low_elem = 0,
                mid_elem = -1,
                high_elem = array->num_elems - 1,
                result = 0;
    Datum       arrdatum;
 
    Assert(cur->sk_flags & SK_SEARCHARRAY);
    Assert(!(cur->sk_flags & SK_BT_SKIP));
    Assert(!(cur->sk_flags & SK_ISNULL));   /* SAOP arrays never have NULLs */
    Assert(cur->sk_strategy == BTEqualStrategyNumber);
 
    if (cur_elem_trig)
    {
        Assert(!ScanDirectionIsNoMovement(dir));
        Assert(cur->sk_flags & SK_BT_REQFWD);
 
        /*
         * When the scan key that triggered array advancement is a required
         * array scan key, it is now certain that the current array element
         * (plus all prior elements relative to the current scan direction)
         * cannot possibly be at or ahead of the corresponding tuple value.
         * (_bt_checkkeys must have called _bt_tuple_before_array_skeys, which
         * makes sure this is true as a condition of advancing the arrays.)
         *
         * This makes it safe to exclude array elements up to and including
         * the former-current array element from our search.
         *
         * Separately, when array advancement was triggered by a required scan
         * key, the array element immediately after the former-current element
         * is often either an exact tupdatum match, or a "close by" near-match
         * (a near-match tupdatum is one whose key space falls _between_ the
         * former-current and new-current array elements).  We'll detect both
         * cases via an optimistic comparison of the new search lower bound
         * (or new search upper bound in the case of backwards scans).
         */
        if (ScanDirectionIsForward(dir))
        {
            low_elem = array->cur_elem + 1; /* old cur_elem exhausted */
 
            /* Compare prospective new cur_elem (also the new lower bound) */
            if (high_elem >= low_elem)
            {
                arrdatum = array->elem_values[low_elem];
                result = _bt_compare_array_skey(orderproc, tupdatum, tupnull,
                                                arrdatum, cur);
 
                if (result <= 0)
                {
                    /* Optimistic comparison optimization worked out */
                    *set_elem_result = result;
                    return low_elem;
                }
                mid_elem = low_elem;
                low_elem++;     /* this cur_elem exhausted, too */
            }
 
            if (high_elem < low_elem)
            {
                /* Caller needs to perform "beyond end" array advancement */
                *set_elem_result = 1;
                return high_elem;
            }
        }
        else
        {
            high_elem = array->cur_elem - 1;    /* old cur_elem exhausted */
 
            /* Compare prospective new cur_elem (also the new upper bound) */
            if (high_elem >= low_elem)
            {
                arrdatum = array->elem_values[high_elem];
                result = _bt_compare_array_skey(orderproc, tupdatum, tupnull,
                                                arrdatum, cur);
 
                if (result >= 0)
                {
                    /* Optimistic comparison optimization worked out */
                    *set_elem_result = result;
                    return high_elem;
                }
                mid_elem = high_elem;
                high_elem--;    /* this cur_elem exhausted, too */
            }
 
            if (high_elem < low_elem)
            {
                /* Caller needs to perform "beyond end" array advancement */
                *set_elem_result = -1;
                return low_elem;
            }
        }
    }
 
    while (high_elem > low_elem)
    {
        mid_elem = low_elem + ((high_elem - low_elem) / 2);
        arrdatum = array->elem_values[mid_elem];
 
        result = _bt_compare_array_skey(orderproc, tupdatum, tupnull,
                                        arrdatum, cur);
 
        if (result == 0)
        {
            /*
             * It's safe to quit as soon as we see an equal array element.
             * This often saves an extra comparison or two...
             */
            low_elem = mid_elem;
            break;
        }
 
        if (result > 0)
            low_elem = mid_elem + 1;
        else
            high_elem = mid_elem;
    }
 
    /*
     * ...but our caller also cares about how its searched-for tuple datum
     * compares to the low_elem datum.  Must always set *set_elem_result with
     * the result of that comparison specifically.
     */
    if (low_elem != mid_elem)
        result = _bt_compare_array_skey(orderproc, tupdatum, tupnull,
                                        array->elem_values[low_elem], cur);
 
    *set_elem_result = result;
 
    return low_elem;
}
 
/*
 * _bt_binsrch_skiparray_skey() -- "Binary search" within a skip array
 *
 * Does not return an index into the array, since skip arrays don't really
 * contain elements (they generate their array elements procedurally instead).
 * Our interface matches that of _bt_binsrch_array_skey in every other way.
 *
 * Sets *set_elem_result just like _bt_binsrch_array_skey would with a true
 * array.  The value 0 indicates that tupdatum/tupnull is within the range of
 * the skip array.  We return -1 when tupdatum/tupnull is lower that any value
 * within the range of the array, and 1 when it is higher than every value.
 * Caller should pass *set_elem_result to _bt_skiparray_set_element to advance
 * the array.
 *
 * cur_elem_trig indicates if array advancement was triggered by this array's
 * scan key.  We use this to optimize-away comparisons that are known by our
 * caller to be unnecessary from context, just like _bt_binsrch_array_skey.
 */
static void
_bt_binsrch_skiparray_skey(bool cur_elem_trig, ScanDirection dir,
                           Datum tupdatum, bool tupnull,
                           BTArrayKeyInfo *array, ScanKey cur,
                           int32 *set_elem_result)
{
    Assert(cur->sk_flags & SK_BT_SKIP);
    Assert(cur->sk_flags & SK_SEARCHARRAY);
    Assert(cur->sk_flags & SK_BT_REQFWD);
    Assert(array->num_elems == -1);
    Assert(!ScanDirectionIsNoMovement(dir));
 
    if (array->null_elem)
    {
        Assert(!array->low_compare && !array->high_compare);
 
