nbtutils.c

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/*-------------------------------------------------------------------------
 *
 * nbtutils.c
 *    Utility code for Postgres btree implementation.
 *
 * Portions Copyright (c) 1996-2024, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *    src/backend/access/nbtree/nbtutils.c
 *
 *-------------------------------------------------------------------------
 */
 
#include "postgres.h"
 
#include <time.h>
 
#include "access/nbtree.h"
#include "access/reloptions.h"
#include "access/relscan.h"
#include "commands/progress.h"
#include "lib/qunique.h"
#include "miscadmin.h"
#include "utils/array.h"
#include "utils/datum.h"
#include "utils/lsyscache.h"
#include "utils/memutils.h"
#include "utils/rel.h"
 
#define LOOK_AHEAD_REQUIRED_RECHECKS    3
#define LOOK_AHEAD_DEFAULT_DISTANCE     5
 
typedef struct BTSortArrayContext
{
    FmgrInfo   *sortproc;
    Oid         collation;
    bool        reverse;
} BTSortArrayContext;
 
typedef struct BTScanKeyPreproc
{
    ScanKey     skey;
    int         ikey;
    int         arrayidx;
} BTScanKeyPreproc;
 
static void _bt_setup_array_cmp(IndexScanDesc scan, ScanKey skey, Oid elemtype,
                                FmgrInfo *orderproc, FmgrInfo **sortprocp);
static Datum _bt_find_extreme_element(IndexScanDesc scan, ScanKey skey,
                                      Oid elemtype, StrategyNumber strat,
                                      Datum *elems, int nelems);
static int  _bt_sort_array_elements(ScanKey skey, FmgrInfo *sortproc,
                                    bool reverse, Datum *elems, int nelems);
static bool _bt_merge_arrays(IndexScanDesc scan, ScanKey skey,
                             FmgrInfo *sortproc, bool reverse,
                             Oid origelemtype, Oid nextelemtype,
                             Datum *elems_orig, int *nelems_orig,
                             Datum *elems_next, int nelems_next);
static bool _bt_compare_array_scankey_args(IndexScanDesc scan,
                                           ScanKey arraysk, ScanKey skey,
                                           FmgrInfo *orderproc, BTArrayKeyInfo *array,
                                           bool *qual_ok);
static ScanKey _bt_preprocess_array_keys(IndexScanDesc scan);
static void _bt_preprocess_array_keys_final(IndexScanDesc scan, int *keyDataMap);
static int  _bt_compare_array_elements(const void *a, const void *b, void *arg);
static inline int32 _bt_compare_array_skey(FmgrInfo *orderproc,
                                           Datum tupdatum, bool tupnull,
                                           Datum arrdatum, ScanKey cur);
static 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);
static bool _bt_advance_array_keys_increment(IndexScanDesc scan, ScanDirection dir);
static void _bt_rewind_nonrequired_arrays(IndexScanDesc scan, ScanDirection dir);
static bool _bt_tuple_before_array_skeys(IndexScanDesc scan, ScanDirection dir,
                                         IndexTuple tuple, TupleDesc tupdesc, int tupnatts,
                                         bool readpagetup, int sktrig, bool *scanBehind);
static bool _bt_advance_array_keys(IndexScanDesc scan, BTReadPageState *pstate,
                                   IndexTuple tuple, int tupnatts, TupleDesc tupdesc,
                                   int sktrig, bool sktrig_required);
#ifdef USE_ASSERT_CHECKING
static bool _bt_verify_arrays_bt_first(IndexScanDesc scan, ScanDirection dir);
static bool _bt_verify_keys_with_arraykeys(IndexScanDesc scan);
#endif
static bool _bt_compare_scankey_args(IndexScanDesc scan, ScanKey op,
                                     ScanKey leftarg, ScanKey rightarg,
                                     BTArrayKeyInfo *array, FmgrInfo *orderproc,
                                     bool *result);
static bool _bt_fix_scankey_strategy(ScanKey skey, int16 *indoption);
static void _bt_mark_scankey_required(ScanKey skey);
static bool _bt_check_compare(IndexScanDesc scan, ScanDirection dir,
                              IndexTuple tuple, int tupnatts, TupleDesc tupdesc,
                              bool advancenonrequired, bool prechecked, bool firstmatch,
                              bool *continuescan, int *ikey);
static bool _bt_check_rowcompare(ScanKey skey,
                                 IndexTuple tuple, int tupnatts, TupleDesc tupdesc,
                                 ScanDirection dir, bool *continuescan);
static void _bt_checkkeys_look_ahead(IndexScanDesc scan, BTReadPageState *pstate,
                                     int tupnatts, TupleDesc tupdesc);
static int  _bt_keep_natts(Relation rel, IndexTuple lastleft,
                           IndexTuple firstright, BTScanInsert itup_key);
 
 
/*
 * _bt_mkscankey
 *      Build an insertion scan key that contains comparison data from itup
 *      as well as comparator routines appropriate to the key datatypes.
 *
 *      The result is intended for use with _bt_compare() and _bt_truncate().
 *      Callers that don't need to fill out the insertion scankey arguments
 *      (e.g. they use an ad-hoc comparison routine, or only need a scankey
 *      for _bt_truncate()) can pass a NULL index tuple.  The scankey will
 *      be initialized as if an "all truncated" pivot tuple was passed
 *      instead.
 *
 *      Note that we may occasionally have to share lock the metapage to
 *      determine whether or not the keys in the index are expected to be
 *      unique (i.e. if this is a "heapkeyspace" index).  We assume a
 *      heapkeyspace index when caller passes a NULL tuple, allowing index
 *      build callers to avoid accessing the non-existent metapage.  We
 *      also assume that the index is _not_ allequalimage when a NULL tuple
 *      is passed; CREATE INDEX callers call _bt_allequalimage() to set the
 *      field themselves.
 */
BTScanInsert
_bt_mkscankey(Relation rel, IndexTuple itup)
{
    BTScanInsert key;
    ScanKey     skey;
    TupleDesc   itupdesc;
    int         indnkeyatts;
    int16      *indoption;
    int         tupnatts;
    int         i;
 
    itupdesc = RelationGetDescr(rel);
    indnkeyatts = IndexRelationGetNumberOfKeyAttributes(rel);
    indoption = rel->rd_indoption;
    tupnatts = itup ? BTreeTupleGetNAtts(itup, rel) : 0;
 
    Assert(tupnatts <= IndexRelationGetNumberOfAttributes(rel));
 
    /*
     * We'll execute search using scan key constructed on key columns.
     * Truncated attributes and non-key attributes are omitted from the final
     * scan key.
     */
    key = palloc(offsetof(BTScanInsertData, scankeys) +
                 sizeof(ScanKeyData) * indnkeyatts);
    if (itup)
        _bt_metaversion(rel, &key->heapkeyspace, &key->allequalimage);
    else
    {
        /* Utility statement callers can set these fields themselves */
        key->heapkeyspace = true;
        key->allequalimage = false;
    }
    key->anynullkeys = false;   /* initial assumption */
    key->nextkey = false;       /* usual case, required by btinsert */
    key->backward = false;      /* usual case, required by btinsert */
    key->keysz = Min(indnkeyatts, tupnatts);
    key->scantid = key->heapkeyspace && itup ?
        BTreeTupleGetHeapTID(itup) : NULL;
    skey = key->scankeys;
    for (i = 0; i < indnkeyatts; i++)
    {
        FmgrInfo   *procinfo;
        Datum       arg;
        bool        null;
        int         flags;
 
        /*
         * We can use the cached (default) support procs since no cross-type
         * comparison can be needed.
         */
        procinfo = index_getprocinfo(rel, i + 1, BTORDER_PROC);
 
        /*
         * Key arguments built from truncated attributes (or when caller
         * provides no tuple) are defensively represented as NULL values. They
         * should never be used.
         */
        if (i < tupnatts)
            arg = index_getattr(itup, i + 1, itupdesc, &null);
        else
        {
            arg = (Datum) 0;
            null = true;
        }
        flags = (null ? SK_ISNULL : 0) | (indoption[i] << SK_BT_INDOPTION_SHIFT);
        ScanKeyEntryInitializeWithInfo(&skey[i],
                                       flags,
                                       (AttrNumber) (i + 1),
                                       InvalidStrategy,
                                       InvalidOid,
                                       rel->rd_indcollation[i],
                                       procinfo,
                                       arg);
        /* Record if any key attribute is NULL (or truncated) */
        if (null)
            key->anynullkeys = true;
    }
 
    /*
     * In NULLS NOT DISTINCT mode, we pretend that there are no null keys, so
     * that full uniqueness check is done.
     */
    if (rel->rd_index->indnullsnotdistinct)
        key->anynullkeys = false;
 
    return key;
}
 
/*
 * free a retracement stack made by _bt_search.
 */
void
_bt_freestack(BTStack stack)
{
    BTStack     ostack;
 
    while (stack != NULL)
    {
        ostack = stack;
        stack = stack->bts_parent;
        pfree(ostack);
    }
}
 
 
/*
 *  _bt_preprocess_array_keys() -- Preprocess SK_SEARCHARRAY scan keys
 *
 * If there are any SK_SEARCHARRAY scan keys, deconstruct the array(s) and
 * set up BTArrayKeyInfo info for each one that is an equality-type key.
 * Returns modified scan keys as input for further, standard preprocessing.
 *
 * Currently we perform two kinds of preprocessing to deal with redundancies.
 * For inequality array keys, it's sufficient to find the extreme element
 * value and replace the whole array with that scalar value.  This eliminates
 * all but one array element as redundant.  Similarly, we are capable of
 * "merging together" multiple equality array keys (from two or more input
 * scan keys) into a single output scan key containing only the intersecting
 * array elements.  This can eliminate many redundant array elements, as well
 * as eliminating whole array scan keys as redundant.  It can also allow us to
 * detect contradictory quals.
 *
 * It is convenient for _bt_preprocess_keys caller to have to deal with no
 * more than one equality strategy array scan key per index attribute.  We'll
 * always be able to set things up that way when complete opfamilies are used.
 * Eliminated array scan keys can be recognized as those that have had their
 * sk_strategy field set to InvalidStrategy here by us.  Caller should avoid
 * including these in the scan's so->keyData[] output array.
 *
 * We set the scan key references from the scan's BTArrayKeyInfo info array to
 * offsets into the temp modified input array returned to caller.  Scans that
 * have array keys should call _bt_preprocess_array_keys_final when standard
 * preprocessing steps are complete.  This will convert the scan key offset
 * references into references to the scan's so->keyData[] output scan keys.
 *
 * Note: the reason we need to return a temp scan key array, rather than just
 * scribbling on scan->keyData, is that callers are permitted to call btrescan
 * without supplying a new set of scankey data.
 */
static ScanKey
_bt_preprocess_array_keys(IndexScanDesc scan)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    Relation    rel = scan->indexRelation;
    int         numberOfKeys = scan->numberOfKeys;
    int16      *indoption = rel->rd_indoption;
    int         numArrayKeys;
    int         origarrayatt = InvalidAttrNumber,
                origarraykey = -1;
    Oid         origelemtype = InvalidOid;
    ScanKey     cur;
    MemoryContext oldContext;
    ScanKey     arrayKeyData;   /* modified copy of scan->keyData */
 
    Assert(numberOfKeys);
 
    /* Quick check to see if there are any array keys */
    numArrayKeys = 0;
    for (int i = 0; i < numberOfKeys; i++)
    {
        cur = &scan->keyData[i];
        if (cur->sk_flags & SK_SEARCHARRAY)
        {
            numArrayKeys++;
            Assert(!(cur->sk_flags & (SK_ROW_HEADER | SK_SEARCHNULL | SK_SEARCHNOTNULL)));
            /* If any arrays are null as a whole, we can quit right now. */
            if (cur->sk_flags & SK_ISNULL)
            {
                so->qual_ok = false;
                return NULL;
            }
        }
    }
 
    /* Quit if nothing to do. */
    if (numArrayKeys == 0)
        return NULL;
 
    /*
     * Make a scan-lifespan context to hold array-associated data, or reset it
     * if we already have one from a previous rescan cycle.
     */
    if (so->arrayContext == NULL)
        so->arrayContext = AllocSetContextCreate(CurrentMemoryContext,
                                                 "BTree array context",
                                                 ALLOCSET_SMALL_SIZES);
    else
        MemoryContextReset(so->arrayContext);
 
    oldContext = MemoryContextSwitchTo(so->arrayContext);
 
    /* Create modifiable copy of scan->keyData in the workspace context */
    arrayKeyData = (ScanKey) palloc(numberOfKeys * sizeof(ScanKeyData));
    memcpy(arrayKeyData, scan->keyData, numberOfKeys * sizeof(ScanKeyData));
 
    /* Allocate space for per-array data in the workspace context */
    so->arrayKeys = (BTArrayKeyInfo *) palloc(numArrayKeys * sizeof(BTArrayKeyInfo));
 
    /* Allocate space for ORDER procs used to help _bt_checkkeys */
    so->orderProcs = (FmgrInfo *) palloc(numberOfKeys * sizeof(FmgrInfo));
 
    /* Now process each array key */
    numArrayKeys = 0;
    for (int i = 0; i < numberOfKeys; i++)
    {
        FmgrInfo    sortproc;
        FmgrInfo   *sortprocp = &sortproc;
        Oid         elemtype;
        bool        reverse;
        ArrayType  *arrayval;
        int16       elmlen;
        bool        elmbyval;
        char        elmalign;
        int         num_elems;
        Datum      *elem_values;
        bool       *elem_nulls;
        int         num_nonnulls;
        int         j;
 
        cur = &arrayKeyData[i];
        if (!(cur->sk_flags & SK_SEARCHARRAY))
            continue;
 
        /*
         * First, deconstruct the array into elements.  Anything allocated
         * here (including a possibly detoasted array value) is in the
         * workspace context.
         */
        arrayval = DatumGetArrayTypeP(cur->sk_argument);
        /* We could cache this data, but not clear it's worth it */
        get_typlenbyvalalign(ARR_ELEMTYPE(arrayval),
                             &elmlen, &elmbyval, &elmalign);
        deconstruct_array(arrayval,
                          ARR_ELEMTYPE(arrayval),
                          elmlen, elmbyval, elmalign,
                          &elem_values, &elem_nulls, &num_elems);
 
        /*
         * Compress out any null elements.  We can ignore them since we assume
         * all btree operators are strict.
         */
        num_nonnulls = 0;
        for (j = 0; j < num_elems; j++)
        {
            if (!elem_nulls[j])
                elem_values[num_nonnulls++] = elem_values[j];
        }
 
        /* We could pfree(elem_nulls) now, but not worth the cycles */
 
        /* If there's no non-nulls, the scan qual is unsatisfiable */
        if (num_nonnulls == 0)
        {
            so->qual_ok = false;
            break;
        }
 
        /*
         * Determine the nominal datatype of the array elements.  We have to
         * support the convention that sk_subtype == InvalidOid means the
         * opclass input type; this is a hack to simplify life for
         * ScanKeyInit().
         */
        elemtype = cur->sk_subtype;
        if (elemtype == InvalidOid)
            elemtype = rel->rd_opcintype[cur->sk_attno - 1];
 
        /*
         * If the comparison operator is not equality, then the array qual
         * degenerates to a simple comparison against the smallest or largest
         * non-null array element, as appropriate.
         */
        switch (cur->sk_strategy)
        {
            case BTLessStrategyNumber:
            case BTLessEqualStrategyNumber:
                cur->sk_argument =
                    _bt_find_extreme_element(scan, cur, elemtype,
                                             BTGreaterStrategyNumber,
                                             elem_values, num_nonnulls);
                continue;
            case BTEqualStrategyNumber:
                /* proceed with rest of loop */
                break;
            case BTGreaterEqualStrategyNumber:
            case BTGreaterStrategyNumber:
                cur->sk_argument =
                    _bt_find_extreme_element(scan, cur, elemtype,
                                             BTLessStrategyNumber,
                                             elem_values, num_nonnulls);
                continue;
            default:
                elog(ERROR, "unrecognized StrategyNumber: %d",
                     (int) cur->sk_strategy);
                break;
        }
 
        /*
         * We'll need a 3-way ORDER proc to perform binary searches for the
         * next matching array element.  Set that up now.
         *
         * Array scan keys with cross-type equality operators will require a
         * separate same-type ORDER proc for sorting their array.  Otherwise,
         * sortproc just points to the same proc used during binary searches.
         */
        _bt_setup_array_cmp(scan, cur, elemtype,
                            &so->orderProcs[i], &sortprocp);
 
        /*
         * Sort the non-null elements and eliminate any duplicates.  We must
         * sort in the same ordering used by the index column, so that the
         * arrays can be advanced in lockstep with the scan's progress through
         * the index's key space.
         */
        reverse = (indoption[cur->sk_attno - 1] & INDOPTION_DESC) != 0;
        num_elems = _bt_sort_array_elements(cur, sortprocp, reverse,
                                            elem_values, num_nonnulls);
 
        if (origarrayatt == cur->sk_attno)
        {
            BTArrayKeyInfo *orig = &so->arrayKeys[origarraykey];
 
