nbtutils.c

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/*-------------------------------------------------------------------------
 *
 * nbtutils.c
 *    Utility code for Postgres btree implementation.
 *
 * Portions Copyright (c) 1996-2021, 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 "catalog/catalog.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"


typedef struct BTSortArrayContext
{
    FmgrInfo    flinfo;
    Oid         collation;
    bool        reverse;
} BTSortArrayContext;

static Datum _bt_find_extreme_element(IndexScanDesc scan, ScanKey skey,
                                      StrategyNumber strat,
                                      Datum *elems, int nelems);
static int  _bt_sort_array_elements(IndexScanDesc scan, ScanKey skey,
                                    bool reverse,
                                    Datum *elems, int nelems);
static int  _bt_compare_array_elements(const void *a, const void *b, void *arg);
static bool _bt_compare_scankey_args(IndexScanDesc scan, ScanKey op,
                                     ScanKey leftarg, ScanKey rightarg,
                                     bool *result);
static bool _bt_fix_scankey_strategy(ScanKey skey, int16 *indoption);
static void _bt_mark_scankey_required(ScanKey skey);
static bool _bt_check_rowcompare(ScanKey skey,
                                 IndexTuple tuple, int tupnatts, TupleDesc tupdesc,
                                 ScanDirection dir, bool *continuescan);
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.
 *
 *      When itup is a non-pivot tuple, the returned insertion scan key is
 *      suitable for finding a place for it to go on the leaf level.  Pivot
 *      tuples can be used to re-find leaf page with matching high key, but
 *      then caller needs to set scan key's pivotsearch field to true.  This
 *      allows caller to search for a leaf page with a matching high key,
 *      which is usually to the left of the first leaf page a non-pivot match
 *      might appear on.
 *
 *      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;
    key->pivotsearch = false;
    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;
    }

    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.
 * Prepare modified scan keys in so->arrayKeyData, which will hold the current
 * array elements during each primitive indexscan operation.  For inequality
 * array keys, it's sufficient to find the extreme element value and replace
 * the whole array with that scalar value.
 *
 * Note: the reason we need so->arrayKeyData, rather than just scribbling
 * on scan->keyData, is that callers are permitted to call btrescan without
 * supplying a new set of scankey data.
 */
void
_bt_preprocess_array_keys(IndexScanDesc scan)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    int         numberOfKeys = scan->numberOfKeys;
    int16      *indoption = scan->indexRelation->rd_indoption;
    int         numArrayKeys;
    ScanKey     cur;
    int         i;
    MemoryContext oldContext;

    /* Quick check to see if there are any array keys */
    numArrayKeys = 0;
    for (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->numArrayKeys = -1;
                so->arrayKeyData = NULL;
                return;
            }
        }
    }

    /* Quit if nothing to do. */
    if (numArrayKeys == 0)
    {
        so->numArrayKeys = 0;
        so->arrayKeyData = NULL;
        return;
    }

    /*
     * 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 */
    so->arrayKeyData = (ScanKey) palloc(scan->numberOfKeys * sizeof(ScanKeyData));
    memcpy(so->arrayKeyData,
           scan->keyData,
           scan->numberOfKeys * sizeof(ScanKeyData));

    /* Allocate space for per-array data in the workspace context */
    so->arrayKeys = (BTArrayKeyInfo *) palloc0(numArrayKeys * sizeof(BTArrayKeyInfo));

    /* Now process each array key */
    numArrayKeys = 0;
    for (i = 0; i < numberOfKeys; i++)
    {
        ArrayType  *arrayval;
        int16       elmlen;
        bool        elmbyval;
        char        elmalign;
        int         num_elems;
        Datum      *elem_values;
        bool       *elem_nulls;
        int         num_nonnulls;
        int         j;

        cur = &so->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)
        {
            numArrayKeys = -1;
            break;
        }

        /*
         * 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,
                                             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,
                                             BTLessStrategyNumber,
                                             elem_values, num_nonnulls);
                continue;
            default:
                elog(ERROR, "unrecognized StrategyNumber: %d",
                     (int) cur->sk_strategy);
                break;
        }

