/src/postgres/src/backend/access/nbtree/nbtutils.c

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/*-------------------------------------------------------------------------
 *
 * nbtutils.c
 *    Utility code for Postgres btree implementation.
 *
 * Portions Copyright (c) 1996-2025, 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 "commands/progress.h"
#include "miscadmin.h"
#include "utils/datum.h"
#include "utils/lsyscache.h"

#define LOOK_AHEAD_REQUIRED_RECHECKS  3
#define LOOK_AHEAD_DEFAULT_DISTANCE   5
#define NSKIPADVANCES_THRESHOLD     3

static inline int32 _bt_compare_array_skey(FmgrInfo *orderproc,
                       Datum tupdatum, bool tupnull,
                       Datum arrdatum, ScanKey cur);
static void _bt_binsrch_skiparray_skey(bool cur_elem_trig, ScanDirection dir,
                     Datum tupdatum, bool tupnull,
                     BTArrayKeyInfo *array, ScanKey cur,
                     int32 *set_elem_result);
static void _bt_skiparray_set_element(Relation rel, ScanKey skey, BTArrayKeyInfo *array,
                    int32 set_elem_result, Datum tupdatum, bool tupnull);
static void _bt_skiparray_set_isnull(Relation rel, ScanKey skey, BTArrayKeyInfo *array);
static void _bt_array_set_low_or_high(Relation rel, ScanKey skey,
                    BTArrayKeyInfo *array, bool low_not_high);
static bool _bt_array_decrement(Relation rel, ScanKey skey, BTArrayKeyInfo *array);
static bool _bt_array_increment(Relation rel, ScanKey skey, BTArrayKeyInfo *array);
static bool _bt_advance_array_keys_increment(IndexScanDesc scan, ScanDirection dir,
                       bool *skip_array_set);
static void _bt_rewind_nonrequired_arrays(IndexScanDesc scan, ScanDirection dir);
static bool _bt_tuple_before_array_skeys(IndexScanDesc scan, ScanDirection dir,
                     IndexTuple tuple, TupleDesc tupdesc, int tupnatts,
                     bool readpagetup, int sktrig, bool *scanBehind);
static bool _bt_advance_array_keys(IndexScanDesc scan, BTReadPageState *pstate,
                   IndexTuple tuple, int tupnatts, TupleDesc tupdesc,
                   int sktrig, bool sktrig_required);
#ifdef USE_ASSERT_CHECKING
static bool _bt_verify_arrays_bt_first(IndexScanDesc scan, ScanDirection dir);
static bool _bt_verify_keys_with_arraykeys(IndexScanDesc scan);
#endif
static bool _bt_oppodir_checkkeys(IndexScanDesc scan, ScanDirection dir,
                  IndexTuple finaltup);
static bool _bt_check_compare(IndexScanDesc scan, ScanDirection dir,
                IndexTuple tuple, int tupnatts, TupleDesc tupdesc,
                bool advancenonrequired, bool forcenonrequired,
                bool *continuescan, int *ikey);
static bool _bt_check_rowcompare(ScanKey skey,
                 IndexTuple tuple, int tupnatts, TupleDesc tupdesc,
                 ScanDirection dir, bool forcenonrequired, bool *continuescan);
static void _bt_checkkeys_look_ahead(IndexScanDesc scan, BTReadPageState *pstate,
                   int tupnatts, TupleDesc tupdesc);
static int  _bt_keep_natts(Relation rel, IndexTuple lastleft,
               IndexTuple firstright, BTScanInsert itup_key);


/*
 * _bt_mkscankey
 *    Build an insertion scan key that contains comparison data from itup
 *    as well as comparator routines appropriate to the key datatypes.
 *
 *    The result is intended for use with _bt_compare() and _bt_truncate().
 *    Callers that don't need to fill out the insertion scankey arguments
 *    (e.g. they use an ad-hoc comparison routine, or only need a scankey
 *    for _bt_truncate()) can pass a NULL index tuple.  The scankey will
 *    be initialized as if an "all truncated" pivot tuple was passed
 *    instead.
 *
 *    Note that we may occasionally have to share lock the metapage to
 *    determine whether or not the keys in the index are expected to be
 *    unique (i.e. if this is a "heapkeyspace" index).  We assume a
 *    heapkeyspace index when caller passes a NULL tuple, allowing index
 *    build callers to avoid accessing the non-existent metapage.  We
 *    also assume that the index is _not_ allequalimage when a NULL tuple
 *    is passed; CREATE INDEX callers call _bt_allequalimage() to set the
 *    field themselves.
 */
BTScanInsert
_bt_mkscankey(Relation rel, IndexTuple itup)
{
  BTScanInsert key;
  ScanKey   skey;
  TupleDesc itupdesc;
  int     indnkeyatts;
  int16    *indoption;
  int     tupnatts;
  int     i;