            /*
             * This array scan key is redundant with a previous equality
             * operator array scan key.  Merge the two arrays together to
             * eliminate contradictory non-intersecting elements (or try to).
             *
             * We merge this next array back into attribute's original array.
             */
            Assert(arrayKeyData[orig->scan_key].sk_attno == cur->sk_attno);
            Assert(arrayKeyData[orig->scan_key].sk_collation ==
                   cur->sk_collation);
            if (_bt_merge_arrays(scan, cur, sortprocp, reverse,
                                 origelemtype, elemtype,
                                 orig->elem_values, &orig->num_elems,
                                 elem_values, num_elems))
            {
                /* Successfully eliminated this array */
                pfree(elem_values);
 
                /*
                 * If no intersecting elements remain in the original array,
                 * the scan qual is unsatisfiable
                 */
                if (orig->num_elems == 0)
                {
                    so->qual_ok = false;
                    break;
                }
 
                /*
                 * Indicate to _bt_preprocess_keys caller that it must ignore
                 * this scan key
                 */
                cur->sk_strategy = InvalidStrategy;
                continue;
            }
 
            /*
             * Unable to merge this array with previous array due to a lack of
             * suitable cross-type opfamily support.  Will need to keep both
             * scan keys/arrays.
             */
        }
        else
        {
            /*
             * This array is the first for current index attribute.
             *
             * If it turns out to not be the last array (that is, if the next
             * array is redundantly applied to this same index attribute),
             * we'll then treat this array as the attribute's "original" array
             * when merging.
             */
            origarrayatt = cur->sk_attno;
            origarraykey = numArrayKeys;
            origelemtype = elemtype;
        }
 
        /*
         * And set up the BTArrayKeyInfo data.
         *
         * Note: _bt_preprocess_array_keys_final will fix-up each array's
         * scan_key field later on, after so->keyData[] has been finalized.
         */
        so->arrayKeys[numArrayKeys].scan_key = i;
        so->arrayKeys[numArrayKeys].num_elems = num_elems;
        so->arrayKeys[numArrayKeys].elem_values = elem_values;
        numArrayKeys++;
    }
 
    so->numArrayKeys = numArrayKeys;
 
    MemoryContextSwitchTo(oldContext);
 
    return arrayKeyData;
}
 
/*
 *  _bt_preprocess_array_keys_final() -- fix up array scan key references
 *
 * When _bt_preprocess_array_keys performed initial array preprocessing, it
 * set each array's array->scan_key to the array's arrayKeys[] entry offset
 * (that also work as references into the original scan->keyData[] array).
 * This function handles translation of the scan key references from the
 * BTArrayKeyInfo info array, from input scan key references (to the keys in
 * scan->keyData[]), into output references (to the keys in so->keyData[]).
 * Caller's keyDataMap[] array tells us how to perform this remapping.
 *
 * Also finalizes so->orderProcs[] for the scan.  Arrays already have an ORDER
 * proc, which might need to be repositioned to its so->keyData[]-wise offset
 * (very much like the remapping that we apply to array->scan_key references).
 * Non-array equality strategy scan keys (that survived preprocessing) don't
 * yet have an so->orderProcs[] entry, so we set one for them here.
 *
 * Also converts single-element array scan keys into equivalent non-array
 * equality scan keys, which decrements so->numArrayKeys.  It's possible that
 * this will leave this new btrescan without any arrays at all.  This isn't
 * necessary for correctness; it's just an optimization.  Non-array equality
 * scan keys are slightly faster than equivalent array scan keys at runtime.
 */
static void
_bt_preprocess_array_keys_final(IndexScanDesc scan, int *keyDataMap)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    Relation    rel = scan->indexRelation;
    int         arrayidx = 0;
    int         last_equal_output_ikey PG_USED_FOR_ASSERTS_ONLY = -1;
 
    Assert(so->qual_ok);
 
    /*
     * Nothing for us to do when _bt_preprocess_array_keys only had to deal
     * with array inequalities
     */
    if (so->numArrayKeys == 0)
        return;
 
    for (int output_ikey = 0; output_ikey < so->numberOfKeys; output_ikey++)
    {
        ScanKey     outkey = so->keyData + output_ikey;
        int         input_ikey;
        bool        found PG_USED_FOR_ASSERTS_ONLY = false;
 
        Assert(outkey->sk_strategy != InvalidStrategy);
 
        if (outkey->sk_strategy != BTEqualStrategyNumber)
            continue;
 
        input_ikey = keyDataMap[output_ikey];
 
        Assert(last_equal_output_ikey < output_ikey);
        Assert(last_equal_output_ikey < input_ikey);
        last_equal_output_ikey = output_ikey;
 
        /*
         * We're lazy about looking up ORDER procs for non-array keys, since
         * not all input keys become output keys.  Take care of it now.
         */
        if (!(outkey->sk_flags & SK_SEARCHARRAY))
        {
            Oid         elemtype;
 
            /* No need for an ORDER proc given an IS NULL scan key */
            if (outkey->sk_flags & SK_SEARCHNULL)
                continue;
 
            /*
             * A non-required scan key doesn't need an ORDER proc, either
             * (unless it's associated with an array, which this one isn't)
             */
            if (!(outkey->sk_flags & SK_BT_REQFWD))
                continue;
 
            elemtype = outkey->sk_subtype;
            if (elemtype == InvalidOid)
                elemtype = rel->rd_opcintype[outkey->sk_attno - 1];
 
            _bt_setup_array_cmp(scan, outkey, elemtype,
                                &so->orderProcs[output_ikey], NULL);
            continue;
        }
 
        /*
         * Reorder existing array scan key so->orderProcs[] entries.
         *
         * Doing this in-place is safe because preprocessing is required to
         * output all equality strategy scan keys in original input order
         * (among each group of entries against the same index attribute).
         * This is also the order that the arrays themselves appear in.
         */
        so->orderProcs[output_ikey] = so->orderProcs[input_ikey];
 
        /* Fix-up array->scan_key references for arrays */
        for (; arrayidx < so->numArrayKeys; arrayidx++)
        {
            BTArrayKeyInfo *array = &so->arrayKeys[arrayidx];
 
            Assert(array->num_elems > 0);
 
            if (array->scan_key == input_ikey)
            {
                /* found it */
                array->scan_key = output_ikey;
                found = true;
 
                /*
                 * Transform array scan keys that have exactly 1 element
                 * remaining (following all prior preprocessing) into
                 * equivalent non-array scan keys.
                 */
                if (array->num_elems == 1)
                {
                    outkey->sk_flags &= ~SK_SEARCHARRAY;
                    outkey->sk_argument = array->elem_values[0];
                    so->numArrayKeys--;
 
                    /* If we're out of array keys, we can quit right away */
                    if (so->numArrayKeys == 0)
                        return;
 
                    /* Shift other arrays forward */
                    memmove(array, array + 1,
                            sizeof(BTArrayKeyInfo) *
                            (so->numArrayKeys - arrayidx));
 
                    /*
                     * Don't increment arrayidx (there was an entry that was
                     * just shifted forward to the offset at arrayidx, which
                     * will still need to be matched)
                     */
                }
                else
                {
                    /* Match found, so done with this array */
                    arrayidx++;
                }
 
                break;
            }
        }
 
        Assert(found);
    }
 
    /*
     * Parallel index scans require space in shared memory to store the
     * current array elements (for arrays kept by preprocessing) to schedule
     * the next primitive index scan.  The underlying structure is protected
     * using a spinlock, so defensively limit its size.  In practice this can
     * only affect parallel scans that use an incomplete opfamily.
     */
    if (scan->parallel_scan && so->numArrayKeys > INDEX_MAX_KEYS)
        ereport(ERROR,
                (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
                 errmsg_internal("number of array scan keys left by preprocessing (%d) exceeds the maximum allowed by parallel btree index scans (%d)",
                                 so->numArrayKeys, INDEX_MAX_KEYS)));
}
 
/*
 * _bt_setup_array_cmp() -- Set up array comparison functions
 *
 * Sets ORDER proc in caller's orderproc argument, which is used during binary
 * searches of arrays during the index scan.  Also sets a same-type ORDER proc
 * in caller's *sortprocp argument, which is used when sorting the array.
 *
 * Preprocessing calls here with all equality strategy scan keys (when scan
 * uses equality array keys), including those not associated with any array.
 * See _bt_advance_array_keys for an explanation of why it'll need to treat
 * simple scalar equality scan keys as degenerate single element arrays.
 *
 * Caller should pass an orderproc pointing to space that'll store the ORDER
 * proc for the scan, and a *sortprocp pointing to its own separate space.
 * When calling here for a non-array scan key, sortprocp arg should be NULL.
 *
 * In the common case where we don't need to deal with cross-type operators,
 * only one ORDER proc is actually required by caller.  We'll set *sortprocp
 * to point to the same memory that caller's orderproc continues to point to.
 * Otherwise, *sortprocp will continue to point to caller's own space.  Either
 * way, *sortprocp will point to a same-type ORDER proc (since that's the only
 * safe way to sort/deduplicate the array associated with caller's scan key).
 */
static void
_bt_setup_array_cmp(IndexScanDesc scan, ScanKey skey, Oid elemtype,
                    FmgrInfo *orderproc, FmgrInfo **sortprocp)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    Relation    rel = scan->indexRelation;
    RegProcedure cmp_proc;
    Oid         opcintype = rel->rd_opcintype[skey->sk_attno - 1];
 
    Assert(skey->sk_strategy == BTEqualStrategyNumber);
    Assert(OidIsValid(elemtype));
 
    /*
     * If scankey operator is not a cross-type comparison, we can use the
     * cached comparison function; otherwise gotta look it up in the catalogs
     */
    if (elemtype == opcintype)
    {
        /* Set same-type ORDER procs for caller */
        *orderproc = *index_getprocinfo(rel, skey->sk_attno, BTORDER_PROC);
        if (sortprocp)
            *sortprocp = orderproc;
 
        return;
    }
 
    /*
     * Look up the appropriate cross-type comparison function in the opfamily.
     *
     * Use the opclass input type as the left hand arg type, and the array
     * element type as the right hand arg type (since binary searches use an
     * index tuple's attribute value to search for a matching array element).
     *
     * Note: it's possible that this would fail, if the opfamily is
     * incomplete, but only in cases where it's quite likely that _bt_first
     * would fail in just the same way (had we not failed before it could).
     */
    cmp_proc = get_opfamily_proc(rel->rd_opfamily[skey->sk_attno - 1],
                                 opcintype, elemtype, BTORDER_PROC);
    if (!RegProcedureIsValid(cmp_proc))
        elog(ERROR, "missing support function %d(%u,%u) for attribute %d of index \"%s\"",
             BTORDER_PROC, opcintype, elemtype, skey->sk_attno,
             RelationGetRelationName(rel));
 
    /* Set cross-type ORDER proc for caller */
    fmgr_info_cxt(cmp_proc, orderproc, so->arrayContext);
 
    /* Done if caller doesn't actually have an array they'll need to sort */
    if (!sortprocp)
        return;
 
    /*
     * Look up the appropriate same-type comparison function in the opfamily.
     *
     * Note: it's possible that this would fail, if the opfamily is
     * incomplete, but it seems quite unlikely that an opfamily would omit
     * non-cross-type comparison procs for any datatype that it supports at
     * all.
     */
    cmp_proc = get_opfamily_proc(rel->rd_opfamily[skey->sk_attno - 1],
                                 elemtype, elemtype, BTORDER_PROC);
    if (!RegProcedureIsValid(cmp_proc))
        elog(ERROR, "missing support function %d(%u,%u) for attribute %d of index \"%s\"",
             BTORDER_PROC, elemtype, elemtype,
             skey->sk_attno, RelationGetRelationName(rel));
 
    /* Set same-type ORDER proc for caller */
    fmgr_info_cxt(cmp_proc, *sortprocp, so->arrayContext);
}
 
/*
 * _bt_find_extreme_element() -- get least or greatest array element
 *
 * scan and skey identify the index column, whose opfamily determines the
 * comparison semantics.  strat should be BTLessStrategyNumber to get the
 * least element, or BTGreaterStrategyNumber to get the greatest.
 */
static Datum
_bt_find_extreme_element(IndexScanDesc scan, ScanKey skey, Oid elemtype,
                         StrategyNumber strat,
                         Datum *elems, int nelems)
{
    Relation    rel = scan->indexRelation;
    Oid         cmp_op;
    RegProcedure cmp_proc;
    FmgrInfo    flinfo;
    Datum       result;
    int         i;
 
    /*
     * Look up the appropriate comparison operator in the opfamily.
     *
     * Note: it's possible that this would fail, if the opfamily is
     * incomplete, but it seems quite unlikely that an opfamily would omit
     * non-cross-type comparison operators for any datatype that it supports
     * at all.
     */
    Assert(skey->sk_strategy != BTEqualStrategyNumber);
    Assert(OidIsValid(elemtype));
    cmp_op = get_opfamily_member(rel->rd_opfamily[skey->sk_attno - 1],
                                 elemtype,
                                 elemtype,
                                 strat);
    if (!OidIsValid(cmp_op))
        elog(ERROR, "missing operator %d(%u,%u) in opfamily %u",
             strat, elemtype, elemtype,
             rel->rd_opfamily[skey->sk_attno - 1]);
    cmp_proc = get_opcode(cmp_op);
    if (!RegProcedureIsValid(cmp_proc))
        elog(ERROR, "missing oprcode for operator %u", cmp_op);
 
    fmgr_info(cmp_proc, &flinfo);
 
    Assert(nelems > 0);
    result = elems[0];
    for (i = 1; i < nelems; i++)
    {
        if (DatumGetBool(FunctionCall2Coll(&flinfo,
                                           skey->sk_collation,
                                           elems[i],
                                           result)))
            result = elems[i];
    }
 
    return result;
}
 
/*
 * _bt_sort_array_elements() -- sort and de-dup array elements
 *
 * The array elements are sorted in-place, and the new number of elements
 * after duplicate removal is returned.
 *
 * skey identifies the index column whose opfamily determines the comparison
 * semantics, and sortproc is a corresponding ORDER proc.  If reverse is true,
 * we sort in descending order.
 */
static int
_bt_sort_array_elements(ScanKey skey, FmgrInfo *sortproc, bool reverse,
                        Datum *elems, int nelems)
{
    BTSortArrayContext cxt;
 
    if (nelems <= 1)
        return nelems;          /* no work to do */
 
    /* Sort the array elements */
    cxt.sortproc = sortproc;
    cxt.collation = skey->sk_collation;
    cxt.reverse = reverse;
    qsort_arg(elems, nelems, sizeof(Datum),
              _bt_compare_array_elements, &cxt);
 
    /* Now scan the sorted elements and remove duplicates */
    return qunique_arg(elems, nelems, sizeof(Datum),
                       _bt_compare_array_elements, &cxt);
}
 
/*
 * _bt_merge_arrays() -- merge next array's elements into an original array
 *
 * Called when preprocessing encounters a pair of array equality scan keys,
 * both against the same index attribute (during initial array preprocessing).
 * Merging reorganizes caller's original array (the left hand arg) in-place,
 * without ever copying elements from one array into the other. (Mixing the
 * elements together like this would be wrong, since they don't necessarily
 * use the same underlying element type, despite all the other similarities.)
 *
 * Both arrays must have already been sorted and deduplicated by calling
 * _bt_sort_array_elements.  sortproc is the same-type ORDER proc that was
 * just used to sort and deduplicate caller's "next" array.  We'll usually be
 * able to reuse that order PROC to merge the arrays together now.  If not,
 * then we'll perform a separate ORDER proc lookup.
 *
 * If the opfamily doesn't supply a complete set of cross-type ORDER procs we
 * may not be able to determine which elements are contradictory.  If we have
 * the required ORDER proc then we return true (and validly set *nelems_orig),
 * guaranteeing that at least the next array can be considered redundant.  We
 * return false if the required comparisons cannot not be made (caller must
 * keep both arrays when this happens).
 */
static bool
_bt_merge_arrays(IndexScanDesc scan, ScanKey skey, FmgrInfo *sortproc,
                 bool reverse, Oid origelemtype, Oid nextelemtype,
                 Datum *elems_orig, int *nelems_orig,
                 Datum *elems_next, int nelems_next)
{
    Relation    rel = scan->indexRelation;
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    BTSortArrayContext cxt;
    int         nelems_orig_start = *nelems_orig,
                nelems_orig_merged = 0;
    FmgrInfo   *mergeproc = sortproc;
    FmgrInfo    crosstypeproc;
 
    Assert(skey->sk_strategy == BTEqualStrategyNumber);
    Assert(OidIsValid(origelemtype) && OidIsValid(nextelemtype));
 
    if (origelemtype != nextelemtype)
    {
        RegProcedure cmp_proc;
 
        /*
         * Cross-array-element-type merging is required, so can't just reuse
         * sortproc when merging
         */
        cmp_proc = get_opfamily_proc(rel->rd_opfamily[skey->sk_attno - 1],
                                     origelemtype, nextelemtype, BTORDER_PROC);
        if (!RegProcedureIsValid(cmp_proc))
        {
            /* Can't make the required comparisons */
            return false;
        }
 