        /*
         * Sort the non-null elements and eliminate any duplicates.  We must
         * sort in the same ordering used by the index column, so that the
         * successive primitive indexscans produce data in index order.
         */
        num_elems = _bt_sort_array_elements(scan, cur,
                                            (indoption[cur->sk_attno - 1] & INDOPTION_DESC) != 0,
                                            elem_values, num_nonnulls);

        /*
         * And set up the BTArrayKeyInfo data.
         */
        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);
}

/*
 * _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,
                         StrategyNumber strat,
                         Datum *elems, int nelems)
{
    Relation    rel = scan->indexRelation;
    Oid         elemtype,
                cmp_op;
    RegProcedure cmp_proc;
    FmgrInfo    flinfo;
    Datum       result;
    int         i;

    /*
     * 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 = skey->sk_subtype;
    if (elemtype == InvalidOid)
        elemtype = rel->rd_opcintype[skey->sk_attno - 1];

    /*
     * 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.
     */
    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.
 *
 * scan and skey identify the index column, whose opfamily determines the
 * comparison semantics.  If reverse is true, we sort in descending order.
 */
static int
_bt_sort_array_elements(IndexScanDesc scan, ScanKey skey,
                        bool reverse,
                        Datum *elems, int nelems)
{
    Relation    rel = scan->indexRelation;
    Oid         elemtype;
    RegProcedure cmp_proc;
    BTSortArrayContext cxt;

    if (nelems <= 1)
        return nelems;          /* no work to do */

    /*
     * 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 = skey->sk_subtype;
    if (elemtype == InvalidOid)
        elemtype = rel->rd_opcintype[skey->sk_attno - 1];

    /*
     * Look up the appropriate 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 support functions 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) in opfamily %u",
             BTORDER_PROC, elemtype, elemtype,
             rel->rd_opfamily[skey->sk_attno - 1]);

    /* Sort the array elements */
    fmgr_info(cmp_proc, &cxt.flinfo);
    cxt.collation = skey->sk_collation;
    cxt.reverse = reverse;
    qsort_arg((void *) elems, nelems, sizeof(Datum),
              _bt_compare_array_elements, (void *) &cxt);

    /* Now scan the sorted elements and remove duplicates */
    return qunique_arg(elems, nelems, sizeof(Datum),
                       _bt_compare_array_elements, &cxt);
}

/*
 * 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->flinfo,
                                              cxt->collation,
                                              da, db));
    if (cxt->reverse)
        INVERT_COMPARE_RESULT(compare);
    return compare;
}

/*
 * _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.  We can't do this until we know the scan direction.
 */
void
_bt_start_array_keys(IndexScanDesc scan, ScanDirection dir)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    int         i;

    for (i = 0; i < so->numArrayKeys; i++)
    {
        BTArrayKeyInfo *curArrayKey = &so->arrayKeys[i];
        ScanKey     skey = &so->arrayKeyData[curArrayKey->scan_key];

        Assert(curArrayKey->num_elems > 0);
        if (ScanDirectionIsBackward(dir))
            curArrayKey->cur_elem = curArrayKey->num_elems - 1;
        else
            curArrayKey->cur_elem = 0;
        skey->sk_argument = curArrayKey->elem_values[curArrayKey->cur_elem];
    }
}

/*
 * _bt_advance_array_keys() -- Advance to next set of array elements
 *
 * 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.
 */
bool
_bt_advance_array_keys(IndexScanDesc scan, ScanDirection dir)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    bool        found = false;
    int         i;

    /*
     * We must advance the last array key most quickly, since it will
     * correspond to the lowest-order index column among the available
     * qualifications. This is necessary to ensure correct ordering of output
     * when there are multiple array keys.
     */
    for (i = so->numArrayKeys - 1; i >= 0; i--)
    {
        BTArrayKeyInfo *curArrayKey = &so->arrayKeys[i];
        ScanKey     skey = &so->arrayKeyData[curArrayKey->scan_key];
        int         cur_elem = curArrayKey->cur_elem;
        int         num_elems = curArrayKey->num_elems;

        if (ScanDirectionIsBackward(dir))
        {
            if (--cur_elem < 0)
            {
                cur_elem = num_elems - 1;
                found = false;  /* need to advance next array key */
            }
            else
                found = true;
        }
        else
        {
            if (++cur_elem >= num_elems)
            {
                cur_elem = 0;
                found = false;  /* need to advance next array key */
            }
            else
                found = true;
        }

        curArrayKey->cur_elem = cur_elem;
        skey->sk_argument = curArrayKey->elem_values[cur_elem];
        if (found)
            break;
    }