  itupdesc = RelationGetDescr(rel);
  indnkeyatts = IndexRelationGetNumberOfKeyAttributes(rel);
  indoption = rel->rd_indoption;
  tupnatts = itup ? BTreeTupleGetNAtts(itup, rel) : 0;

  Assert(tupnatts <= IndexRelationGetNumberOfAttributes(rel));

  /*
   * We'll execute search using scan key constructed on key columns.
   * Truncated attributes and non-key attributes are omitted from the final
   * scan key.
   */
  key = palloc(offsetof(BTScanInsertData, scankeys) +
         sizeof(ScanKeyData) * indnkeyatts);
  if (itup)
    _bt_metaversion(rel, &key->heapkeyspace, &key->allequalimage);
  else
  {
    /* Utility statement callers can set these fields themselves */
    key->heapkeyspace = true;
    key->allequalimage = false;
  }
  key->anynullkeys = false; /* initial assumption */
  key->nextkey = false;   /* usual case, required by btinsert */
  key->backward = false;    /* usual case, required by btinsert */
  key->keysz = Min(indnkeyatts, tupnatts);
  key->scantid = key->heapkeyspace && itup ?
    BTreeTupleGetHeapTID(itup) : NULL;
  skey = key->scankeys;
  for (i = 0; i < indnkeyatts; i++)
  {
    FmgrInfo   *procinfo;
    Datum   arg;
    bool    null;
    int     flags;

    /*
     * We can use the cached (default) support procs since no cross-type
     * comparison can be needed.
     */
    procinfo = index_getprocinfo(rel, i + 1, BTORDER_PROC);

    /*
     * Key arguments built from truncated attributes (or when caller
     * provides no tuple) are defensively represented as NULL values. They
     * should never be used.
     */
    if (i < tupnatts)
      arg = index_getattr(itup, i + 1, itupdesc, &null);
    else
    {
      arg = (Datum) 0;
      null = true;
    }
    flags = (null ? SK_ISNULL : 0) | (indoption[i] << SK_BT_INDOPTION_SHIFT);
    ScanKeyEntryInitializeWithInfo(&skey[i],
                     flags,
                     (AttrNumber) (i + 1),
                     InvalidStrategy,
                     InvalidOid,
                     rel->rd_indcollation[i],
                     procinfo,
                     arg);
    /* Record if any key attribute is NULL (or truncated) */
    if (null)
      key->anynullkeys = true;
  }

  /*
   * In NULLS NOT DISTINCT mode, we pretend that there are no null keys, so
   * that full uniqueness check is done.
   */
  if (rel->rd_index->indnullsnotdistinct)
    key->anynullkeys = false;

  return key;
}

/*
 * free a retracement stack made by _bt_search.
 */
void
_bt_freestack(BTStack stack)
{
  BTStack   ostack;

  while (stack != NULL)
  {
    ostack = stack;
    stack = stack->bts_parent;
    pfree(ostack);
  }
}

/*
 * _bt_compare_array_skey() -- apply array comparison function
 *
 * Compares caller's tuple attribute value to a scan key/array element.
 * Helper function used during binary searches of SK_SEARCHARRAY arrays.
 *
 *    This routine returns:
 *      <0 if tupdatum < arrdatum;
 *       0 if tupdatum == arrdatum;
 *      >0 if tupdatum > arrdatum.
 *
 * This is essentially the same interface as _bt_compare: both functions
 * compare the value that they're searching for to a binary search pivot.
 * However, unlike _bt_compare, this function's "tuple argument" comes first,
 * while its "array/scankey argument" comes second.
*/
static inline int32
_bt_compare_array_skey(FmgrInfo *orderproc,
             Datum tupdatum, bool tupnull,
             Datum arrdatum, ScanKey cur)
{
  int32   result = 0;