        /* We have all we need to determine redundancy/contradictoriness */
        mergeproc = &crosstypeproc;
        fmgr_info_cxt(cmp_proc, mergeproc, so->arrayContext);
    }
 
    cxt.sortproc = mergeproc;
    cxt.collation = skey->sk_collation;
    cxt.reverse = reverse;
 
    for (int i = 0, j = 0; i < nelems_orig_start && j < nelems_next;)
    {
        Datum      *oelem = elems_orig + i,
                   *nelem = elems_next + j;
        int         res = _bt_compare_array_elements(oelem, nelem, &cxt);
 
        if (res == 0)
        {
            elems_orig[nelems_orig_merged++] = *oelem;
            i++;
            j++;
        }
        else if (res < 0)
            i++;
        else                    /* res > 0 */
            j++;
    }
 
    *nelems_orig = nelems_orig_merged;
 
    return true;
}
 
/*
 * Compare an array scan key to a scalar scan key, eliminating contradictory
 * array elements such that the scalar scan key becomes redundant.
 *
 * Array elements can be eliminated as contradictory when excluded by some
 * other operator on the same attribute.  For example, with an index scan qual
 * "WHERE a IN (1, 2, 3) AND a < 2", all array elements except the value "1"
 * are eliminated, and the < scan key is eliminated as redundant.  Cases where
 * every array element is eliminated by a redundant scalar scan key have an
 * unsatisfiable qual, which we handle by setting *qual_ok=false for caller.
 *
 * If the opfamily doesn't supply a complete set of cross-type ORDER procs we
 * may not be able to determine which elements are contradictory.  If we have
 * the required ORDER proc then we return true (and validly set *qual_ok),
 * guaranteeing that at least the scalar scan key can be considered redundant.
 * We return false if the comparison could not be made (caller must keep both
 * scan keys when this happens).
 */
static bool
_bt_compare_array_scankey_args(IndexScanDesc scan, ScanKey arraysk, ScanKey skey,
                               FmgrInfo *orderproc, BTArrayKeyInfo *array,
                               bool *qual_ok)
{
    Relation    rel = scan->indexRelation;
    Oid         opcintype = rel->rd_opcintype[arraysk->sk_attno - 1];
    int         cmpresult = 0,
                cmpexact = 0,
                matchelem,
                new_nelems = 0;
    FmgrInfo    crosstypeproc;
    FmgrInfo   *orderprocp = orderproc;
 
    Assert(arraysk->sk_attno == skey->sk_attno);
    Assert(array->num_elems > 0);
    Assert(!(arraysk->sk_flags & (SK_ISNULL | SK_ROW_HEADER | SK_ROW_MEMBER)));
    Assert((arraysk->sk_flags & SK_SEARCHARRAY) &&
           arraysk->sk_strategy == BTEqualStrategyNumber);
    Assert(!(skey->sk_flags & (SK_ISNULL | SK_ROW_HEADER | SK_ROW_MEMBER)));
    Assert(!(skey->sk_flags & SK_SEARCHARRAY) ||
           skey->sk_strategy != BTEqualStrategyNumber);
 
    /*
     * _bt_binsrch_array_skey searches an array for the entry best matching a
     * datum of opclass input type for the index's attribute (on-disk type).
     * We can reuse the array's ORDER proc whenever the non-array scan key's
     * type is a match for the corresponding attribute's input opclass type.
     * Otherwise, we have to do another ORDER proc lookup so that our call to
     * _bt_binsrch_array_skey applies the correct comparator.
     *
     * Note: we have to support the convention that sk_subtype == InvalidOid
     * means the opclass input type; this is a hack to simplify life for
     * ScanKeyInit().
     */
    if (skey->sk_subtype != opcintype && skey->sk_subtype != InvalidOid)
    {
        RegProcedure cmp_proc;
        Oid         arraysk_elemtype;
 
        /*
         * Need an ORDER proc lookup to detect redundancy/contradictoriness
         * with this pair of scankeys.
         *
         * Scalar scan key's argument will be passed to _bt_compare_array_skey
         * as its tupdatum/lefthand argument (rhs arg is for array elements).
         */
        arraysk_elemtype = arraysk->sk_subtype;
        if (arraysk_elemtype == InvalidOid)
            arraysk_elemtype = rel->rd_opcintype[arraysk->sk_attno - 1];
        cmp_proc = get_opfamily_proc(rel->rd_opfamily[arraysk->sk_attno - 1],
                                     skey->sk_subtype, arraysk_elemtype,
                                     BTORDER_PROC);
        if (!RegProcedureIsValid(cmp_proc))
        {
            /* Can't make the comparison */
            *qual_ok = false;   /* suppress compiler warnings */
            return false;
        }
 
        /* We have all we need to determine redundancy/contradictoriness */
        orderprocp = &crosstypeproc;
        fmgr_info(cmp_proc, orderprocp);
    }
 
    matchelem = _bt_binsrch_array_skey(orderprocp, false,
                                       NoMovementScanDirection,
                                       skey->sk_argument, false, array,
                                       arraysk, &cmpresult);
 
    switch (skey->sk_strategy)
    {
        case BTLessStrategyNumber:
            cmpexact = 1;       /* exclude exact match, if any */
            /* FALL THRU */
        case BTLessEqualStrategyNumber:
            if (cmpresult >= cmpexact)
                matchelem++;
            /* Resize, keeping elements from the start of the array */
            new_nelems = matchelem;
            break;
        case BTEqualStrategyNumber:
            if (cmpresult != 0)
            {
                /* qual is unsatisfiable */
                new_nelems = 0;
            }
            else
            {
                /* Shift matching element to the start of the array, resize */
                array->elem_values[0] = array->elem_values[matchelem];
                new_nelems = 1;
            }
            break;
        case BTGreaterEqualStrategyNumber:
            cmpexact = 1;       /* include exact match, if any */
            /* FALL THRU */
        case BTGreaterStrategyNumber:
            if (cmpresult >= cmpexact)
                matchelem++;
            /* Shift matching elements to the start of the array, resize */
            new_nelems = array->num_elems - matchelem;
            memmove(array->elem_values, array->elem_values + matchelem,
                    sizeof(Datum) * new_nelems);
            break;
        default:
            elog(ERROR, "unrecognized StrategyNumber: %d",
                 (int) skey->sk_strategy);
            break;
    }
 
    Assert(new_nelems >= 0);
    Assert(new_nelems <= array->num_elems);
 
    array->num_elems = new_nelems;
    *qual_ok = new_nelems > 0;
 
    return true;
}
 
/*
 * qsort_arg comparator for sorting array elements
 */
static int
_bt_compare_array_elements(const void *a, const void *b, void *arg)
{
    Datum       da = *((const Datum *) a);
    Datum       db = *((const Datum *) b);
    BTSortArrayContext *cxt = (BTSortArrayContext *) arg;
    int32       compare;
 
    compare = DatumGetInt32(FunctionCall2Coll(cxt->sortproc,
                                              cxt->collation,
                                              da, db));
    if (cxt->reverse)
        INVERT_COMPARE_RESULT(compare);
    return compare;
}
 
/*
 * _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);
 
    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.
 */
static 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_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_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)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    int         i;
 
    Assert(so->numArrayKeys);
    Assert(so->qual_ok);
 
    for (i = 0; i < so->numArrayKeys; i++)
    {
        BTArrayKeyInfo *curArrayKey = &so->arrayKeys[i];
        ScanKey     skey = &so->keyData[curArrayKey->scan_key];
 
        Assert(curArrayKey->num_elems > 0);
        Assert(skey->sk_flags & SK_SEARCHARRAY);
 
        if (ScanDirectionIsBackward(dir))
            curArrayKey->cur_elem = curArrayKey->num_elems - 1;
        else
            curArrayKey->cur_elem = 0;
        skey->sk_argument = curArrayKey->elem_values[curArrayKey->cur_elem];
    }
    so->scanBehind = 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)
{
    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 *curArrayKey = &so->arrayKeys[i];
        ScanKey     skey = &so->keyData[curArrayKey->scan_key];
        int         cur_elem = curArrayKey->cur_elem;
        int         num_elems = curArrayKey->num_elems;
        bool        rolled = false;
 
        if (ScanDirectionIsForward(dir) && ++cur_elem >= num_elems)
        {
            cur_elem = 0;
            rolled = true;
        }
        else if (ScanDirectionIsBackward(dir) && --cur_elem < 0)
        {
            cur_elem = num_elems - 1;
            rolled = true;
        }
 
        curArrayKey->cur_elem = cur_elem;
        skey->sk_argument = curArrayKey->elem_values[cur_elem];
        if (!rolled)
            return true;
 
        /* Need to advance next array key, if any */
    }
 
    /*
     * The array keys are now exhausted.  (There isn't actually a distinct
     * state that represents array exhaustion, since index scans don't always
     * end after btgettuple returns "false".)
     *
     * 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 would overlook matching
     * tuples if and when the scan's direction was subsequently reversed.
     */
    _bt_start_array_keys(scan, -dir);
 
    return false;
}
 
/*
 * _bt_rewind_nonrequired_arrays() -- Rewind non-required arrays
 *
 * Called when _bt_advance_array_keys decides to start a new primitive index
 * scan on the basis of the current scan position being before the position
 * that _bt_first is capable of repositioning the scan to by applying an
 * inequality operator required in the opposite-to-scan direction only.
 *
 * Although equality strategy scan keys (for both arrays and non-arrays alike)
 * are either marked required in both directions or in neither direction,
 * there is a sense in which non-required arrays behave like required arrays.
 * With a qual such as "WHERE a IN (100, 200) AND b >= 3 AND c IN (5, 6, 7)",
 * the scan key on "c" is non-required, but nevertheless enables positioning
 * the scan at the first tuple >= "(100, 3, 5)" on the leaf level during the
 * first descent of the tree by _bt_first.  Later on, there could also be a
 * second descent, that places the scan right before tuples >= "(200, 3, 5)".
 * _bt_first must never be allowed to build an insertion scan key whose "c"
 * entry is set to a value other than 5, the "c" array's first element/value.
 * (Actually, it's the first in the current scan direction.  This example uses
 * a forward scan.)
 *
 * Calling here resets the array scan key elements for the scan's non-required
 * arrays.  This is strictly necessary for correctness in a subset of cases
 * involving "required in opposite direction"-triggered primitive index scans.
 * Not all callers are at risk of _bt_first using a non-required array like
 * this, but advancement always resets the arrays when another primitive scan
 * is scheduled, just to keep things simple.  Array advancement even makes
 * sure to reset non-required arrays during scans that have no inequalities.
 * (Advancement still won't call here when there are no inequalities, though
 * that's just because it's all handled indirectly instead.)
 *
 * Note: _bt_verify_arrays_bt_first is called by an assertion to enforce that
 * everybody got this right.
 */
static void
_bt_rewind_nonrequired_arrays(IndexScanDesc scan, ScanDirection dir)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    int         arrayidx = 0;
 
    for (int ikey = 0; ikey < so->numberOfKeys; ikey++)
    {
        ScanKey     cur = so->keyData + ikey;
        BTArrayKeyInfo *array = NULL;
        int         first_elem_dir;
 
        if (!(cur->sk_flags & SK_SEARCHARRAY) ||
            cur->sk_strategy != BTEqualStrategyNumber)
            continue;
 
        array = &so->arrayKeys[arrayidx++];
        Assert(array->scan_key == ikey);
 
        if ((cur->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD)))
            continue;
 
        if (ScanDirectionIsForward(dir))
            first_elem_dir = 0;
        else
            first_elem_dir = array->num_elems - 1;
 
        if (array->cur_elem != first_elem_dir)
        {
            array->cur_elem = first_elem_dir;
            cur->sk_argument = array->elem_values[first_elem_dir];
        }
    }
}
 
/*
 * _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 distinguishing 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);
 
        result = _bt_compare_array_skey(&so->orderProcs[ikey],
                                        tupdatum, tupnull,
                                        cur->sk_argument, cur);
 
        /*
         * 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;
}
 
/*
 * _bt_start_prim_scan() -- start scheduled primitive index scan?
 *
 * Returns true if _bt_checkkeys scheduled another primitive index scan, just
 * as the last one ended.  Otherwise returns false, indicating that the array
 * keys are now fully exhausted.
 *
 * Only call here during scans with one or more equality type array scan keys,
 * after _bt_first or _bt_next return false.
 */
bool
_bt_start_prim_scan(IndexScanDesc scan, ScanDirection dir)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
 
    Assert(so->numArrayKeys);
 
    /* scanBehind flag doesn't persist across primitive index scans - reset */
    so->scanBehind = false;
 
    /*
     * Array keys are advanced within _bt_checkkeys when the scan reaches the
     * leaf level (more precisely, they're advanced when the scan reaches the
     * end of each distinct set of array elements).  This process avoids
     * repeat access to leaf pages (across multiple primitive index scans) by
     * advancing the scan's array keys when it allows the primitive index scan
     * to find nearby matching tuples (or when it eliminates ranges of array
     * key space that can't possibly be satisfied by any index tuple).
     *
     * _bt_checkkeys sets a simple flag variable to schedule another primitive
     * index scan.  The flag tells us what to do.
     *
     * We cannot rely on _bt_first always reaching _bt_checkkeys.  There are
     * various cases where that won't happen.  For example, if the index is
     * completely empty, then _bt_first won't call _bt_readpage/_bt_checkkeys.
     * We also don't expect a call to _bt_checkkeys during searches for a
     * non-existent value that happens to be lower/higher than any existing
     * value in the index.
     *
     * We don't require special handling for these cases -- we don't need to
     * be explicitly instructed to _not_ perform another primitive index scan.
     * It's up to code under the control of _bt_first to always set the flag
     * when another primitive index scan will be required.
     *
     * This works correctly, even with the tricky cases listed above, which
     * all involve access to leaf pages "near the boundaries of the key space"
     * (whether it's from a leftmost/rightmost page, or an imaginary empty
     * leaf root page).  If _bt_checkkeys cannot be reached by a primitive
     * index scan for one set of array keys, then it also won't be reached for
     * any later set ("later" in terms of the direction that we scan the index
     * and advance the arrays).  The array keys won't have advanced in these
     * cases, but that's the correct behavior (even _bt_advance_array_keys
     * won't always advance the arrays at the point they become "exhausted").
     */
    if (so->needPrimScan)
    {
        Assert(_bt_verify_arrays_bt_first(scan, dir));
 
        /*
         * Flag was set -- must call _bt_first again, which will reset the
         * scan's needPrimScan flag
         */
        return true;
    }
 
    /* The top-level index scan ran out of tuples in this scan direction */
    if (scan->parallel_scan != NULL)
        _bt_parallel_done(scan);
 
    return false;
}
 
/*
 * _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.  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,
                has_required_opposite_direction_only = false,
                oppodir_inequality_sktrig = false,
                all_required_satisfied = true,
                all_satisfied = true;
 
    if (sktrig_required)
    {
        /*
         * Precondition array state assertion
         */
        Assert(!_bt_tuple_before_array_skeys(scan, dir, tuple, tupdesc,
                                             tupnatts, false, 0, NULL));
 
        so->scanBehind = false; /* reset */
 
        /*
         * Required scan key wasn't satisfied, so required arrays will have to
         * advance.  Invalidate page-level state that tracks whether the
         * scan's required-in-opposite-direction-only keys are known to be
         * satisfied by page's remaining tuples.
         */
        pstate->firstmatch = false;
 
        /* Shouldn't have to invalidate 'prechecked', though */
        Assert(!pstate->prechecked);
 
        /*
         * 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;
    }
 
    Assert(_bt_verify_keys_with_arraykeys(scan));
 
    for (int ikey = 0; ikey < so->numberOfKeys; ikey++)
    {
        ScanKey     cur = so->keyData + ikey;
        BTArrayKeyInfo *array = NULL;
        Datum       tupdatum;
        bool        required = false,
                    required_opposite_direction_only = 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 =
                    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))
        {
            Assert(sktrig_required);
 
            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;
 
            /*
             * Set a flag that remembers that this was an inequality required
             * in the opposite scan direction only, that nevertheless
             * triggered the call here.
             *
             * This only happens when an inequality operator (which must be
             * strict) encounters a group of NULLs that indicate the end of
             * non-NULL values for tuples in the current scan direction.
             */
            if (unlikely(required_opposite_direction_only))
                oppodir_inequality_sktrig = true;
 
            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)
        {
            int         final_elem_dir;
 
            if (ScanDirectionIsBackward(dir) || !array)
                final_elem_dir = 0;
            else
                final_elem_dir = array->num_elems - 1;
 
            if (array && array->cur_elem != final_elem_dir)
            {
                array->cur_elem = final_elem_dir;
                cur->sk_argument = array->elem_values[final_elem_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)
        {
            int         first_elem_dir;
 
            if (ScanDirectionIsForward(dir) || !array)
                first_elem_dir = 0;
            else
                first_elem_dir = array->num_elems - 1;
 
            if (array && array->cur_elem != first_elem_dir)
            {
                array->cur_elem = first_elem_dir;
                cur->sk_argument = array->elem_values[first_elem_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 for closest match that's available from the array
             */
            set_elem = _bt_binsrch_array_skey(&so->orderProcs[ikey],
                                              cur_elem_trig, dir,
                                              tupdatum, tupnull, array, cur,
                                              &result);
 