        *set_elem_result = 0;
        return;
    }
 
    if (tupnull)                /* NULL tupdatum */
    {
        if (cur->sk_flags & SK_BT_NULLS_FIRST)
            *set_elem_result = -1;  /* NULL "<" NOT_NULL */
        else
            *set_elem_result = 1;   /* NULL ">" NOT_NULL */
        return;
    }
 
    /*
     * Array inequalities determine whether tupdatum is within the range of
     * caller's skip array
     */
    *set_elem_result = 0;
    if (ScanDirectionIsForward(dir))
    {
        /*
         * Evaluate low_compare first (unless cur_elem_trig tells us that it
         * cannot possibly fail to be satisfied), then evaluate high_compare
         */
        if (!cur_elem_trig && array->low_compare &&
            !DatumGetBool(FunctionCall2Coll(&array->low_compare->sk_func,
                                            array->low_compare->sk_collation,
                                            tupdatum,
                                            array->low_compare->sk_argument)))
            *set_elem_result = -1;
        else if (array->high_compare &&
                 !DatumGetBool(FunctionCall2Coll(&array->high_compare->sk_func,
                                                 array->high_compare->sk_collation,
                                                 tupdatum,
                                                 array->high_compare->sk_argument)))
            *set_elem_result = 1;
    }
    else
    {
        /*
         * Evaluate high_compare first (unless cur_elem_trig tells us that it
         * cannot possibly fail to be satisfied), then evaluate low_compare
         */
        if (!cur_elem_trig && array->high_compare &&
            !DatumGetBool(FunctionCall2Coll(&array->high_compare->sk_func,
                                            array->high_compare->sk_collation,
                                            tupdatum,
                                            array->high_compare->sk_argument)))
            *set_elem_result = 1;
        else if (array->low_compare &&
                 !DatumGetBool(FunctionCall2Coll(&array->low_compare->sk_func,
                                                 array->low_compare->sk_collation,
                                                 tupdatum,
                                                 array->low_compare->sk_argument)))
            *set_elem_result = -1;
    }
 
    /*
     * Assert that any keys that were assumed to be satisfied already (due to
     * caller passing cur_elem_trig=true) really are satisfied as expected
     */
#ifdef USE_ASSERT_CHECKING
    if (cur_elem_trig)
    {
        if (ScanDirectionIsForward(dir) && array->low_compare)
            Assert(DatumGetBool(FunctionCall2Coll(&array->low_compare->sk_func,
                                                  array->low_compare->sk_collation,
                                                  tupdatum,
                                                  array->low_compare->sk_argument)));
 
        if (ScanDirectionIsBackward(dir) && array->high_compare)
            Assert(DatumGetBool(FunctionCall2Coll(&array->high_compare->sk_func,
                                                  array->high_compare->sk_collation,
                                                  tupdatum,
                                                  array->high_compare->sk_argument)));
    }
#endif
}
 
#ifdef USE_ASSERT_CHECKING
/*
 * Verify that the scan's "so->keyData[]" scan keys are in agreement with
 * its array key state
 */
static bool
_bt_verify_keys_with_arraykeys(IndexScanDesc scan)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    int         last_sk_attno = InvalidAttrNumber,
                arrayidx = 0;
    bool        nonrequiredseen = false;
 
    if (!so->qual_ok)
        return false;
 
    for (int ikey = 0; ikey < so->numberOfKeys; ikey++)
    {
        ScanKey     cur = so->keyData + ikey;
        BTArrayKeyInfo *array;
 
        if (cur->sk_strategy != BTEqualStrategyNumber ||
            !(cur->sk_flags & SK_SEARCHARRAY))
            continue;
 
        array = &so->arrayKeys[arrayidx++];
        if (array->scan_key != ikey)
            return false;
 
        if (array->num_elems == 0 || array->num_elems < -1)
            return false;
 
        if (array->num_elems != -1 &&
            cur->sk_argument != array->elem_values[array->cur_elem])
            return false;
        if (cur->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD))
        {
            if (last_sk_attno > cur->sk_attno)
                return false;
            if (nonrequiredseen)
                return false;
        }
        else
            nonrequiredseen = true;
 
        last_sk_attno = cur->sk_attno;
    }
 
    if (arrayidx != so->numArrayKeys)
        return false;
 
    return true;
}
#endif