  Assert(cur->sk_strategy == BTEqualStrategyNumber);
  Assert(!(cur->sk_flags & (SK_BT_MINVAL | SK_BT_MAXVAL)));

  if (tupnull)       /* NULL tupdatum */
  {
    if (cur->sk_flags & SK_ISNULL)
      result = 0;     /* NULL "=" NULL */
    else if (cur->sk_flags & SK_BT_NULLS_FIRST)
      result = -1;   /* NULL "<" NOT_NULL */
    else
      result = 1;     /* NULL ">" NOT_NULL */
  }
  else if (cur->sk_flags & SK_ISNULL) /* NOT_NULL tupdatum, NULL arrdatum */
  {
    if (cur->sk_flags & SK_BT_NULLS_FIRST)
      result = 1;     /* NOT_NULL ">" NULL */
    else
      result = -1;   /* NOT_NULL "<" NULL */
  }
  else
  {
    /*
     * Like _bt_compare, we need to be careful of cross-type comparisons,
     * so the left value has to be the value that came from an index tuple
     */
    result = DatumGetInt32(FunctionCall2Coll(orderproc, cur->sk_collation,
                         tupdatum, arrdatum));

    /*
     * We flip the sign by following the obvious rule: flip whenever the
     * column is a DESC column.
     *
     * _bt_compare does it the wrong way around (flip when *ASC*) in order
     * to compensate for passing its orderproc arguments backwards.  We
     * don't need to play these games because we find it natural to pass
     * tupdatum as the left value (and arrdatum as the right value).
     */
    if (cur->sk_flags & SK_BT_DESC)
      INVERT_COMPARE_RESULT(result);
  }

  return result;
}

/*
 * _bt_binsrch_array_skey() -- Binary search for next matching array key
 *
 * Returns an index to the first array element >= caller's tupdatum argument.
 * This convention is more natural for forwards scan callers, but that can't
 * really matter to backwards scan callers.  Both callers require handling for
 * the case where the match we return is < tupdatum, and symmetric handling
 * for the case where our best match is > tupdatum.
 *
 * Also sets *set_elem_result to the result _bt_compare_array_skey returned
 * when we used it to compare the matching array element to tupdatum/tupnull.
 *
 * cur_elem_trig indicates if array advancement was triggered by this array's
 * scan key, and that the array is for a required scan key.  We can apply this
 * information to find the next matching array element in the current scan
 * direction using far fewer comparisons (fewer on average, compared to naive
 * binary search).  This scheme takes advantage of an important property of
 * required arrays: required arrays always advance in lockstep with the index
 * scan's progress through the index's key space.
 */
int
_bt_binsrch_array_skey(FmgrInfo *orderproc,
             bool cur_elem_trig, ScanDirection dir,
             Datum tupdatum, bool tupnull,
             BTArrayKeyInfo *array, ScanKey cur,
             int32 *set_elem_result)
{
  int     low_elem = 0,
        mid_elem = -1,
        high_elem = array->num_elems - 1,
        result = 0;
  Datum   arrdatum;

  Assert(cur->sk_flags & SK_SEARCHARRAY);
  Assert(!(cur->sk_flags & SK_BT_SKIP));
  Assert(!(cur->sk_flags & SK_ISNULL)); /* SAOP arrays never have NULLs */
  Assert(cur->sk_strategy == BTEqualStrategyNumber);

  if (cur_elem_trig)
  {
    Assert(!ScanDirectionIsNoMovement(dir));
    Assert(cur->sk_flags & SK_BT_REQFWD);