            Assert(set_elem >= 0 && set_elem < array->num_elems);
        }
        else
        {
            Assert(sktrig_required && 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 (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 (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 set_elem isn't an exact match */
        if (array && array->cur_elem != set_elem)
        {
            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))
        goto end_toplevel_scan;
 
    Assert(_bt_verify_keys_with_arraykeys(scan));
 
    /*
     * 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'.
     */
    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, false, false,
                              &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. (Actually, oppodir_inequality_sktrig trigger
     * scan keys are tracked by all_required_satisfied, since it's convenient
     * for _bt_check_compare to behave as if they are required in the current
     * scan direction to deal with NULLs.  We'll account for that separately.)
     */
    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 check 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_checkkeys (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.
     *
     * You can think of this as a speculative bet on what the scan is likely
     * to find on the next page.  It's not much of a gamble, though, since the
     * untruncated prefix of attributes must strictly satisfy the new qual
     * (though it's okay if any non-required scan keys fail to be satisfied).
     */
    if (so->scanBehind && has_required_opposite_direction_only)
    {
        /*
         * However, we avoid this behavior whenever the scan involves a scan
         * key required in the opposite direction to the scan only, along with
         * a finaltup with at least one truncated attribute that's associated
         * with a scan key marked required (required in either direction).
         *
         * _bt_check_compare simply won't stop the scan for a scan key that's
         * marked required in the opposite scan direction only.  That leaves
         * us without any reliable way of reconsidering any opposite-direction
         * inequalities if it turns out that starting a new primitive index
         * scan will allow _bt_first to skip ahead by a great many leaf pages
         * (see next section for details of how that works).
         */
        goto new_prim_scan;
    }
 
    /*
     * 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.  We need a separate test for this case so that
     * we don't miss our only opportunity to skip over such a group of pages.
     * (_bt_first is expected to skip over the group of NULLs by applying a
     * similar "deduce NOT NULL" rule, where it finishes its insertion scan
     * key by consing up an explicit SK_SEARCHNOTNULL key.)
     *
     * Apply a test against finaltup to detect and recover from these 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.
     */
    if (has_required_opposite_direction_only && pstate->finaltup &&
        (all_required_satisfied || oppodir_inequality_sktrig))
    {
        int         nfinaltupatts = BTreeTupleGetNAtts(pstate->finaltup, rel);
        ScanDirection flipped;
        bool        continuescanflip;
        int         opsktrig;
 
        /*
         * We're checking finaltup (which is usually not caller's tuple), so
         * cannot reuse work from caller's earlier _bt_check_compare call.
         *
         * Flip the scan direction when calling _bt_check_compare this time,
         * so that it will set continuescanflip=false when it encounters an
         * inequality required in the opposite scan direction.
         */
        Assert(!so->scanBehind);
        opsktrig = 0;
        flipped = -dir;
        _bt_check_compare(scan, flipped,
                          pstate->finaltup, nfinaltupatts, tupdesc,
                          false, false, false,
                          &continuescanflip, &opsktrig);
 
        /*
         * If we ended up here due to the all_required_satisfied criteria,
         * test opsktrig in a way that ensures that finaltup contains the same
         * prefix of key columns as caller's tuple (a prefix that satisfies
         * earlier required-in-current-direction scan keys).
         *
         * If we ended up here due to the oppodir_inequality_sktrig criteria,
         * test opsktrig in a way that ensures that the same scan key that our
         * caller found to be unsatisfied (by the scan's tuple) was also the
         * one unsatisfied just now (by finaltup).  That way we'll only start
         * a new primitive scan when we're sure that both tuples _don't_ share
         * the same prefix of satisfied equality-constrained attribute values,
         * and that finaltup has a non-NULL attribute value indicated by the
         * unsatisfied scan key at offset opsktrig/sktrig.  (This depends on
         * _bt_check_compare not caring about the direction that inequalities
         * are required in whenever NULL attribute values are unsatisfied.  It
         * only cares about the scan direction, and its relationship to
         * whether NULLs are stored first or last relative to non-NULLs.)
         */
        Assert(all_required_satisfied != oppodir_inequality_sktrig);
        if (unlikely(!continuescanflip &&
                     ((all_required_satisfied && opsktrig > sktrig) ||
                      (oppodir_inequality_sktrig && opsktrig >= sktrig))))
        {
            Assert(so->keyData[opsktrig].sk_strategy != BTEqualStrategyNumber);
 
            /*
             * Make sure that any non-required arrays are set to the first
             * array element for the current scan direction
             */
            _bt_rewind_nonrequired_arrays(scan, dir);
 
            goto new_prim_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)
    {
        /* Optimization: skip by setting "look ahead" mechanism's offnum */
        Assert(ScanDirectionIsForward(dir));
        pstate->skip = pstate->maxoff + 1;
    }
 
    /* Caller's tuple doesn't match the new qual */
    return false;
 
new_prim_scan:
 
    /*
     * End this primitive index scan, but schedule another.
     *
     * Note: If the scan direction happens to change, this scheduled primitive
     * index scan won't go ahead after all.
     */
    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, pstate->prev_scan_page);
 
    /* 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;   /* ...don't call _bt_first again, though */
 
    /* Caller's tuple doesn't match any qual */
    return false;
}
 
/*
 *  _bt_preprocess_keys() -- Preprocess scan keys
 *
 * The given search-type keys (taken from scan->keyData[])
 * are copied to so->keyData[] with possible transformation.
 * scan->numberOfKeys is the number of input keys, so->numberOfKeys gets
 * the number of output keys (possibly less, never greater).
 *
 * The output keys are marked with additional sk_flags bits beyond the
 * system-standard bits supplied by the caller.  The DESC and NULLS_FIRST
 * indoption bits for the relevant index attribute are copied into the flags.
 * Also, for a DESC column, we commute (flip) all the sk_strategy numbers
 * so that the index sorts in the desired direction.
 *
 * One key purpose of this routine is to discover which scan keys must be
 * satisfied to continue the scan.  It also attempts to eliminate redundant
 * keys and detect contradictory keys.  (If the index opfamily provides
 * incomplete sets of cross-type operators, we may fail to detect redundant
 * or contradictory keys, but we can survive that.)
 *
 * The output keys must be sorted by index attribute.  Presently we expect
 * (but verify) that the input keys are already so sorted --- this is done
 * by match_clauses_to_index() in indxpath.c.  Some reordering of the keys
 * within each attribute may be done as a byproduct of the processing here.
 * That process must leave array scan keys (within an attribute) in the same
 * order as corresponding entries from the scan's BTArrayKeyInfo array info.
 *
 * The output keys are marked with flags SK_BT_REQFWD and/or SK_BT_REQBKWD
 * if they must be satisfied in order to continue the scan forward or backward
 * respectively.  _bt_checkkeys uses these flags.  For example, if the quals
 * are "x = 1 AND y < 4 AND z < 5", then _bt_checkkeys will reject a tuple
 * (1,2,7), but we must continue the scan in case there are tuples (1,3,z).
 * But once we reach tuples like (1,4,z) we can stop scanning because no
 * later tuples could match.  This is reflected by marking the x and y keys,
 * but not the z key, with SK_BT_REQFWD.  In general, the keys for leading
 * attributes with "=" keys are marked both SK_BT_REQFWD and SK_BT_REQBKWD.
 * For the first attribute without an "=" key, any "<" and "<=" keys are
 * marked SK_BT_REQFWD while any ">" and ">=" keys are marked SK_BT_REQBKWD.
 * This can be seen to be correct by considering the above example.  Note
 * in particular that if there are no keys for a given attribute, the keys for
 * subsequent attributes can never be required; for instance "WHERE y = 4"
 * requires a full-index scan.
 *
 * If possible, redundant keys are eliminated: we keep only the tightest
 * >/>= bound and the tightest </<= bound, and if there's an = key then
 * that's the only one returned.  (So, we return either a single = key,
 * or one or two boundary-condition keys for each attr.)  However, if we
 * cannot compare two keys for lack of a suitable cross-type operator,
 * we cannot eliminate either.  If there are two such keys of the same
 * operator strategy, the second one is just pushed into the output array
 * without further processing here.  We may also emit both >/>= or both
 * </<= keys if we can't compare them.  The logic about required keys still
 * works if we don't eliminate redundant keys.
 *
 * Note that one reason we need direction-sensitive required-key flags is
 * precisely that we may not be able to eliminate redundant keys.  Suppose
 * we have "x > 4::int AND x > 10::bigint", and we are unable to determine
 * which key is more restrictive for lack of a suitable cross-type operator.
 * _bt_first will arbitrarily pick one of the keys to do the initial
 * positioning with.  If it picks x > 4, then the x > 10 condition will fail
 * until we reach index entries > 10; but we can't stop the scan just because
 * x > 10 is failing.  On the other hand, if we are scanning backwards, then
 * failure of either key is indeed enough to stop the scan.  (In general, when
 * inequality keys are present, the initial-positioning code only promises to
 * position before the first possible match, not exactly at the first match,
 * for a forward scan; or after the last match for a backward scan.)
 *
 * As a byproduct of this work, we can detect contradictory quals such
 * as "x = 1 AND x > 2".  If we see that, we return so->qual_ok = false,
 * indicating the scan need not be run at all since no tuples can match.
 * (In this case we do not bother completing the output key array!)
 * Again, missing cross-type operators might cause us to fail to prove the
 * quals contradictory when they really are, but the scan will work correctly.
 *
 * Row comparison keys are currently also treated without any smarts:
 * we just transfer them into the preprocessed array without any
 * editorialization.  We can treat them the same as an ordinary inequality
 * comparison on the row's first index column, for the purposes of the logic
 * about required keys.
 *
 * Note: the reason we have to copy the preprocessed scan keys into private
 * storage is that we are modifying the array based on comparisons of the
 * key argument values, which could change on a rescan.  Therefore we can't
 * overwrite the source data.
 */
void
_bt_preprocess_keys(IndexScanDesc scan)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    int         numberOfKeys = scan->numberOfKeys;
    int16      *indoption = scan->indexRelation->rd_indoption;
    int         new_numberOfKeys;
    int         numberOfEqualCols;
    ScanKey     inkeys;
    ScanKey     outkeys;
    ScanKey     cur;
    BTScanKeyPreproc xform[BTMaxStrategyNumber];
    bool        test_result;
    int         i,
                j;
    AttrNumber  attno;
    ScanKey     arrayKeyData;
    int        *keyDataMap = NULL;
    int         arrayidx = 0;
 
    if (so->numberOfKeys > 0)
    {
        /*
         * Only need to do preprocessing once per btrescan, at most.  All
         * calls after the first are handled as no-ops.
         *
         * If there are array scan keys in so->keyData[], then the now-current
         * array elements must already be present in each array's scan key.
         * Verify that that happened using an assertion.
         */
        Assert(_bt_verify_keys_with_arraykeys(scan));
        return;
    }
 
    /* initialize result variables */
    so->qual_ok = true;
    so->numberOfKeys = 0;
 
    if (numberOfKeys < 1)
        return;                 /* done if qual-less scan */
 
    /* If any keys are SK_SEARCHARRAY type, set up array-key info */
    arrayKeyData = _bt_preprocess_array_keys(scan);
    if (!so->qual_ok)
    {
        /* unmatchable array, so give up */
        return;
    }
 
    /*
     * Treat arrayKeyData[] (a partially preprocessed copy of scan->keyData[])
     * as our input if _bt_preprocess_array_keys just allocated it, else just
     * use scan->keyData[]
     */
    if (arrayKeyData)
    {
        inkeys = arrayKeyData;
 
        /* Also maintain keyDataMap for remapping so->orderProc[] later */
        keyDataMap = MemoryContextAlloc(so->arrayContext,
                                        numberOfKeys * sizeof(int));
    }
    else
        inkeys = scan->keyData;
 
    outkeys = so->keyData;
    cur = &inkeys[0];
    /* we check that input keys are correctly ordered */
    if (cur->sk_attno < 1)
        elog(ERROR, "btree index keys must be ordered by attribute");
 
    /* We can short-circuit most of the work if there's just one key */
    if (numberOfKeys == 1)
    {
        /* Apply indoption to scankey (might change sk_strategy!) */
        if (!_bt_fix_scankey_strategy(cur, indoption))
            so->qual_ok = false;
        memcpy(outkeys, cur, sizeof(ScanKeyData));
        so->numberOfKeys = 1;
        /* We can mark the qual as required if it's for first index col */
        if (cur->sk_attno == 1)
            _bt_mark_scankey_required(outkeys);
        if (arrayKeyData)
        {
            /*
             * Don't call _bt_preprocess_array_keys_final in this fast path
             * (we'll miss out on the single value array transformation, but
             * that's not nearly as important when there's only one scan key)
             */
            Assert(cur->sk_flags & SK_SEARCHARRAY);
            Assert(cur->sk_strategy != BTEqualStrategyNumber ||
                   (so->arrayKeys[0].scan_key == 0 &&
                    OidIsValid(so->orderProcs[0].fn_oid)));
        }
 
        return;
    }
 
    /*
     * Otherwise, do the full set of pushups.
     */
    new_numberOfKeys = 0;
    numberOfEqualCols = 0;
 
    /*
     * Initialize for processing of keys for attr 1.
     *
     * xform[i] points to the currently best scan key of strategy type i+1; it
     * is NULL if we haven't yet found such a key for this attr.
     */
    attno = 1;
    memset(xform, 0, sizeof(xform));
 
    /*
     * Loop iterates from 0 to numberOfKeys inclusive; we use the last pass to
     * handle after-last-key processing.  Actual exit from the loop is at the
     * "break" statement below.
     */
    for (i = 0;; cur++, i++)
    {
        if (i < numberOfKeys)
        {
            /* Apply indoption to scankey (might change sk_strategy!) */
            if (!_bt_fix_scankey_strategy(cur, indoption))
            {
                /* NULL can't be matched, so give up */
                so->qual_ok = false;
                return;
            }
        }
 
        /*
         * If we are at the end of the keys for a particular attr, finish up
         * processing and emit the cleaned-up keys.
         */
        if (i == numberOfKeys || cur->sk_attno != attno)
        {
            int         priorNumberOfEqualCols = numberOfEqualCols;
 
            /* check input keys are correctly ordered */
            if (i < numberOfKeys && cur->sk_attno < attno)
                elog(ERROR, "btree index keys must be ordered by attribute");
 
            /*
             * If = has been specified, all other keys can be eliminated as
             * redundant.  If we have a case like key = 1 AND key > 2, we can
             * set qual_ok to false and abandon further processing.
             *
             * We also have to deal with the case of "key IS NULL", which is
             * unsatisfiable in combination with any other index condition. By
             * the time we get here, that's been classified as an equality
             * check, and we've rejected any combination of it with a regular
             * equality condition; but not with other types of conditions.
             */
            if (xform[BTEqualStrategyNumber - 1].skey)
            {
                ScanKey     eq = xform[BTEqualStrategyNumber - 1].skey;
                BTArrayKeyInfo *array = NULL;
                FmgrInfo   *orderproc = NULL;
 
                if (arrayKeyData && (eq->sk_flags & SK_SEARCHARRAY))
                {
                    int         eq_in_ikey,
                                eq_arrayidx;
 
                    eq_in_ikey = xform[BTEqualStrategyNumber - 1].ikey;
                    eq_arrayidx = xform[BTEqualStrategyNumber - 1].arrayidx;
                    array = &so->arrayKeys[eq_arrayidx - 1];
                    orderproc = so->orderProcs + eq_in_ikey;
 
                    Assert(array->scan_key == eq_in_ikey);
                    Assert(OidIsValid(orderproc->fn_oid));
                }
 
                for (j = BTMaxStrategyNumber; --j >= 0;)
                {
                    ScanKey     chk = xform[j].skey;
 
                    if (!chk || j == (BTEqualStrategyNumber - 1))
                        continue;
 
                    if (eq->sk_flags & SK_SEARCHNULL)
                    {
                        /* IS NULL is contradictory to anything else */
                        so->qual_ok = false;
                        return;
                    }
 
                    if (_bt_compare_scankey_args(scan, chk, eq, chk,
                                                 array, orderproc,
                                                 &test_result))
                    {
                        if (!test_result)
                        {
                            /* keys proven mutually contradictory */
                            so->qual_ok = false;
                            return;
                        }
                        /* else discard the redundant non-equality key */
                        Assert(!array || array->num_elems > 0);
                        xform[j].skey = NULL;
                        xform[j].ikey = -1;
                    }
                    /* else, cannot determine redundancy, keep both keys */
                }
                /* track number of attrs for which we have "=" keys */
                numberOfEqualCols++;
            }
 
            /* try to keep only one of <, <= */
            if (xform[BTLessStrategyNumber - 1].skey
                && xform[BTLessEqualStrategyNumber - 1].skey)
            {
                ScanKey     lt = xform[BTLessStrategyNumber - 1].skey;
                ScanKey     le = xform[BTLessEqualStrategyNumber - 1].skey;
 
                if (_bt_compare_scankey_args(scan, le, lt, le, NULL, NULL,
                                             &test_result))
                {
                    if (test_result)
                        xform[BTLessEqualStrategyNumber - 1].skey = NULL;
                    else
                        xform[BTLessStrategyNumber - 1].skey = NULL;
                }
            }
 