    /* advance parallel scan */
    if (scan->parallel_scan != NULL)
        _bt_parallel_advance_array_keys(scan);

    return found;
}

/*
 * _bt_mark_array_keys() -- Handle array keys during btmarkpos
 *
 * Save the current state of the array keys as the "mark" position.
 */
void
_bt_mark_array_keys(IndexScanDesc scan)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    int         i;

    for (i = 0; i < so->numArrayKeys; i++)
    {
        BTArrayKeyInfo *curArrayKey = &so->arrayKeys[i];

        curArrayKey->mark_elem = curArrayKey->cur_elem;
    }
}

/*
 * _bt_restore_array_keys() -- Handle array keys during btrestrpos
 *
 * Restore the array keys to where they were when the mark was set.
 */
void
_bt_restore_array_keys(IndexScanDesc scan)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    bool        changed = false;
    int         i;

    /* Restore each array key to its position when the mark was set */
    for (i = 0; i < so->numArrayKeys; i++)
    {
        BTArrayKeyInfo *curArrayKey = &so->arrayKeys[i];
        ScanKey     skey = &so->arrayKeyData[curArrayKey->scan_key];
        int         mark_elem = curArrayKey->mark_elem;

        if (curArrayKey->cur_elem != mark_elem)
        {
            curArrayKey->cur_elem = mark_elem;
            skey->sk_argument = curArrayKey->elem_values[mark_elem];
            changed = true;
        }
    }

    /*
     * If we changed any keys, we must redo _bt_preprocess_keys.  That might
     * sound like overkill, but in cases with multiple keys per index column
     * it seems necessary to do the full set of pushups.
     */
    if (changed)
    {
        _bt_preprocess_keys(scan);
        /* The mark should have been set on a consistent set of keys... */
        Assert(so->qual_ok);
    }
}


/*
 *  _bt_preprocess_keys() -- Preprocess scan keys
 *
 * The given search-type keys (in scan->keyData[] or so->arrayKeyData[])
 * 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,
 * but no other code depends on that.
 *
 * 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 or after moving to
 * new elements of array keys.  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;
    ScanKey     xform[BTMaxStrategyNumber];
    bool        test_result;
    int         i,
                j;
    AttrNumber  attno;

    /* initialize result variables */
    so->qual_ok = true;
    so->numberOfKeys = 0;

    if (numberOfKeys < 1)
        return;                 /* done if qual-less scan */

    /*
     * Read so->arrayKeyData if array keys are present, else scan->keyData
     */
    if (so->arrayKeyData != NULL)
        inkeys = so->arrayKeyData;
    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);
        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])
            {
                ScanKey     eq = xform[BTEqualStrategyNumber - 1];

                for (j = BTMaxStrategyNumber; --j >= 0;)
                {
                    ScanKey     chk = xform[j];

                    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,
                                                 &test_result))
                    {
                        if (!test_result)
                        {
                            /* keys proven mutually contradictory */
                            so->qual_ok = false;
                            return;
                        }
                        /* else discard the redundant non-equality key */
                        xform[j] = NULL;
                    }
                    /* 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]
                && xform[BTLessEqualStrategyNumber - 1])
            {
                ScanKey     lt = xform[BTLessStrategyNumber - 1];
                ScanKey     le = xform[BTLessEqualStrategyNumber - 1];

                if (_bt_compare_scankey_args(scan, le, lt, le,
                                             &test_result))
                {
                    if (test_result)
                        xform[BTLessEqualStrategyNumber - 1] = NULL;
                    else
                        xform[BTLessStrategyNumber - 1] = NULL;
                }
            }