    /*
     * When the scan key that triggered array advancement is a required
     * array scan key, it is now certain that the current array element
     * (plus all prior elements relative to the current scan direction)
     * cannot possibly be at or ahead of the corresponding tuple value.
     * (_bt_checkkeys must have called _bt_tuple_before_array_skeys, which
     * makes sure this is true as a condition of advancing the arrays.)
     *
     * This makes it safe to exclude array elements up to and including
     * the former-current array element from our search.
     *
     * Separately, when array advancement was triggered by a required scan
     * key, the array element immediately after the former-current element
     * is often either an exact tupdatum match, or a "close by" near-match
     * (a near-match tupdatum is one whose key space falls _between_ the
     * former-current and new-current array elements).  We'll detect both
     * cases via an optimistic comparison of the new search lower bound
     * (or new search upper bound in the case of backwards scans).
     */
    if (ScanDirectionIsForward(dir))
    {
      low_elem = array->cur_elem + 1; /* old cur_elem exhausted */

      /* Compare prospective new cur_elem (also the new lower bound) */
      if (high_elem >= low_elem)
      {
        arrdatum = array->elem_values[low_elem];
        result = _bt_compare_array_skey(orderproc, tupdatum, tupnull,
                        arrdatum, cur);

        if (result <= 0)
        {
          /* Optimistic comparison optimization worked out */
          *set_elem_result = result;
          return low_elem;
        }
        mid_elem = low_elem;
        low_elem++;   /* this cur_elem exhausted, too */
      }

      if (high_elem < low_elem)
      {
        /* Caller needs to perform "beyond end" array advancement */
        *set_elem_result = 1;
        return high_elem;
      }
    }
    else
    {
      high_elem = array->cur_elem - 1;  /* old cur_elem exhausted */

      /* Compare prospective new cur_elem (also the new upper bound) */
      if (high_elem >= low_elem)
      {
        arrdatum = array->elem_values[high_elem];
        result = _bt_compare_array_skey(orderproc, tupdatum, tupnull,
                        arrdatum, cur);

        if (result >= 0)
        {
          /* Optimistic comparison optimization worked out */
          *set_elem_result = result;
          return high_elem;
        }
        mid_elem = high_elem;
        high_elem--;  /* this cur_elem exhausted, too */
      }

      if (high_elem < low_elem)
      {
        /* Caller needs to perform "beyond end" array advancement */
        *set_elem_result = -1;
        return low_elem;
      }
    }
  }

  while (high_elem > low_elem)
  {
    mid_elem = low_elem + ((high_elem - low_elem) / 2);
    arrdatum = array->elem_values[mid_elem];

    result = _bt_compare_array_skey(orderproc, tupdatum, tupnull,
                    arrdatum, cur);

    if (result == 0)
    {
      /*
       * It's safe to quit as soon as we see an equal array element.
       * This often saves an extra comparison or two...
       */
      low_elem = mid_elem;
      break;
    }

    if (result > 0)
      low_elem = mid_elem + 1;
    else
      high_elem = mid_elem;
  }

  /*
   * ...but our caller also cares about how its searched-for tuple datum
   * compares to the low_elem datum.  Must always set *set_elem_result with
   * the result of that comparison specifically.
   */
  if (low_elem != mid_elem)
    result = _bt_compare_array_skey(orderproc, tupdatum, tupnull,
                    array->elem_values[low_elem], cur);

  *set_elem_result = result;

  return low_elem;
}

/*
 * _bt_binsrch_skiparray_skey() -- "Binary search" within a skip array
 *
 * Does not return an index into the array, since skip arrays don't really
 * contain elements (they generate their array elements procedurally instead).
 * Our interface matches that of _bt_binsrch_array_skey in every other way.
 *
 * Sets *set_elem_result just like _bt_binsrch_array_skey would with a true
 * array.  The value 0 indicates that tupdatum/tupnull is within the range of
 * the skip array.  We return -1 when tupdatum/tupnull is lower that any value
 * within the range of the array, and 1 when it is higher than every value.
 * Caller should pass *set_elem_result to _bt_skiparray_set_element to advance
 * the array.
 *
 * cur_elem_trig indicates if array advancement was triggered by this array's
 * scan key.  We use this to optimize-away comparisons that are known by our
 * caller to be unnecessary from context, just like _bt_binsrch_array_skey.
 */
static void
_bt_binsrch_skiparray_skey(bool cur_elem_trig, ScanDirection dir,
               Datum tupdatum, bool tupnull,
               BTArrayKeyInfo *array, ScanKey cur,
               int32 *set_elem_result)
{
  Assert(cur->sk_flags & SK_BT_SKIP);
  Assert(cur->sk_flags & SK_SEARCHARRAY);
  Assert(cur->sk_flags & SK_BT_REQFWD);
  Assert(array->num_elems == -1);
  Assert(!ScanDirectionIsNoMovement(dir));

  if (array->null_elem)
  {
    Assert(!array->low_compare && !array->high_compare);