            /* try to keep only one of >, >= */
            if (xform[BTGreaterStrategyNumber - 1].skey
                && xform[BTGreaterEqualStrategyNumber - 1].skey)
            {
                ScanKey     gt = xform[BTGreaterStrategyNumber - 1].skey;
                ScanKey     ge = xform[BTGreaterEqualStrategyNumber - 1].skey;
 
                if (_bt_compare_scankey_args(scan, ge, gt, ge, NULL, NULL,
                                             &test_result))
                {
                    if (test_result)
                        xform[BTGreaterEqualStrategyNumber - 1].skey = NULL;
                    else
                        xform[BTGreaterStrategyNumber - 1].skey = NULL;
                }
            }
 
            /*
             * Emit the cleaned-up keys into the outkeys[] array, and then
             * mark them if they are required.  They are required (possibly
             * only in one direction) if all attrs before this one had "=".
             */
            for (j = BTMaxStrategyNumber; --j >= 0;)
            {
                if (xform[j].skey)
                {
                    ScanKey     outkey = &outkeys[new_numberOfKeys++];
 
                    memcpy(outkey, xform[j].skey, sizeof(ScanKeyData));
                    if (arrayKeyData)
                        keyDataMap[new_numberOfKeys - 1] = xform[j].ikey;
                    if (priorNumberOfEqualCols == attno - 1)
                        _bt_mark_scankey_required(outkey);
                }
            }
 
            /*
             * Exit loop here if done.
             */
            if (i == numberOfKeys)
                break;
 
            /* Re-initialize for new attno */
            attno = cur->sk_attno;
            memset(xform, 0, sizeof(xform));
        }
 
        /* check strategy this key's operator corresponds to */
        j = cur->sk_strategy - 1;
 
        /* if row comparison, push it directly to the output array */
        if (cur->sk_flags & SK_ROW_HEADER)
        {
            ScanKey     outkey = &outkeys[new_numberOfKeys++];
 
            memcpy(outkey, cur, sizeof(ScanKeyData));
            if (arrayKeyData)
                keyDataMap[new_numberOfKeys - 1] = i;
            if (numberOfEqualCols == attno - 1)
                _bt_mark_scankey_required(outkey);
 
            /*
             * We don't support RowCompare using equality; such a qual would
             * mess up the numberOfEqualCols tracking.
             */
            Assert(j != (BTEqualStrategyNumber - 1));
            continue;
        }
 
        /*
         * Does this input scan key require further processing as an array?
         */
        if (cur->sk_strategy == InvalidStrategy)
        {
            /* _bt_preprocess_array_keys marked this array key redundant */
            Assert(arrayKeyData);
            Assert(cur->sk_flags & SK_SEARCHARRAY);
            continue;
        }
 
        if (cur->sk_strategy == BTEqualStrategyNumber &&
            (cur->sk_flags & SK_SEARCHARRAY))
        {
            /* _bt_preprocess_array_keys kept this array key */
            Assert(arrayKeyData);
            arrayidx++;
        }
 
        /*
         * have we seen a scan key for this same attribute and using this same
         * operator strategy before now?
         */
        if (xform[j].skey == NULL)
        {
            /* nope, so this scan key wins by default (at least for now) */
            xform[j].skey = cur;
            xform[j].ikey = i;
            xform[j].arrayidx = arrayidx;
        }
        else
        {
            FmgrInfo   *orderproc = NULL;
            BTArrayKeyInfo *array = NULL;
 
            /*
             * Seen one of these before, so keep only the more restrictive key
             * if possible
             */
            if (j == (BTEqualStrategyNumber - 1) && arrayKeyData)
            {
                /*
                 * Have to set up array keys
                 */
                if ((cur->sk_flags & SK_SEARCHARRAY))
                {
                    array = &so->arrayKeys[arrayidx - 1];
                    orderproc = so->orderProcs + i;
 
                    Assert(array->scan_key == i);
                    Assert(OidIsValid(orderproc->fn_oid));
                }
                else if ((xform[j].skey->sk_flags & SK_SEARCHARRAY))
                {
                    array = &so->arrayKeys[xform[j].arrayidx - 1];
                    orderproc = so->orderProcs + xform[j].ikey;
 
                    Assert(array->scan_key == xform[j].ikey);
                    Assert(OidIsValid(orderproc->fn_oid));
                }
 
                /*
                 * Both scan keys might have arrays, in which case we'll
                 * arbitrarily pass only one of the arrays.  That won't
                 * matter, since _bt_compare_scankey_args is aware that two
                 * SEARCHARRAY scan keys mean that _bt_preprocess_array_keys
                 * failed to eliminate redundant arrays through array merging.
                 * _bt_compare_scankey_args just returns false when it sees
                 * this; it won't even try to examine either array.
                 */
            }
 
            if (_bt_compare_scankey_args(scan, cur, cur, xform[j].skey,
                                         array, orderproc, &test_result))
            {
                /* Have all we need to determine redundancy */
                if (test_result)
                {
                    Assert(!array || array->num_elems > 0);
 
                    /*
                     * New key is more restrictive, and so replaces old key...
                     */
                    if (j != (BTEqualStrategyNumber - 1) ||
                        !(xform[j].skey->sk_flags & SK_SEARCHARRAY))
                    {
                        xform[j].skey = cur;
                        xform[j].ikey = i;
                        xform[j].arrayidx = arrayidx;
                    }
                    else
                    {
                        /*
                         * ...unless we have to keep the old key because it's
                         * an array that rendered the new key redundant.  We
                         * need to make sure that we don't throw away an array
                         * scan key.  _bt_compare_scankey_args expects us to
                         * always keep arrays (and discard non-arrays).
                         */
                        Assert(!(cur->sk_flags & SK_SEARCHARRAY));
                    }
                }
                else if (j == (BTEqualStrategyNumber - 1))
                {
                    /* key == a && key == b, but a != b */
                    so->qual_ok = false;
                    return;
                }
                /* else old key is more restrictive, keep it */
            }
            else
            {
                /*
                 * We can't determine which key is more restrictive.  Push
                 * xform[j] directly to the output array, then set xform[j] to
                 * the new scan key.
                 *
                 * Note: We do things this way around so that our arrays are
                 * always in the same order as their corresponding scan keys,
                 * even with incomplete opfamilies.  _bt_advance_array_keys
                 * depends on this.
                 */
                ScanKey     outkey = &outkeys[new_numberOfKeys++];
 
                memcpy(outkey, xform[j].skey, sizeof(ScanKeyData));
                if (arrayKeyData)
                    keyDataMap[new_numberOfKeys - 1] = xform[j].ikey;
                if (numberOfEqualCols == attno - 1)
                    _bt_mark_scankey_required(outkey);
                xform[j].skey = cur;
                xform[j].ikey = i;
                xform[j].arrayidx = arrayidx;
            }
        }
    }
 
    so->numberOfKeys = new_numberOfKeys;
 
    /*
     * Now that we've built a temporary mapping from so->keyData[] (output
     * scan keys) to scan->keyData[] (input scan keys), fix array->scan_key
     * references.  Also consolidate the so->orderProc[] array such that it
     * can be subscripted using so->keyData[]-wise offsets.
     */
    if (arrayKeyData)
        _bt_preprocess_array_keys_final(scan, keyDataMap);
 
    /* Could pfree arrayKeyData/keyDataMap now, but not worth the cycles */
}
 
#ifdef USE_ASSERT_CHECKING
/*
 * Verify that the scan's qual state matches what we expect at the point that
 * _bt_start_prim_scan is about to start a just-scheduled new primitive scan.
 *
 * We enforce a rule against non-required array scan keys: they must start out
 * with whatever element is the first for the scan's current scan direction.
 * See _bt_rewind_nonrequired_arrays comments for an explanation.
 */
static bool
_bt_verify_arrays_bt_first(IndexScanDesc scan, ScanDirection dir)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    int         arrayidx = 0;
 
    for (int ikey = 0; ikey < so->numberOfKeys; ikey++)
    {
        ScanKey     cur = so->keyData + ikey;
        BTArrayKeyInfo *array = NULL;
        int         first_elem_dir;
 
        if (!(cur->sk_flags & SK_SEARCHARRAY) ||
            cur->sk_strategy != BTEqualStrategyNumber)
            continue;
 
        array = &so->arrayKeys[arrayidx++];
 
        if (((cur->sk_flags & SK_BT_REQFWD) && ScanDirectionIsForward(dir)) ||
            ((cur->sk_flags & SK_BT_REQBKWD) && ScanDirectionIsBackward(dir)))
            continue;
 
        if (ScanDirectionIsForward(dir))
            first_elem_dir = 0;
        else
            first_elem_dir = array->num_elems - 1;
 
        if (array->cur_elem != first_elem_dir)
            return false;
    }
 
    return _bt_verify_keys_with_arraykeys(scan);
}
 
/*
 * 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;
 
    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)
            return false;
 
        if (cur->sk_argument != array->elem_values[array->cur_elem])
            return false;
        if (last_sk_attno > cur->sk_attno)
            return false;
        last_sk_attno = cur->sk_attno;
    }
 
    if (arrayidx != so->numArrayKeys)
        return false;
 
    return true;
}
#endif
 
/*
 * Compare two scankey values using a specified operator.
 *
 * The test we want to perform is logically "leftarg op rightarg", where
 * leftarg and rightarg are the sk_argument values in those ScanKeys, and
 * the comparison operator is the one in the op ScanKey.  However, in
 * cross-data-type situations we may need to look up the correct operator in
 * the index's opfamily: it is the one having amopstrategy = op->sk_strategy
 * and amoplefttype/amoprighttype equal to the two argument datatypes.
 *
 * If the opfamily doesn't supply a complete set of cross-type operators we
 * may not be able to make the comparison.  If we can make the comparison
 * we store the operator result in *result and return true.  We return false
 * if the comparison could not be made.
 *
 * If either leftarg or rightarg are an array, we'll apply array-specific
 * rules to determine which array elements are redundant on behalf of caller.
 * It is up to our caller to save whichever of the two scan keys is the array,
 * and discard the non-array scan key (the non-array scan key is guaranteed to
 * be redundant with any complete opfamily).  Caller isn't expected to call
 * here with a pair of array scan keys provided we're dealing with a complete
 * opfamily (_bt_preprocess_array_keys will merge array keys together to make
 * sure of that).
 *
 * Note: we'll also shrink caller's array as needed to eliminate redundant
 * array elements.  One reason why caller should prefer to discard non-array
 * scan keys is so that we'll have the opportunity to shrink the array
 * multiple times, in multiple calls (for each of several other scan keys on
 * the same index attribute).
 *
 * Note: op always points at the same ScanKey as either leftarg or rightarg.
 * Since we don't scribble on the scankeys themselves, this aliasing should
 * cause no trouble.
 *
 * Note: this routine needs to be insensitive to any DESC option applied
 * to the index column.  For example, "x < 4" is a tighter constraint than
 * "x < 5" regardless of which way the index is sorted.
 */
static bool
_bt_compare_scankey_args(IndexScanDesc scan, ScanKey op,
                         ScanKey leftarg, ScanKey rightarg,
                         BTArrayKeyInfo *array, FmgrInfo *orderproc,
                         bool *result)
{
    Relation    rel = scan->indexRelation;
    Oid         lefttype,
                righttype,
                optype,
                opcintype,
                cmp_op;
    StrategyNumber strat;
 
    /*
     * First, deal with cases where one or both args are NULL.  This should
     * only happen when the scankeys represent IS NULL/NOT NULL conditions.
     */
    if ((leftarg->sk_flags | rightarg->sk_flags) & SK_ISNULL)
    {
        bool        leftnull,
                    rightnull;
 
        if (leftarg->sk_flags & SK_ISNULL)
        {
            Assert(leftarg->sk_flags & (SK_SEARCHNULL | SK_SEARCHNOTNULL));
            leftnull = true;
        }
        else
            leftnull = false;
        if (rightarg->sk_flags & SK_ISNULL)
        {
            Assert(rightarg->sk_flags & (SK_SEARCHNULL | SK_SEARCHNOTNULL));
            rightnull = true;
        }
        else
            rightnull = false;
 
        /*
         * We treat NULL as either greater than or less than all other values.
         * Since true > false, the tests below work correctly for NULLS LAST
         * logic.  If the index is NULLS FIRST, we need to flip the strategy.
         */
        strat = op->sk_strategy;
        if (op->sk_flags & SK_BT_NULLS_FIRST)
            strat = BTCommuteStrategyNumber(strat);
 
        switch (strat)
        {
            case BTLessStrategyNumber:
                *result = (leftnull < rightnull);
                break;
            case BTLessEqualStrategyNumber:
                *result = (leftnull <= rightnull);
                break;
            case BTEqualStrategyNumber:
                *result = (leftnull == rightnull);
                break;
            case BTGreaterEqualStrategyNumber:
                *result = (leftnull >= rightnull);
                break;
            case BTGreaterStrategyNumber:
                *result = (leftnull > rightnull);
                break;
            default:
                elog(ERROR, "unrecognized StrategyNumber: %d", (int) strat);
                *result = false;    /* keep compiler quiet */
                break;
        }
        return true;
    }
 
    /*
     * If either leftarg or rightarg are equality-type array scankeys, we need
     * specialized handling (since by now we know that IS NULL wasn't used)
     */
    if (array)
    {
        bool        leftarray,
                    rightarray;
 
        leftarray = ((leftarg->sk_flags & SK_SEARCHARRAY) &&
                     leftarg->sk_strategy == BTEqualStrategyNumber);
        rightarray = ((rightarg->sk_flags & SK_SEARCHARRAY) &&
                      rightarg->sk_strategy == BTEqualStrategyNumber);
 
        /*
         * _bt_preprocess_array_keys is responsible for merging together array
         * scan keys, and will do so whenever the opfamily has the required
         * cross-type support.  If it failed to do that, we handle it just
         * like the case where we can't make the comparison ourselves.
         */
        if (leftarray && rightarray)
        {
            /* Can't make the comparison */
            *result = false;    /* suppress compiler warnings */
            return false;
        }
 
        /*
         * Otherwise we need to determine if either one of leftarg or rightarg
         * uses an array, then pass this through to a dedicated helper
         * function.
         */
        if (leftarray)
            return _bt_compare_array_scankey_args(scan, leftarg, rightarg,
                                                  orderproc, array, result);
        else if (rightarray)
            return _bt_compare_array_scankey_args(scan, rightarg, leftarg,
                                                  orderproc, array, result);
 
        /* FALL THRU */
    }
 
    /*
     * The opfamily we need to worry about is identified by the index column.
     */
    Assert(leftarg->sk_attno == rightarg->sk_attno);
 
    opcintype = rel->rd_opcintype[leftarg->sk_attno - 1];
 
    /*
     * Determine the actual datatypes of the ScanKey arguments.  We have to
     * support the convention that sk_subtype == InvalidOid means the opclass
     * input type; this is a hack to simplify life for ScanKeyInit().
     */
    lefttype = leftarg->sk_subtype;
    if (lefttype == InvalidOid)
        lefttype = opcintype;
    righttype = rightarg->sk_subtype;
    if (righttype == InvalidOid)
        righttype = opcintype;
    optype = op->sk_subtype;
    if (optype == InvalidOid)
        optype = opcintype;
 
    /*
     * If leftarg and rightarg match the types expected for the "op" scankey,
     * we can use its already-looked-up comparison function.
     */
    if (lefttype == opcintype && righttype == optype)
    {
        *result = DatumGetBool(FunctionCall2Coll(&op->sk_func,
                                                 op->sk_collation,
                                                 leftarg->sk_argument,
                                                 rightarg->sk_argument));
        return true;
    }
 
    /*
     * Otherwise, we need to go to the syscache to find the appropriate
     * operator.  (This cannot result in infinite recursion, since no
     * indexscan initiated by syscache lookup will use cross-data-type
     * operators.)
     *
     * If the sk_strategy was flipped by _bt_fix_scankey_strategy, we have to
     * un-flip it to get the correct opfamily member.
     */
    strat = op->sk_strategy;
    if (op->sk_flags & SK_BT_DESC)
        strat = BTCommuteStrategyNumber(strat);
 
    cmp_op = get_opfamily_member(rel->rd_opfamily[leftarg->sk_attno - 1],
                                 lefttype,
                                 righttype,
                                 strat);
    if (OidIsValid(cmp_op))
    {
        RegProcedure cmp_proc = get_opcode(cmp_op);
 
        if (RegProcedureIsValid(cmp_proc))
        {
            *result = DatumGetBool(OidFunctionCall2Coll(cmp_proc,
                                                        op->sk_collation,
                                                        leftarg->sk_argument,
                                                        rightarg->sk_argument));
            return true;
        }
    }
 
    /* Can't make the comparison */
    *result = false;            /* suppress compiler warnings */
    return false;
}
 