            /* try to keep only one of >, >= */
            if (xform[BTGreaterStrategyNumber - 1]
                && xform[BTGreaterEqualStrategyNumber - 1])
            {
                ScanKey     gt = xform[BTGreaterStrategyNumber - 1];
                ScanKey     ge = xform[BTGreaterEqualStrategyNumber - 1];

                if (_bt_compare_scankey_args(scan, ge, gt, ge,
                                             &test_result))
                {
                    if (test_result)
                        xform[BTGreaterEqualStrategyNumber - 1] = NULL;
                    else
                        xform[BTGreaterStrategyNumber - 1] = 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])
                {
                    ScanKey     outkey = &outkeys[new_numberOfKeys++];

                    memcpy(outkey, xform[j], sizeof(ScanKeyData));
                    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 (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;
        }

        /* have we seen one of these before? */
        if (xform[j] == NULL)
        {
            /* nope, so remember this scankey */
            xform[j] = cur;
        }
        else
        {
            /* yup, keep only the more restrictive key */
            if (_bt_compare_scankey_args(scan, cur, cur, xform[j],
                                         &test_result))
            {
                if (test_result)
                    xform[j] = cur;
                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.  Keep the
                 * previous one in xform[j] and push this one directly to the
                 * output array.
                 */
                ScanKey     outkey = &outkeys[new_numberOfKeys++];

                memcpy(outkey, cur, sizeof(ScanKeyData));
                if (numberOfEqualCols == attno - 1)
                    _bt_mark_scankey_required(outkey);
            }
        }
    }

    so->numberOfKeys = new_numberOfKeys;
}

/*
 * 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.
 *
 * Note: op always points at the same ScanKey as either leftarg or rightarg.
 * Since we don't scribble on the scankeys, 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,
                         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;
    }

    /*
     * 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;
    }

    /* 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 *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.
 *
 * scan: index scan descriptor (containing a search-type scankey)
 * tuple: index tuple to test
 * tupnatts: number of attributes in tupnatts (high key may be truncated)
 * dir: direction we are scanning in
 * continuescan: output parameter (will be set correctly in all cases)
 */
bool
_bt_checkkeys(IndexScanDesc scan, IndexTuple tuple, int tupnatts,
              ScanDirection dir, bool *continuescan)
{
    TupleDesc   tupdesc;
    BTScanOpaque so;
    int         keysz;
    int         ikey;
    ScanKey     key;

    Assert(BTreeTupleGetNAtts(tuple, scan->indexRelation) == tupnatts);

    *continuescan = true;       /* default assumption */

    tupdesc = RelationGetDescr(scan->indexRelation);
    so = (BTScanOpaque) scan->opaque;
    keysz = so->numberOfKeys;

    for (key = so->keyData, ikey = 0; ikey < keysz; key++, ikey++)
    {
        Datum       datum;
        bool        isNull;
        Datum       test;

        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(ScanDirectionIsForward(dir));
            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 ((key->sk_flags & SK_BT_REQFWD) &&
                ScanDirectionIsForward(dir))
                *continuescan = false;
            else if ((key->sk_flags & SK_BT_REQBKWD) &&
                     ScanDirectionIsBackward(dir))
                *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.
                 */
                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.
                 */
                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;
        }

        test = FunctionCall2Coll(&key->sk_func, key->sk_collation,
                                 datum, key->sk_argument);

        if (!DatumGetBool(test))
        {
            /*
             * 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 ((key->sk_flags & SK_BT_REQFWD) &&
                ScanDirectionIsForward(dir))
                *continuescan = false;
            else if ((key->sk_flags & SK_BT_REQBKWD) &&
                     ScanDirectionIsBackward(dir))
                *continuescan = false;

            /*
             * In any case, 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, which see for more info.
 */
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(ScanDirectionIsForward(dir));
            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.
                 */
                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.
                 */
                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;
}

/*
 * _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 = (BTPageOpaque) PageGetSpecialPointer(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 = (BTPageOpaque) PageGetSpecialPointer(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));

    /*
     * Mask allocated for number of keys in index tuple must be able to fit
     * maximum possible number of index attributes
     */
    StaticAssertStmt(BT_OFFSET_MASK >= INDEX_MAX_KEYS,
                     "BT_OFFSET_MASK can't fit INDEX_MAX_KEYS");

    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 = (BTPageOpaque) PageGetSpecialPointer(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;
}