    *set_elem_result = 0;
    return;
  }

  if (tupnull)       /* NULL tupdatum */
  {
    if (cur->sk_flags & SK_BT_NULLS_FIRST)
      *set_elem_result = -1; /* NULL "<" NOT_NULL */
    else
      *set_elem_result = 1; /* NULL ">" NOT_NULL */
    return;
  }

  /*
   * Array inequalities determine whether tupdatum is within the range of
   * caller's skip array
   */
  *set_elem_result = 0;
  if (ScanDirectionIsForward(dir))
  {
    /*
     * Evaluate low_compare first (unless cur_elem_trig tells us that it
     * cannot possibly fail to be satisfied), then evaluate high_compare
     */
    if (!cur_elem_trig && array->low_compare &&
      !DatumGetBool(FunctionCall2Coll(&array->low_compare->sk_func,
                      array->low_compare->sk_collation,
                      tupdatum,
                      array->low_compare->sk_argument)))
      *set_elem_result = -1;
    else if (array->high_compare &&
         !DatumGetBool(FunctionCall2Coll(&array->high_compare->sk_func,
                         array->high_compare->sk_collation,
                         tupdatum,
                         array->high_compare->sk_argument)))
      *set_elem_result = 1;
  }
  else
  {
    /*
     * Evaluate high_compare first (unless cur_elem_trig tells us that it
     * cannot possibly fail to be satisfied), then evaluate low_compare
     */
    if (!cur_elem_trig && array->high_compare &&
      !DatumGetBool(FunctionCall2Coll(&array->high_compare->sk_func,
                      array->high_compare->sk_collation,
                      tupdatum,
                      array->high_compare->sk_argument)))
      *set_elem_result = 1;
    else if (array->low_compare &&
         !DatumGetBool(FunctionCall2Coll(&array->low_compare->sk_func,
                         array->low_compare->sk_collation,
                         tupdatum,
                         array->low_compare->sk_argument)))
      *set_elem_result = -1;
  }

  /*
   * Assert that any keys that were assumed to be satisfied already (due to
   * caller passing cur_elem_trig=true) really are satisfied as expected
   */
#ifdef USE_ASSERT_CHECKING
  if (cur_elem_trig)
  {
    if (ScanDirectionIsForward(dir) && array->low_compare)
      Assert(DatumGetBool(FunctionCall2Coll(&array->low_compare->sk_func,
                          array->low_compare->sk_collation,
                          tupdatum,
                          array->low_compare->sk_argument)));

    if (ScanDirectionIsBackward(dir) && array->high_compare)
      Assert(DatumGetBool(FunctionCall2Coll(&array->high_compare->sk_func,
                          array->high_compare->sk_collation,
                          tupdatum,
                          array->high_compare->sk_argument)));
  }
#endif
}

/*
 * _bt_skiparray_set_element() -- Set skip array scan key's sk_argument
 *
 * Caller passes set_elem_result returned by _bt_binsrch_skiparray_skey for
 * caller's tupdatum/tupnull.
 *
 * We copy tupdatum/tupnull into skey's sk_argument iff set_elem_result == 0.
 * Otherwise, we set skey to either the lowest or highest value that's within
 * the range of caller's skip array (whichever is the best available match to
 * tupdatum/tupnull that is still within the range of the skip array according
 * to _bt_binsrch_skiparray_skey/set_elem_result).
 */
static void
_bt_skiparray_set_element(Relation rel, ScanKey skey, BTArrayKeyInfo *array,
              int32 set_elem_result, Datum tupdatum, bool tupnull)
{
  Assert(skey->sk_flags & SK_BT_SKIP);
  Assert(skey->sk_flags & SK_SEARCHARRAY);

  if (set_elem_result)
  {
    /* tupdatum/tupnull is out of the range of the skip array */
    Assert(!array->null_elem);