/*
 * Adjust a scankey's strategy and flags setting as needed for indoptions.
 *
 * We copy the appropriate indoption value into the scankey sk_flags
 * (shifting to avoid clobbering system-defined flag bits).  Also, if
 * the DESC option is set, commute (flip) the operator strategy number.
 *
 * A secondary purpose is to check for IS NULL/NOT NULL scankeys and set up
 * the strategy field correctly for them.
 *
 * Lastly, for ordinary scankeys (not IS NULL/NOT NULL), we check for a
 * NULL comparison value.  Since all btree operators are assumed strict,
 * a NULL means that the qual cannot be satisfied.  We return true if the
 * comparison value isn't NULL, or false if the scan should be abandoned.
 *
 * This function is applied to the *input* scankey structure; therefore
 * on a rescan we will be looking at already-processed scankeys.  Hence
 * we have to be careful not to re-commute the strategy if we already did it.
 * It's a bit ugly to modify the caller's copy of the scankey but in practice
 * there shouldn't be any problem, since the index's indoptions are certainly
 * not going to change while the scankey survives.
 */
static bool
_bt_fix_scankey_strategy(ScanKey skey, int16 *indoption)
{
    int         addflags;
 
    addflags = indoption[skey->sk_attno - 1] << SK_BT_INDOPTION_SHIFT;
 
    /*
     * We treat all btree operators as strict (even if they're not so marked
     * in pg_proc). This means that it is impossible for an operator condition
     * with a NULL comparison constant to succeed, and we can reject it right
     * away.
     *
     * However, we now also support "x IS NULL" clauses as search conditions,
     * so in that case keep going. The planner has not filled in any
     * particular strategy in this case, so set it to BTEqualStrategyNumber
     * --- we can treat IS NULL as an equality operator for purposes of search
     * strategy.
     *
     * Likewise, "x IS NOT NULL" is supported.  We treat that as either "less
     * than NULL" in a NULLS LAST index, or "greater than NULL" in a NULLS
     * FIRST index.
     *
     * Note: someday we might have to fill in sk_collation from the index
     * column's collation.  At the moment this is a non-issue because we'll
     * never actually call the comparison operator on a NULL.
     */
    if (skey->sk_flags & SK_ISNULL)
    {
        /* SK_ISNULL shouldn't be set in a row header scankey */
        Assert(!(skey->sk_flags & SK_ROW_HEADER));
 
        /* Set indoption flags in scankey (might be done already) */
        skey->sk_flags |= addflags;
 
        /* Set correct strategy for IS NULL or NOT NULL search */
        if (skey->sk_flags & SK_SEARCHNULL)
        {
            skey->sk_strategy = BTEqualStrategyNumber;
            skey->sk_subtype = InvalidOid;
            skey->sk_collation = InvalidOid;
        }
        else if (skey->sk_flags & SK_SEARCHNOTNULL)
        {
            if (skey->sk_flags & SK_BT_NULLS_FIRST)
                skey->sk_strategy = BTGreaterStrategyNumber;
            else
                skey->sk_strategy = BTLessStrategyNumber;
            skey->sk_subtype = InvalidOid;
            skey->sk_collation = InvalidOid;
        }
        else
        {
            /* regular qual, so it cannot be satisfied */
            return false;
        }
 
        /* Needn't do the rest */
        return true;
    }
 
    if (skey->sk_strategy == InvalidStrategy)
    {
        /* Already-eliminated array scan key; don't need to fix anything */
        Assert(skey->sk_flags & SK_SEARCHARRAY);
        return true;
    }
 
    /* Adjust strategy for DESC, if we didn't already */
    if ((addflags & SK_BT_DESC) && !(skey->sk_flags & SK_BT_DESC))
        skey->sk_strategy = BTCommuteStrategyNumber(skey->sk_strategy);
    skey->sk_flags |= addflags;
 
    /* If it's a row header, fix row member flags and strategies similarly */
    if (skey->sk_flags & SK_ROW_HEADER)
    {
        ScanKey     subkey = (ScanKey) DatumGetPointer(skey->sk_argument);
 
        for (;;)
        {
            Assert(subkey->sk_flags & SK_ROW_MEMBER);
            addflags = indoption[subkey->sk_attno - 1] << SK_BT_INDOPTION_SHIFT;
            if ((addflags & SK_BT_DESC) && !(subkey->sk_flags & SK_BT_DESC))
                subkey->sk_strategy = BTCommuteStrategyNumber(subkey->sk_strategy);
            subkey->sk_flags |= addflags;
            if (subkey->sk_flags & SK_ROW_END)
                break;
            subkey++;
        }
    }
 
    return true;
}
 
/*
 * Mark a scankey as "required to continue the scan".
 *
 * Depending on the operator type, the key may be required for both scan
 * directions or just one.  Also, if the key is a row comparison header,
 * we have to mark its first subsidiary ScanKey as required.  (Subsequent
 * subsidiary ScanKeys are normally for lower-order columns, and thus
 * cannot be required, since they're after the first non-equality scankey.)
 *
 * Note: when we set required-key flag bits in a subsidiary scankey, we are
 * scribbling on a data structure belonging to the index AM's caller, not on
 * our private copy.  This should be OK because the marking will not change
 * from scan to scan within a query, and so we'd just re-mark the same way
 * anyway on a rescan.  Something to keep an eye on though.
 */
static void
_bt_mark_scankey_required(ScanKey skey)
{
    int         addflags;
 
    switch (skey->sk_strategy)
    {
        case BTLessStrategyNumber:
        case BTLessEqualStrategyNumber:
            addflags = SK_BT_REQFWD;
            break;
        case BTEqualStrategyNumber:
            addflags = SK_BT_REQFWD | SK_BT_REQBKWD;
            break;
        case BTGreaterEqualStrategyNumber:
        case BTGreaterStrategyNumber:
            addflags = SK_BT_REQBKWD;
            break;
        default:
            elog(ERROR, "unrecognized StrategyNumber: %d",
                 (int) skey->sk_strategy);
            addflags = 0;       /* keep compiler quiet */
            break;
    }
 
    skey->sk_flags |= addflags;
 
    if (skey->sk_flags & SK_ROW_HEADER)
    {
        ScanKey     subkey = (ScanKey) DatumGetPointer(skey->sk_argument);
 
        /* First subkey should be same column/operator as the header */
        Assert(subkey->sk_flags & SK_ROW_MEMBER);
        Assert(subkey->sk_attno == skey->sk_attno);
        Assert(subkey->sk_strategy == skey->sk_strategy);
        subkey->sk_flags |= addflags;
    }
}
 
/*
 * 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(), above, 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.
 * Caller can avoid all array related side-effects when calling just to do a
 * page continuescan precheck -- pass arrayKeys=false for that.  Scans without
 * any arrays 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 (or possibly the
 * first call after an initial continuescan-setting page precheck call).  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)
 */
bool
_bt_checkkeys(IndexScanDesc scan, BTReadPageState *pstate, bool arrayKeys,
              IndexTuple tuple, int tupnatts)
{
    TupleDesc   tupdesc = RelationGetDescr(scan->indexRelation);
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    ScanDirection dir = pstate->dir;
    int         ikey = 0;
    bool        res;
 
    Assert(BTreeTupleGetNAtts(tuple, scan->indexRelation) == tupnatts);
 
    res = _bt_check_compare(scan, dir, tuple, tupnatts, tupdesc,
                            arrayKeys, pstate->prechecked, pstate->firstmatch,
                            &pstate->continuescan, &ikey);
 
#ifdef USE_ASSERT_CHECKING
    if (!arrayKeys && so->numArrayKeys)
    {
        /*
         * This is a continuescan precheck call for a scan with array keys.
         *
         * Assert that the scan isn't in danger of becoming confused.
         */
        Assert(!so->scanBehind && !pstate->prechecked && !pstate->firstmatch);
        Assert(!_bt_tuple_before_array_skeys(scan, dir, tuple, tupdesc,
                                             tupnatts, false, 0, NULL));
    }
    if (pstate->prechecked || pstate->firstmatch)
    {
        bool        dcontinuescan;
        int         dikey = 0;
 
        /*
         * Call relied on continuescan/firstmatch prechecks -- assert that we
         * get the same answer without those optimizations
         */
        Assert(res == _bt_check_compare(scan, dir, tuple, tupnatts, tupdesc,
                                        false, false, false,
                                        &dcontinuescan, &dikey));
        Assert(pstate->continuescan == dcontinuescan);
    }
#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.
     */
    if (_bt_tuple_before_array_skeys(scan, dir, tuple, tupdesc, tupnatts, true,
                                     ikey, NULL))
    {
        /*
         * Tuple is still before the start of matches according to the scan's
         * required array keys (according to _all_ of its required equality
         * strategy keys, actually).
         *
         * _bt_advance_array_keys occasionally sets so->scanBehind to signal
         * that the scan's current position/tuples might be significantly
         * behind (multiple pages behind) its current array keys.  When this
         * happens, we need to be prepared to recover by starting a new
         * primitive index scan here, on our own.
         */
        Assert(!so->scanBehind ||
               so->keyData[ikey].sk_strategy == BTEqualStrategyNumber);
        if (unlikely(so->scanBehind) && pstate->finaltup &&
            _bt_tuple_before_array_skeys(scan, dir, pstate->finaltup, tupdesc,
                                         BTreeTupleGetNAtts(pstate->finaltup,
                                                            scan->indexRelation),
                                         false, 0, NULL))
        {
            /* Cut our losses -- start a new primitive index scan now */
            pstate->continuescan = false;
            so->needPrimScan = true;
        }
        else
        {
            /* 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).
 *
 * Though we advance non-required array keys on our own, that shouldn't have
 * any lasting consequences for the scan.  By definition, non-required arrays
 * have no fixed relationship with the scan's progress.  (There are delicate
 * considerations for non-required arrays when the arrays need to be advanced
 * following our setting continuescan to false, but that doesn't concern us.)
 *
 * Pass advancenonrequired=false to avoid all array related side effects.
 * This allows _bt_advance_array_keys caller to avoid infinite recursion.
 */
static bool
_bt_check_compare(IndexScanDesc scan, ScanDirection dir,
                  IndexTuple tuple, int tupnatts, TupleDesc tupdesc,
                  bool advancenonrequired, bool prechecked, bool firstmatch,
                  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
         */
        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 the caller told us the *continuescan flag is known to be true
         * for the last item on the page, then we know the keys required for
         * the current direction scan should be matched.  Otherwise, the
         * *continuescan flag would be set for the current item and
         * subsequently the last item on the page accordingly.
         *
         * If the key is required for the opposite direction scan, we can skip
         * the check if the caller tells us there was already at least one
         * matching item on the page. Also, we require the *continuescan flag
         * to be true for the last item on the page to know there are no
         * NULLs.
         *
         * Both cases above work except for the row keys, where NULLs could be
         * found in the middle of matching values.
         */
        if (prechecked &&
            (requiredSameDir || (requiredOppositeDirOnly && firstmatch)) &&
            !(key->sk_flags & SK_ROW_HEADER))
            continue;
 
        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;
        }
 
        /* row-comparison keys need special processing */
        if (key->sk_flags & SK_ROW_HEADER)
        {
            if (_bt_check_rowcompare(key, tuple, tupnatts, tupdesc, dir,
                                     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);
                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;
 
            /*
             * In any case, this indextuple doesn't match the qual.
             */
            return false;
        }
 
        if (isNull)
        {
            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 ((key->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD)) &&
                    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 ((key->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD)) &&
                    ScanDirectionIsForward(dir))
                    *continuescan = false;
            }
 
            /*
             * In any case, this indextuple doesn't match the qual.
             */
            return false;
        }
 
        /*
         * Apply the key-checking function, though only if we must.
         *
         * When a key is required in the opposite-of-scan direction _only_,
         * then it must already be satisfied if firstmatch=true indicates that
         * an earlier tuple from this same page satisfied it earlier on.
         */
        if (!(requiredOppositeDirOnly && firstmatch) &&
            !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.
             *
             * Note: because we stop the scan as soon as any required equality
             * qual fails, it is critical that equality quals be used for the
             * initial positioning in _bt_first() when they are available. See
             * comments in _bt_first().
             */
            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.
 */
static bool
_bt_check_rowcompare(ScanKey skey, IndexTuple tuple, int tupnatts,
                     TupleDesc tupdesc, ScanDirection dir, bool *continuescan)
{
    ScanKey     subkey = (ScanKey) DatumGetPointer(skey->sk_argument);
    int32       cmpresult = 0;
    bool        result;
 
    /* First subkey should be same as the header says */
    Assert(subkey->sk_attno == skey->sk_attno);
 
    /* Loop over columns of the row condition */
    for (;;)
    {
        Datum       datum;
        bool        isNull;
 
        Assert(subkey->sk_flags & SK_ROW_MEMBER);
 
        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));
            cmpresult = 0;
            if (subkey->sk_flags & SK_ROW_END)
                break;
            subkey++;
            continue;
        }
 
        datum = index_getattr(tuple,
                              subkey->sk_attno,
                              tupdesc,
                              &isNull);
 
        if (isNull)
        {
            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.  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 ((subkey->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD)) &&
                    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 ((subkey->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD)) &&
                    ScanDirectionIsForward(dir))
                    *continuescan = false;
            }
 
            /*
             * In any case, this indextuple doesn't match the qual.
             */
            return false;
        }
 
        if (subkey->sk_flags & SK_ISNULL)
        {
            /*
             * Unlike the simple-scankey case, this isn't a disallowed case.
             * 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.
             */
            if (subkey != (ScanKey) DatumGetPointer(skey->sk_argument))
                subkey--;
            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;
        }
 
        /* 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++;
    }
 
    /*
     * At this point cmpresult indicates the overall result of the row
     * comparison, and subkey points to the deciding column (or the last
     * column if the result is "=").
     */
    switch (subkey->sk_strategy)
    {
            /* EQ and NE cases aren't allowed here */
        case BTLessStrategyNumber:
            result = (cmpresult < 0);
            break;
        case BTLessEqualStrategyNumber:
            result = (cmpresult <= 0);
            break;
        case BTGreaterEqualStrategyNumber:
            result = (cmpresult >= 0);
            break;
        case BTGreaterStrategyNumber:
            result = (cmpresult > 0);
            break;
        default:
            elog(ERROR, "unrecognized RowCompareType: %d",
                 (int) subkey->sk_strategy);
            result = 0;         /* keep compiler quiet */
            break;
    }
 
    if (!result)
    {
        /*
         * 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;
}
 
/*
 * 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;
 
    /* 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
        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_killitems - set LP_DEAD state for items an indexscan caller has
 * told us were killed
 *
 * scan->opaque, referenced locally through so, contains information about the
 * current page and killed tuples thereon (generally, this should only be
 * called if so->numKilled > 0).
 *
 * The caller does not have a lock on the page and may or may not have the
 * page pinned in a buffer.  Note that read-lock is sufficient for setting
 * LP_DEAD status (which is only a hint).
 *
 * We match items by heap TID before assuming they are the right ones to
 * delete.  We cope with cases where items have moved right due to insertions.
 * If an item has moved off the current page due to a split, we'll fail to
 * find it and do nothing (this is not an error case --- we assume the item
 * will eventually get marked in a future indexscan).
 *
 * Note that if we hold a pin on the target page continuously from initially
 * reading the items until applying this function, VACUUM cannot have deleted
 * any items from the page, and so there is no need to search left from the
 * recorded offset.  (This observation also guarantees that the item is still
 * the right one to delete, which might otherwise be questionable since heap
 * TIDs can get recycled.)  This holds true even if the page has been modified
 * by inserts and page splits, so there is no need to consult the LSN.
 *
 * If the pin was released after reading the page, then we re-read it.  If it
 * has been modified since we read it (as determined by the LSN), we dare not
 * flag any entries because it is possible that the old entry was vacuumed
 * away and the TID was re-used by a completely different heap tuple.
 */
void
_bt_killitems(IndexScanDesc scan)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    Page        page;
    BTPageOpaque opaque;
    OffsetNumber minoff;
    OffsetNumber maxoff;
    int         i;
    int         numKilled = so->numKilled;
    bool        killedsomething = false;
    bool        droppedpin PG_USED_FOR_ASSERTS_ONLY;
 
    Assert(BTScanPosIsValid(so->currPos));
 
    /*
     * Always reset the scan state, so we don't look for same items on other
     * pages.
     */
    so->numKilled = 0;
 
    if (BTScanPosIsPinned(so->currPos))
    {
        /*
         * We have held the pin on this page since we read the index tuples,
         * so all we need to do is lock it.  The pin will have prevented
         * re-use of any TID on the page, so there is no need to check the
         * LSN.
         */
        droppedpin = false;
        _bt_lockbuf(scan->indexRelation, so->currPos.buf, BT_READ);
 
        page = BufferGetPage(so->currPos.buf);
    }
    else
    {
        Buffer      buf;
 
        droppedpin = true;
        /* Attempt to re-read the buffer, getting pin and lock. */
        buf = _bt_getbuf(scan->indexRelation, so->currPos.currPage, BT_READ);
 
        page = BufferGetPage(buf);
        if (BufferGetLSNAtomic(buf) == so->currPos.lsn)
            so->currPos.buf = buf;
        else
        {
            /* Modified while not pinned means hinting is not safe. */
            _bt_relbuf(scan->indexRelation, buf);
            return;
        }
    }
 
    opaque = BTPageGetOpaque(page);
    minoff = P_FIRSTDATAKEY(opaque);
    maxoff = PageGetMaxOffsetNumber(page);
 
    for (i = 0; i < numKilled; i++)
    {
        int         itemIndex = so->killedItems[i];
        BTScanPosItem *kitem = &so->currPos.items[itemIndex];
        OffsetNumber offnum = kitem->indexOffset;
 