    _bt_array_set_low_or_high(rel, skey, array, set_elem_result < 0);
    return;
  }

  /* Advance skip array to tupdatum (or tupnull) value */
  if (unlikely(tupnull))
  {
    _bt_skiparray_set_isnull(rel, skey, array);
    return;
  }

  /* Free memory previously allocated for sk_argument if needed */
  if (!array->attbyval && skey->sk_argument)
    pfree(DatumGetPointer(skey->sk_argument));

  /* tupdatum becomes new sk_argument/new current element */
  skey->sk_flags &= ~(SK_SEARCHNULL | SK_ISNULL |
            SK_BT_MINVAL | SK_BT_MAXVAL |
            SK_BT_NEXT | SK_BT_PRIOR);
  skey->sk_argument = datumCopy(tupdatum, array->attbyval, array->attlen);
}

/*
 * _bt_skiparray_set_isnull() -- set skip array scan key to NULL
 */
static void
_bt_skiparray_set_isnull(Relation rel, ScanKey skey, BTArrayKeyInfo *array)
{
  Assert(skey->sk_flags & SK_BT_SKIP);
  Assert(skey->sk_flags & SK_SEARCHARRAY);
  Assert(array->null_elem && !array->low_compare && !array->high_compare);

  /* Free memory previously allocated for sk_argument if needed */
  if (!array->attbyval && skey->sk_argument)
    pfree(DatumGetPointer(skey->sk_argument));

  /* NULL becomes new sk_argument/new current element */
  skey->sk_argument = (Datum) 0;
  skey->sk_flags &= ~(SK_BT_MINVAL | SK_BT_MAXVAL |
            SK_BT_NEXT | SK_BT_PRIOR);
  skey->sk_flags |= (SK_SEARCHNULL | SK_ISNULL);
}

/*
 * _bt_start_array_keys() -- Initialize array keys at start of a scan
 *
 * Set up the cur_elem counters and fill in the first sk_argument value for
 * each array scankey.
 */
void
_bt_start_array_keys(IndexScanDesc scan, ScanDirection dir)
{
  Relation  rel = scan->indexRelation;
  BTScanOpaque so = (BTScanOpaque) scan->opaque;

  Assert(so->numArrayKeys);
  Assert(so->qual_ok);

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

    Assert(skey->sk_flags & SK_SEARCHARRAY);

    _bt_array_set_low_or_high(rel, skey, array,
                  ScanDirectionIsForward(dir));
  }
  so->scanBehind = so->oppositeDirCheck = false;  /* reset */
}

/*
 * _bt_array_set_low_or_high() -- Set array scan key to lowest/highest element
 *
 * Caller also passes associated scan key, which will have its argument set to
 * the lowest/highest array value in passing.
 */
static void
_bt_array_set_low_or_high(Relation rel, ScanKey skey, BTArrayKeyInfo *array,
              bool low_not_high)
{
  Assert(skey->sk_flags & SK_SEARCHARRAY);

  if (array->num_elems != -1)
  {
    /* set low or high element for SAOP array */
    int     set_elem = 0;

    Assert(!(skey->sk_flags & SK_BT_SKIP));

    if (!low_not_high)
      set_elem = array->num_elems - 1;

    /*
     * Just copy over array datum (only skip arrays require freeing and
     * allocating memory for sk_argument)
     */
    array->cur_elem = set_elem;
    skey->sk_argument = array->elem_values[set_elem];

    return;
  }

  /* set low or high element for skip array */
  Assert(skey->sk_flags & SK_BT_SKIP);
  Assert(array->num_elems == -1);

  /* Free memory previously allocated for sk_argument if needed */
  if (!array->attbyval && skey->sk_argument)
    pfree(DatumGetPointer(skey->sk_argument));

  /* Reset flags */
  skey->sk_argument = (Datum) 0;
  skey->sk_flags &= ~(SK_SEARCHNULL | SK_ISNULL |
            SK_BT_MINVAL | SK_BT_MAXVAL |
            SK_BT_NEXT | SK_BT_PRIOR);

  if (array->null_elem &&
    (low_not_high == ((skey->sk_flags & SK_BT_NULLS_FIRST) != 0)))
  {
    /* Requested element (either lowest or highest) has the value NULL */
    skey->sk_flags |= (SK_SEARCHNULL | SK_ISNULL);
  }
  else if (low_not_high)
  {
    /* Setting array to lowest element (according to low_compare) */
    skey->sk_flags |= SK_BT_MINVAL;
  }
  else
  {
    /* Setting array to highest element (according to high_compare) */
    skey->sk_flags |= SK_BT_MAXVAL;
  }
}

/*
 * _bt_array_decrement() -- decrement array scan key's sk_argument
 *
 * Return value indicates whether caller's array was successfully decremented.
 * Cannot decrement an array whose current element is already the first one.
 */
static bool
_bt_array_decrement(Relation rel, ScanKey skey, BTArrayKeyInfo *array)
{
  bool    uflow = false;
  Datum   dec_sk_argument;

  Assert(skey->sk_flags & SK_SEARCHARRAY);
  Assert(!(skey->sk_flags & (SK_BT_MAXVAL | SK_BT_NEXT | SK_BT_PRIOR)));

  /* SAOP array? */
  if (array->num_elems != -1)
  {
    Assert(!(skey->sk_flags & (SK_BT_SKIP | SK_BT_MINVAL | SK_BT_MAXVAL)));
    if (array->cur_elem > 0)
    {
      /*
       * Just decrement current element, and assign its datum to skey
       * (only skip arrays need us to free existing sk_argument memory)
       */
      array->cur_elem--;
      skey->sk_argument = array->elem_values[array->cur_elem];

      /* Successfully decremented array */
      return true;
    }

    /* Cannot decrement to before first array element */
    return false;
  }

  /* Nope, this is a skip array */
  Assert(skey->sk_flags & SK_BT_SKIP);

  /*
   * The sentinel value that represents the minimum value within the range
   * of a skip array (often just -inf) is never decrementable
   */
  if (skey->sk_flags & SK_BT_MINVAL)
    return false;

  /*
   * When the current array element is NULL, and the lowest sorting value in
   * the index is also NULL, we cannot decrement before first array element
   */
  if ((skey->sk_flags & SK_ISNULL) && (skey->sk_flags & SK_BT_NULLS_FIRST))
    return false;

  /*
   * Opclasses without skip support "decrement" the scan key's current
   * element by setting the PRIOR flag.  The true prior value is determined
   * by repositioning to the last index tuple < existing sk_argument/current
   * array element.  Note that this works in the usual way when the scan key
   * is already marked ISNULL (i.e. when the current element is NULL).
   */
  if (!array->sksup)
  {
    /* Successfully "decremented" array */
    skey->sk_flags |= SK_BT_PRIOR;
    return true;
  }

  /*
   * Opclasses with skip support directly decrement sk_argument
   */
  if (skey->sk_flags & SK_ISNULL)
  {
    Assert(!(skey->sk_flags & SK_BT_NULLS_FIRST));

    /*
     * Existing sk_argument/array element is NULL (for an IS NULL qual).
     *
     * "Decrement" from NULL to the high_elem value provided by opclass
     * skip support routine.
     */
    skey->sk_flags &= ~(SK_SEARCHNULL | SK_ISNULL);
    skey->sk_argument = datumCopy(array->sksup->high_elem,
                    array->attbyval, array->attlen);
    return true;
  }

  /*
   * Ask opclass support routine to provide decremented copy of existing
   * non-NULL sk_argument
   */
  dec_sk_argument = array->sksup->decrement(rel, skey->sk_argument, &uflow);
  if (unlikely(uflow))
  {
    /* dec_sk_argument has undefined value (so no pfree) */
    if (array->null_elem && (skey->sk_flags & SK_BT_NULLS_FIRST))
    {
      _bt_skiparray_set_isnull(rel, skey, array);

      /* Successfully "decremented" array to NULL */
      return true;
    }

    /* Cannot decrement to before first array element */
    return false;
  }

  /*
   * Successfully decremented sk_argument to a non-NULL value.  Make sure
   * that the decremented value is still within the range of the array.
   */
  if (array->low_compare &&
    !DatumGetBool(FunctionCall2Coll(&array->low_compare->sk_func,
                    array->low_compare->sk_collation,
                    dec_sk_argument,
                    array->low_compare->sk_argument)))
  {
    /* Keep existing sk_argument after all */
    if (!array->attbyval)
      pfree(DatumGetPointer(dec_sk_argument));