        Assert(itemIndex >= so->currPos.firstItem &&
               itemIndex <= so->currPos.lastItem);
        if (offnum < minoff)
            continue;           /* pure paranoia */
        while (offnum <= maxoff)
        {
            ItemId      iid = PageGetItemId(page, offnum);
            IndexTuple  ituple = (IndexTuple) PageGetItem(page, iid);
            bool        killtuple = false;
 
            if (BTreeTupleIsPosting(ituple))
            {
                int         pi = i + 1;
                int         nposting = BTreeTupleGetNPosting(ituple);
                int         j;
 
                /*
                 * We rely on the convention that heap TIDs in the scanpos
                 * items array are stored in ascending heap TID order for a
                 * group of TIDs that originally came from a posting list
                 * tuple.  This convention even applies during backwards
                 * scans, where returning the TIDs in descending order might
                 * seem more natural.  This is about effectiveness, not
                 * correctness.
                 *
                 * Note that the page may have been modified in almost any way
                 * since we first read it (in the !droppedpin case), so it's
                 * possible that this posting list tuple wasn't a posting list
                 * tuple when we first encountered its heap TIDs.
                 */
                for (j = 0; j < nposting; j++)
                {
                    ItemPointer item = BTreeTupleGetPostingN(ituple, j);
 
                    if (!ItemPointerEquals(item, &kitem->heapTid))
                        break;  /* out of posting list loop */
 
                    /*
                     * kitem must have matching offnum when heap TIDs match,
                     * though only in the common case where the page can't
                     * have been concurrently modified
                     */
                    Assert(kitem->indexOffset == offnum || !droppedpin);
 
                    /*
                     * Read-ahead to later kitems here.
                     *
                     * We rely on the assumption that not advancing kitem here
                     * will prevent us from considering the posting list tuple
                     * fully dead by not matching its next heap TID in next
                     * loop iteration.
                     *
                     * If, on the other hand, this is the final heap TID in
                     * the posting list tuple, then tuple gets killed
                     * regardless (i.e. we handle the case where the last
                     * kitem is also the last heap TID in the last index tuple
                     * correctly -- posting tuple still gets killed).
                     */
                    if (pi < numKilled)
                        kitem = &so->currPos.items[so->killedItems[pi++]];
                }
 
                /*
                 * Don't bother advancing the outermost loop's int iterator to
                 * avoid processing killed items that relate to the same
                 * offnum/posting list tuple.  This micro-optimization hardly
                 * seems worth it.  (Further iterations of the outermost loop
                 * will fail to match on this same posting list's first heap
                 * TID instead, so we'll advance to the next offnum/index
                 * tuple pretty quickly.)
                 */
                if (j == nposting)
                    killtuple = true;
            }
            else if (ItemPointerEquals(&ituple->t_tid, &kitem->heapTid))
                killtuple = true;
 
            /*
             * Mark index item as dead, if it isn't already.  Since this
             * happens while holding a buffer lock possibly in shared mode,
             * it's possible that multiple processes attempt to do this
             * simultaneously, leading to multiple full-page images being sent
             * to WAL (if wal_log_hints or data checksums are enabled), which
             * is undesirable.
             */
            if (killtuple && !ItemIdIsDead(iid))
            {
                /* found the item/all posting list items */
                ItemIdMarkDead(iid);
                killedsomething = true;
                break;          /* out of inner search loop */
            }
            offnum = OffsetNumberNext(offnum);
        }
    }
 
    /*
     * Since this can be redone later if needed, mark as dirty hint.
     *
     * Whenever we mark anything LP_DEAD, we also set the page's
     * BTP_HAS_GARBAGE flag, which is likewise just a hint.  (Note that we
     * only rely on the page-level flag in !heapkeyspace indexes.)
     */
    if (killedsomething)
    {
        opaque->btpo_flags |= BTP_HAS_GARBAGE;
        MarkBufferDirtyHint(so->currPos.buf, true);
    }
 
    _bt_unlockbuf(scan->indexRelation, so->currPos.buf);
}
 
 
/*
 * The following routines manage a shared-memory area in which we track
 * assignment of "vacuum cycle IDs" to currently-active btree vacuuming
 * operations.  There is a single counter which increments each time we
 * start a vacuum to assign it a cycle ID.  Since multiple vacuums could
 * be active concurrently, we have to track the cycle ID for each active
 * vacuum; this requires at most MaxBackends entries (usually far fewer).
 * We assume at most one vacuum can be active for a given index.
 *
 * Access to the shared memory area is controlled by BtreeVacuumLock.
 * In principle we could use a separate lmgr locktag for each index,
 * but a single LWLock is much cheaper, and given the short time that
 * the lock is ever held, the concurrency hit should be minimal.
 */
 
typedef struct BTOneVacInfo
{
    LockRelId   relid;          /* global identifier of an index */
    BTCycleId   cycleid;        /* cycle ID for its active VACUUM */
} BTOneVacInfo;
 
typedef struct BTVacInfo
{
    BTCycleId   cycle_ctr;      /* cycle ID most recently assigned */
    int         num_vacuums;    /* number of currently active VACUUMs */
    int         max_vacuums;    /* allocated length of vacuums[] array */
    BTOneVacInfo vacuums[FLEXIBLE_ARRAY_MEMBER];
} BTVacInfo;
 
static BTVacInfo *btvacinfo;
 
 
/*
 * _bt_vacuum_cycleid --- get the active vacuum cycle ID for an index,
 *      or zero if there is no active VACUUM
 *
 * Note: for correct interlocking, the caller must already hold pin and
 * exclusive lock on each buffer it will store the cycle ID into.  This
 * ensures that even if a VACUUM starts immediately afterwards, it cannot
 * process those pages until the page split is complete.
 */
BTCycleId
_bt_vacuum_cycleid(Relation rel)
{
    BTCycleId   result = 0;
    int         i;
 
    /* Share lock is enough since this is a read-only operation */
    LWLockAcquire(BtreeVacuumLock, LW_SHARED);
 
    for (i = 0; i < btvacinfo->num_vacuums; i++)
    {
        BTOneVacInfo *vac = &btvacinfo->vacuums[i];
 
        if (vac->relid.relId == rel->rd_lockInfo.lockRelId.relId &&
            vac->relid.dbId == rel->rd_lockInfo.lockRelId.dbId)
        {
            result = vac->cycleid;
            break;
        }
    }
 
    LWLockRelease(BtreeVacuumLock);
    return result;
}
 
/*
 * _bt_start_vacuum --- assign a cycle ID to a just-starting VACUUM operation
 *
 * Note: the caller must guarantee that it will eventually call
 * _bt_end_vacuum, else we'll permanently leak an array slot.  To ensure
 * that this happens even in elog(FATAL) scenarios, the appropriate coding
 * is not just a PG_TRY, but
 *      PG_ENSURE_ERROR_CLEANUP(_bt_end_vacuum_callback, PointerGetDatum(rel))
 */
BTCycleId
_bt_start_vacuum(Relation rel)
{
    BTCycleId   result;
    int         i;
    BTOneVacInfo *vac;
 
    LWLockAcquire(BtreeVacuumLock, LW_EXCLUSIVE);
 
    /*
     * Assign the next cycle ID, being careful to avoid zero as well as the
     * reserved high values.
     */
    result = ++(btvacinfo->cycle_ctr);
    if (result == 0 || result > MAX_BT_CYCLE_ID)
        result = btvacinfo->cycle_ctr = 1;
 
    /* Let's just make sure there's no entry already for this index */
    for (i = 0; i < btvacinfo->num_vacuums; i++)
    {
        vac = &btvacinfo->vacuums[i];
        if (vac->relid.relId == rel->rd_lockInfo.lockRelId.relId &&
            vac->relid.dbId == rel->rd_lockInfo.lockRelId.dbId)
        {
            /*
             * Unlike most places in the backend, we have to explicitly
             * release our LWLock before throwing an error.  This is because
             * we expect _bt_end_vacuum() to be called before transaction
             * abort cleanup can run to release LWLocks.
             */
            LWLockRelease(BtreeVacuumLock);
            elog(ERROR, "multiple active vacuums for index \"%s\"",
                 RelationGetRelationName(rel));
        }
    }
 
    /* OK, add an entry */
    if (btvacinfo->num_vacuums >= btvacinfo->max_vacuums)
    {
        LWLockRelease(BtreeVacuumLock);
        elog(ERROR, "out of btvacinfo slots");
    }
    vac = &btvacinfo->vacuums[btvacinfo->num_vacuums];
    vac->relid = rel->rd_lockInfo.lockRelId;
    vac->cycleid = result;
    btvacinfo->num_vacuums++;
 
    LWLockRelease(BtreeVacuumLock);
    return result;
}
 
/*
 * _bt_end_vacuum --- mark a btree VACUUM operation as done
 *
 * Note: this is deliberately coded not to complain if no entry is found;
 * this allows the caller to put PG_TRY around the start_vacuum operation.
 */
void
_bt_end_vacuum(Relation rel)
{
    int         i;
 
    LWLockAcquire(BtreeVacuumLock, LW_EXCLUSIVE);
 
    /* Find the array entry */
    for (i = 0; i < btvacinfo->num_vacuums; i++)
    {
        BTOneVacInfo *vac = &btvacinfo->vacuums[i];
 
        if (vac->relid.relId == rel->rd_lockInfo.lockRelId.relId &&
            vac->relid.dbId == rel->rd_lockInfo.lockRelId.dbId)
        {
            /* Remove it by shifting down the last entry */
            *vac = btvacinfo->vacuums[btvacinfo->num_vacuums - 1];
            btvacinfo->num_vacuums--;
            break;
        }
    }
 
    LWLockRelease(BtreeVacuumLock);
}
 
/*
 * _bt_end_vacuum wrapped as an on_shmem_exit callback function
 */
void
_bt_end_vacuum_callback(int code, Datum arg)
{
    _bt_end_vacuum((Relation) DatumGetPointer(arg));
}
 
/*
 * BTreeShmemSize --- report amount of shared memory space needed
 */
Size
BTreeShmemSize(void)
{
    Size        size;
 
    size = offsetof(BTVacInfo, vacuums);
    size = add_size(size, mul_size(MaxBackends, sizeof(BTOneVacInfo)));
    return size;
}
 
/*
 * BTreeShmemInit --- initialize this module's shared memory
 */
void
BTreeShmemInit(void)
{
    bool        found;
 
    btvacinfo = (BTVacInfo *) ShmemInitStruct("BTree Vacuum State",
                                              BTreeShmemSize(),
                                              &found);
 
    if (!IsUnderPostmaster)
    {
        /* Initialize shared memory area */
        Assert(!found);
 
        /*
         * It doesn't really matter what the cycle counter starts at, but
         * having it always start the same doesn't seem good.  Seed with
         * low-order bits of time() instead.
         */
        btvacinfo->cycle_ctr = (BTCycleId) time(NULL);
 
        btvacinfo->num_vacuums = 0;
        btvacinfo->max_vacuums = MaxBackends;
    }
    else
        Assert(found);
}
 
bytea *
btoptions(Datum reloptions, bool validate)
{
    static const relopt_parse_elt tab[] = {
        {"fillfactor", RELOPT_TYPE_INT, offsetof(BTOptions, fillfactor)},
        {"vacuum_cleanup_index_scale_factor", RELOPT_TYPE_REAL,
        offsetof(BTOptions, vacuum_cleanup_index_scale_factor)},
        {"deduplicate_items", RELOPT_TYPE_BOOL,
        offsetof(BTOptions, deduplicate_items)}
    };
 
    return (bytea *) build_reloptions(reloptions, validate,
                                      RELOPT_KIND_BTREE,
                                      sizeof(BTOptions),
                                      tab, lengthof(tab));
}
 
/*
 *  btproperty() -- Check boolean properties of indexes.
 *
 * This is optional, but handling AMPROP_RETURNABLE here saves opening the rel
 * to call btcanreturn.
 */
bool
btproperty(Oid index_oid, int attno,
           IndexAMProperty prop, const char *propname,
           bool *res, bool *isnull)
{
    switch (prop)
    {
        case AMPROP_RETURNABLE:
            /* answer only for columns, not AM or whole index */
            if (attno == 0)
                return false;
            /* otherwise, btree can always return data */
            *res = true;
            return true;
 
        default:
            return false;       /* punt to generic code */
    }
}
 
/*
 *  btbuildphasename() -- Return name of index build phase.
 */
char *
btbuildphasename(int64 phasenum)
{
    switch (phasenum)
    {
        case PROGRESS_CREATEIDX_SUBPHASE_INITIALIZE:
            return "initializing";
        case PROGRESS_BTREE_PHASE_INDEXBUILD_TABLESCAN:
            return "scanning table";
        case PROGRESS_BTREE_PHASE_PERFORMSORT_1:
            return "sorting live tuples";
        case PROGRESS_BTREE_PHASE_PERFORMSORT_2:
            return "sorting dead tuples";
        case PROGRESS_BTREE_PHASE_LEAF_LOAD:
            return "loading tuples in tree";
        default:
            return NULL;
    }
}
 
/*
 *  _bt_truncate() -- create tuple without unneeded suffix attributes.
 *
 * Returns truncated pivot index tuple allocated in caller's memory context,
 * with key attributes copied from caller's firstright argument.  If rel is
 * an INCLUDE index, non-key attributes will definitely be truncated away,
 * since they're not part of the key space.  More aggressive suffix
 * truncation can take place when it's clear that the returned tuple does not
 * need one or more suffix key attributes.  We only need to keep firstright
 * attributes up to and including the first non-lastleft-equal attribute.
 * Caller's insertion scankey is used to compare the tuples; the scankey's
 * argument values are not considered here.
 *
 * Note that returned tuple's t_tid offset will hold the number of attributes
 * present, so the original item pointer offset is not represented.  Caller
 * should only change truncated tuple's downlink.  Note also that truncated
 * key attributes are treated as containing "minus infinity" values by
 * _bt_compare().
 *
 * In the worst case (when a heap TID must be appended to distinguish lastleft
 * from firstright), the size of the returned tuple is the size of firstright
 * plus the size of an additional MAXALIGN()'d item pointer.  This guarantee
 * is important, since callers need to stay under the 1/3 of a page
 * restriction on tuple size.  If this routine is ever taught to truncate
 * within an attribute/datum, it will need to avoid returning an enlarged
 * tuple to caller when truncation + TOAST compression ends up enlarging the
 * final datum.
 */
IndexTuple
_bt_truncate(Relation rel, IndexTuple lastleft, IndexTuple firstright,
             BTScanInsert itup_key)
{
    TupleDesc   itupdesc = RelationGetDescr(rel);
    int16       nkeyatts = IndexRelationGetNumberOfKeyAttributes(rel);
    int         keepnatts;
    IndexTuple  pivot;
    IndexTuple  tidpivot;
    ItemPointer pivotheaptid;
    Size        newsize;
 
    /*
     * We should only ever truncate non-pivot tuples from leaf pages.  It's
     * never okay to truncate when splitting an internal page.
     */
    Assert(!BTreeTupleIsPivot(lastleft) && !BTreeTupleIsPivot(firstright));
 
    /* Determine how many attributes must be kept in truncated tuple */
    keepnatts = _bt_keep_natts(rel, lastleft, firstright, itup_key);
 
#ifdef DEBUG_NO_TRUNCATE
    /* Force truncation to be ineffective for testing purposes */
    keepnatts = nkeyatts + 1;
#endif
 
    pivot = index_truncate_tuple(itupdesc, firstright,
                                 Min(keepnatts, nkeyatts));
 
    if (BTreeTupleIsPosting(pivot))
    {
        /*
         * index_truncate_tuple() just returns a straight copy of firstright
         * when it has no attributes to truncate.  When that happens, we may
         * need to truncate away a posting list here instead.
         */
        Assert(keepnatts == nkeyatts || keepnatts == nkeyatts + 1);
        Assert(IndexRelationGetNumberOfAttributes(rel) == nkeyatts);
        pivot->t_info &= ~INDEX_SIZE_MASK;
        pivot->t_info |= MAXALIGN(BTreeTupleGetPostingOffset(firstright));
    }
 
    /*
     * If there is a distinguishing key attribute within pivot tuple, we're
     * done
     */
    if (keepnatts <= nkeyatts)
    {
        BTreeTupleSetNAtts(pivot, keepnatts, false);
        return pivot;
    }
 
    /*
     * We have to store a heap TID in the new pivot tuple, since no non-TID
     * key attribute value in firstright distinguishes the right side of the
     * split from the left side.  nbtree conceptualizes this case as an
     * inability to truncate away any key attributes, since heap TID is
     * treated as just another key attribute (despite lacking a pg_attribute
     * entry).
     *
     * Use enlarged space that holds a copy of pivot.  We need the extra space
     * to store a heap TID at the end (using the special pivot tuple
     * representation).  Note that the original pivot already has firstright's
     * possible posting list/non-key attribute values removed at this point.
     */
    newsize = MAXALIGN(IndexTupleSize(pivot)) + MAXALIGN(sizeof(ItemPointerData));
    tidpivot = palloc0(newsize);
    memcpy(tidpivot, pivot, MAXALIGN(IndexTupleSize(pivot)));
    /* Cannot leak memory here */
    pfree(pivot);
 
    /*
     * Store all of firstright's key attribute values plus a tiebreaker heap
     * TID value in enlarged pivot tuple
     */
    tidpivot->t_info &= ~INDEX_SIZE_MASK;
    tidpivot->t_info |= newsize;
    BTreeTupleSetNAtts(tidpivot, nkeyatts, true);
    pivotheaptid = BTreeTupleGetHeapTID(tidpivot);
 
    /*
     * Lehman & Yao use lastleft as the leaf high key in all cases, but don't
     * consider suffix truncation.  It seems like a good idea to follow that
     * example in cases where no truncation takes place -- use lastleft's heap
     * TID.  (This is also the closest value to negative infinity that's
     * legally usable.)
     */
    ItemPointerCopy(BTreeTupleGetMaxHeapTID(lastleft), pivotheaptid);
 
    /*
     * We're done.  Assert() that heap TID invariants hold before returning.
     *
     * Lehman and Yao require that the downlink to the right page, which is to
     * be inserted into the parent page in the second phase of a page split be
     * a strict lower bound on items on the right page, and a non-strict upper
     * bound for items on the left page.  Assert that heap TIDs follow these
     * invariants, since a heap TID value is apparently needed as a
     * tiebreaker.
     */
#ifndef DEBUG_NO_TRUNCATE
    Assert(ItemPointerCompare(BTreeTupleGetMaxHeapTID(lastleft),
                              BTreeTupleGetHeapTID(firstright)) < 0);
    Assert(ItemPointerCompare(pivotheaptid,
                              BTreeTupleGetHeapTID(lastleft)) >= 0);
    Assert(ItemPointerCompare(pivotheaptid,
                              BTreeTupleGetHeapTID(firstright)) < 0);
#else
 
    /*
     * Those invariants aren't guaranteed to hold for lastleft + firstright
     * heap TID attribute values when they're considered here only because
     * DEBUG_NO_TRUNCATE is defined (a heap TID is probably not actually
     * needed as a tiebreaker).  DEBUG_NO_TRUNCATE must therefore use a heap
     * TID value that always works as a strict lower bound for items to the
     * right.  In particular, it must avoid using firstright's leading key
     * attribute values along with lastleft's heap TID value when lastleft's
     * TID happens to be greater than firstright's TID.
     */
    ItemPointerCopy(BTreeTupleGetHeapTID(firstright), pivotheaptid);
 
    /*
     * Pivot heap TID should never be fully equal to firstright.  Note that
     * the pivot heap TID will still end up equal to lastleft's heap TID when
     * that's the only usable value.
     */
    ItemPointerSetOffsetNumber(pivotheaptid,
                               OffsetNumberPrev(ItemPointerGetOffsetNumber(pivotheaptid)));
    Assert(ItemPointerCompare(pivotheaptid,
                              BTreeTupleGetHeapTID(firstright)) < 0);
#endif
 
    return tidpivot;
}
 
/*
 * _bt_keep_natts - how many key attributes to keep when truncating.
 *
 * Caller provides two tuples that enclose a split point.  Caller's insertion
 * scankey is used to compare the tuples; the scankey's argument values are
 * not considered here.
 *
 * This can return a number of attributes that is one greater than the
 * number of key attributes for the index relation.  This indicates that the
 * caller must use a heap TID as a unique-ifier in new pivot tuple.
 */
static int
_bt_keep_natts(Relation rel, IndexTuple lastleft, IndexTuple firstright,
               BTScanInsert itup_key)
{
    int         nkeyatts = IndexRelationGetNumberOfKeyAttributes(rel);
    TupleDesc   itupdesc = RelationGetDescr(rel);
    int         keepnatts;
    ScanKey     scankey;
 
    /*
     * _bt_compare() treats truncated key attributes as having the value minus
     * infinity, which would break searches within !heapkeyspace indexes.  We
     * must still truncate away non-key attribute values, though.
     */
    if (!itup_key->heapkeyspace)
        return nkeyatts;
 
    scankey = itup_key->scankeys;
    keepnatts = 1;
    for (int attnum = 1; attnum <= nkeyatts; attnum++, scankey++)
    {
        Datum       datum1,
                    datum2;
        bool        isNull1,
                    isNull2;
 
        datum1 = index_getattr(lastleft, attnum, itupdesc, &isNull1);
        datum2 = index_getattr(firstright, attnum, itupdesc, &isNull2);
 
        if (isNull1 != isNull2)
            break;
 
        if (!isNull1 &&
            DatumGetInt32(FunctionCall2Coll(&scankey->sk_func,
                                            scankey->sk_collation,
                                            datum1,
                                            datum2)) != 0)
            break;
 
        keepnatts++;
    }
 
    /*
     * Assert that _bt_keep_natts_fast() agrees with us in passing.  This is
     * expected in an allequalimage index.
     */
    Assert(!itup_key->allequalimage ||
           keepnatts == _bt_keep_natts_fast(rel, lastleft, firstright));
 
    return keepnatts;
}
 
/*
 * _bt_keep_natts_fast - fast bitwise variant of _bt_keep_natts.
 *
 * This is exported so that a candidate split point can have its effect on
 * suffix truncation inexpensively evaluated ahead of time when finding a
 * split location.  A naive bitwise approach to datum comparisons is used to
 * save cycles.
 *
 * The approach taken here usually provides the same answer as _bt_keep_natts
 * will (for the same pair of tuples from a heapkeyspace index), since the
 * majority of btree opclasses can never indicate that two datums are equal
 * unless they're bitwise equal after detoasting.  When an index only has
 * "equal image" columns, routine is guaranteed to give the same result as
 * _bt_keep_natts would.
 *
 * Callers can rely on the fact that attributes considered equal here are
 * definitely also equal according to _bt_keep_natts, even when the index uses
 * an opclass or collation that is not "allequalimage"/deduplication-safe.
 * This weaker guarantee is good enough for nbtsplitloc.c caller, since false
 * negatives generally only have the effect of making leaf page splits use a
 * more balanced split point.
 */
int
_bt_keep_natts_fast(Relation rel, IndexTuple lastleft, IndexTuple firstright)
{
    TupleDesc   itupdesc = RelationGetDescr(rel);
    int         keysz = IndexRelationGetNumberOfKeyAttributes(rel);
    int         keepnatts;
 
    keepnatts = 1;
    for (int attnum = 1; attnum <= keysz; attnum++)
    {
        Datum       datum1,
                    datum2;
        bool        isNull1,
                    isNull2;
        Form_pg_attribute att;
 
        datum1 = index_getattr(lastleft, attnum, itupdesc, &isNull1);
        datum2 = index_getattr(firstright, attnum, itupdesc, &isNull2);
        att = TupleDescAttr(itupdesc, attnum - 1);
 
        if (isNull1 != isNull2)
            break;
 
        if (!isNull1 &&
            !datum_image_eq(datum1, datum2, att->attbyval, att->attlen))
            break;
 
        keepnatts++;
    }
 
    return keepnatts;
}
 
/*
 *  _bt_check_natts() -- Verify tuple has expected number of attributes.
 *
 * Returns value indicating if the expected number of attributes were found
 * for a particular offset on page.  This can be used as a general purpose
 * sanity check.
 *
 * Testing a tuple directly with BTreeTupleGetNAtts() should generally be
 * preferred to calling here.  That's usually more convenient, and is always
 * more explicit.  Call here instead when offnum's tuple may be a negative
 * infinity tuple that uses the pre-v11 on-disk representation, or when a low
 * context check is appropriate.  This routine is as strict as possible about
 * what is expected on each version of btree.
 */
bool
_bt_check_natts(Relation rel, bool heapkeyspace, Page page, OffsetNumber offnum)
{
    int16       natts = IndexRelationGetNumberOfAttributes(rel);
    int16       nkeyatts = IndexRelationGetNumberOfKeyAttributes(rel);
    BTPageOpaque opaque = BTPageGetOpaque(page);
    IndexTuple  itup;
    int         tupnatts;
 
    /*
     * We cannot reliably test a deleted or half-dead page, since they have
     * dummy high keys
     */
    if (P_IGNORE(opaque))
        return true;
 
    Assert(offnum >= FirstOffsetNumber &&
           offnum <= PageGetMaxOffsetNumber(page));
 
    itup = (IndexTuple) PageGetItem(page, PageGetItemId(page, offnum));
    tupnatts = BTreeTupleGetNAtts(itup, rel);
 
    /* !heapkeyspace indexes do not support deduplication */
    if (!heapkeyspace && BTreeTupleIsPosting(itup))
        return false;
 
    /* Posting list tuples should never have "pivot heap TID" bit set */
    if (BTreeTupleIsPosting(itup) &&
        (ItemPointerGetOffsetNumberNoCheck(&itup->t_tid) &
         BT_PIVOT_HEAP_TID_ATTR) != 0)
        return false;
 
    /* INCLUDE indexes do not support deduplication */
    if (natts != nkeyatts && BTreeTupleIsPosting(itup))
        return false;
 
    if (P_ISLEAF(opaque))
    {
        if (offnum >= P_FIRSTDATAKEY(opaque))
        {
            /*
             * Non-pivot tuple should never be explicitly marked as a pivot
             * tuple
             */
            if (BTreeTupleIsPivot(itup))
                return false;
 
            /*
             * Leaf tuples that are not the page high key (non-pivot tuples)
             * should never be truncated.  (Note that tupnatts must have been
             * inferred, even with a posting list tuple, because only pivot
             * tuples store tupnatts directly.)
             */
            return tupnatts == natts;
        }
        else
        {
            /*
             * Rightmost page doesn't contain a page high key, so tuple was
             * checked above as ordinary leaf tuple
             */
            Assert(!P_RIGHTMOST(opaque));
 
            /*
             * !heapkeyspace high key tuple contains only key attributes. Note
             * that tupnatts will only have been explicitly represented in
             * !heapkeyspace indexes that happen to have non-key attributes.
             */
            if (!heapkeyspace)
                return tupnatts == nkeyatts;
 
            /* Use generic heapkeyspace pivot tuple handling */
        }
    }
    else                        /* !P_ISLEAF(opaque) */
    {
        if (offnum == P_FIRSTDATAKEY(opaque))
        {
            /*
             * The first tuple on any internal page (possibly the first after
             * its high key) is its negative infinity tuple.  Negative
             * infinity tuples are always truncated to zero attributes.  They
             * are a particular kind of pivot tuple.
             */
            if (heapkeyspace)
                return tupnatts == 0;
 
            /*
             * The number of attributes won't be explicitly represented if the
             * negative infinity tuple was generated during a page split that
             * occurred with a version of Postgres before v11.  There must be
             * a problem when there is an explicit representation that is
             * non-zero, or when there is no explicit representation and the
             * tuple is evidently not a pre-pg_upgrade tuple.
             *
             * Prior to v11, downlinks always had P_HIKEY as their offset.
             * Accept that as an alternative indication of a valid
             * !heapkeyspace negative infinity tuple.
             */
            return tupnatts == 0 ||
                ItemPointerGetOffsetNumber(&(itup->t_tid)) == P_HIKEY;
        }
        else
        {
            /*
             * !heapkeyspace downlink tuple with separator key contains only
             * key attributes.  Note that tupnatts will only have been
             * explicitly represented in !heapkeyspace indexes that happen to
             * have non-key attributes.
             */
            if (!heapkeyspace)
                return tupnatts == nkeyatts;
 
            /* Use generic heapkeyspace pivot tuple handling */
        }
    }
 
    /* Handle heapkeyspace pivot tuples (excluding minus infinity items) */
    Assert(heapkeyspace);
 
    /*
     * Explicit representation of the number of attributes is mandatory with
     * heapkeyspace index pivot tuples, regardless of whether or not there are
     * non-key attributes.
     */
    if (!BTreeTupleIsPivot(itup))
        return false;
 
    /* Pivot tuple should not use posting list representation (redundant) */
    if (BTreeTupleIsPosting(itup))
        return false;
 
    /*
     * Heap TID is a tiebreaker key attribute, so it cannot be untruncated
     * when any other key attribute is truncated
     */
    if (BTreeTupleGetHeapTID(itup) != NULL && tupnatts != nkeyatts)
        return false;
 
    /*
     * Pivot tuple must have at least one untruncated key attribute (minus
     * infinity pivot tuples are the only exception).  Pivot tuples can never
     * represent that there is a value present for a key attribute that
     * exceeds pg_index.indnkeyatts for the index.
     */
    return tupnatts > 0 && tupnatts <= nkeyatts;
}
 
/*
 *
 *  _bt_check_third_page() -- check whether tuple fits on a btree page at all.
 *
 * We actually need to be able to fit three items on every page, so restrict
 * any one item to 1/3 the per-page available space.  Note that itemsz should
 * not include the ItemId overhead.
 *
 * It might be useful to apply TOAST methods rather than throw an error here.
 * Using out of line storage would break assumptions made by suffix truncation
 * and by contrib/amcheck, though.
 */
void
_bt_check_third_page(Relation rel, Relation heap, bool needheaptidspace,
                     Page page, IndexTuple newtup)
{
    Size        itemsz;
    BTPageOpaque opaque;
 
    itemsz = MAXALIGN(IndexTupleSize(newtup));
 
    /* Double check item size against limit */
    if (itemsz <= BTMaxItemSize(page))
        return;
 
    /*
     * Tuple is probably too large to fit on page, but it's possible that the
     * index uses version 2 or version 3, or that page is an internal page, in
     * which case a slightly higher limit applies.
     */
    if (!needheaptidspace && itemsz <= BTMaxItemSizeNoHeapTid(page))
        return;
 
    /*
     * Internal page insertions cannot fail here, because that would mean that
     * an earlier leaf level insertion that should have failed didn't
     */
    opaque = BTPageGetOpaque(page);
    if (!P_ISLEAF(opaque))
        elog(ERROR, "cannot insert oversized tuple of size %zu on internal page of index \"%s\"",
             itemsz, RelationGetRelationName(rel));
 
    ereport(ERROR,
            (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
             errmsg("index row size %zu exceeds btree version %u maximum %zu for index \"%s\"",
                    itemsz,
                    needheaptidspace ? BTREE_VERSION : BTREE_NOVAC_VERSION,
                    needheaptidspace ? BTMaxItemSize(page) :
                    BTMaxItemSizeNoHeapTid(page),
                    RelationGetRelationName(rel)),
             errdetail("Index row references tuple (%u,%u) in relation \"%s\".",
                       ItemPointerGetBlockNumber(BTreeTupleGetHeapTID(newtup)),
                       ItemPointerGetOffsetNumber(BTreeTupleGetHeapTID(newtup)),
                       RelationGetRelationName(heap)),
             errhint("Values larger than 1/3 of a buffer page cannot be indexed.\n"
                     "Consider a function index of an MD5 hash of the value, "
                     "or use full text indexing."),
             errtableconstraint(heap, RelationGetRelationName(rel))));
}
 
/*
 * Are all attributes in rel "equality is image equality" attributes?
 *
 * We use each attribute's BTEQUALIMAGE_PROC opclass procedure.  If any
 * opclass either lacks a BTEQUALIMAGE_PROC procedure or returns false, we
 * return false; otherwise we return true.
 *
 * Returned boolean value is stored in index metapage during index builds.
 * Deduplication can only be used when we return true.
 */
bool
_bt_allequalimage(Relation rel, bool debugmessage)
{
    bool        allequalimage = true;
 
    /* INCLUDE indexes can never support deduplication */
    if (IndexRelationGetNumberOfAttributes(rel) !=
        IndexRelationGetNumberOfKeyAttributes(rel))
        return false;
 
    for (int i = 0; i < IndexRelationGetNumberOfKeyAttributes(rel); i++)
    {
        Oid         opfamily = rel->rd_opfamily[i];
        Oid         opcintype = rel->rd_opcintype[i];
        Oid         collation = rel->rd_indcollation[i];
        Oid         equalimageproc;
 
        equalimageproc = get_opfamily_proc(opfamily, opcintype, opcintype,
                                           BTEQUALIMAGE_PROC);
 
        /*
         * If there is no BTEQUALIMAGE_PROC then deduplication is assumed to
         * be unsafe.  Otherwise, actually call proc and see what it says.
         */
        if (!OidIsValid(equalimageproc) ||
            !DatumGetBool(OidFunctionCall1Coll(equalimageproc, collation,
                                               ObjectIdGetDatum(opcintype))))
        {
            allequalimage = false;
            break;
        }
    }
 
    if (debugmessage)
    {
        if (allequalimage)
            elog(DEBUG1, "index \"%s\" can safely use deduplication",
                 RelationGetRelationName(rel));
        else
            elog(DEBUG1, "index \"%s\" cannot use deduplication",
                 RelationGetRelationName(rel));
    }
 
    return allequalimage;
}