    /* Cannot decrement to before first array element */
    return false;
  }

  /* Accept value returned by opclass decrement callback */
  if (!array->attbyval && skey->sk_argument)
    pfree(DatumGetPointer(skey->sk_argument));
  skey->sk_argument = dec_sk_argument;

  /* Successfully decremented array */
  return true;
}

/*
 * _bt_array_increment() -- increment array scan key's sk_argument
 *
 * Return value indicates whether caller's array was successfully incremented.
 * Cannot increment an array whose current element is already the final one.
 */
static bool
_bt_array_increment(Relation rel, ScanKey skey, BTArrayKeyInfo *array)
{
  bool    oflow = false;
  Datum   inc_sk_argument;

  Assert(skey->sk_flags & SK_SEARCHARRAY);
  Assert(!(skey->sk_flags & (SK_BT_MINVAL | SK_BT_NEXT | SK_BT_PRIOR)));

  /* SAOP array? */
  if (array->num_elems != -1)
  {
    Assert(!(skey->sk_flags & (SK_BT_SKIP | SK_BT_MINVAL | SK_BT_MAXVAL)));
    if (array->cur_elem < array->num_elems - 1)
    {
      /*
       * Just increment current element, and assign its datum to skey
       * (only skip arrays need us to free existing sk_argument memory)
       */
      array->cur_elem++;
      skey->sk_argument = array->elem_values[array->cur_elem];

      /* Successfully incremented array */
      return true;
    }

    /* Cannot increment past final array element */
    return false;
  }

  /* Nope, this is a skip array */
  Assert(skey->sk_flags & SK_BT_SKIP);

  /*
   * The sentinel value that represents the maximum value within the range
   * of a skip array (often just +inf) is never incrementable
   */
  if (skey->sk_flags & SK_BT_MAXVAL)
    return false;

  /*
   * When the current array element is NULL, and the highest sorting value
   * in the index is also NULL, we cannot increment past the final element
   */
  if ((skey->sk_flags & SK_ISNULL) && !(skey->sk_flags & SK_BT_NULLS_FIRST))
    return false;

  /*
   * Opclasses without skip support "increment" the scan key's current
   * element by setting the NEXT flag.  The true next value is determined by
   * repositioning to the first index tuple > existing sk_argument/current
   * array element.  Note that this works in the usual way when the scan key
   * is already marked ISNULL (i.e. when the current element is NULL).
   */
  if (!array->sksup)
  {
    /* Successfully "incremented" array */
    skey->sk_flags |= SK_BT_NEXT;
    return true;
  }

  /*
   * Opclasses with skip support directly increment sk_argument
   */
  if (skey->sk_flags & SK_ISNULL)
  {
    Assert(skey->sk_flags & SK_BT_NULLS_FIRST);

    /*
     * Existing sk_argument/array element is NULL (for an IS NULL qual).
     *
     * "Increment" from NULL to the low_elem value provided by opclass
     * skip support routine.
     */
    skey->sk_flags &= ~(SK_SEARCHNULL | SK_ISNULL);
    skey->sk_argument = datumCopy(array->sksup->low_elem,
                    array->attbyval, array->attlen);
    return true;
  }

  /*
   * Ask opclass support routine to provide incremented copy of existing
   * non-NULL sk_argument
   */
  inc_sk_argument = array->sksup->increment(rel, skey->sk_argument, &oflow);
  if (unlikely(oflow))
  {
    /* inc_sk_argument has undefined value (so no pfree) */
    if (array->null_elem && !(skey->sk_flags & SK_BT_NULLS_FIRST))
    {
      _bt_skiparray_set_isnull(rel, skey, array);

      /* Successfully "incremented" array to NULL */
      return true;
    }

    /* Cannot increment past final array element */
    return false;
  }

  /*
   * Successfully incremented sk_argument to a non-NULL value.  Make sure
   * that the incremented value is still within the range of the array.
   */
  if (array->high_compare &&
    !DatumGetBool(FunctionCall2Coll(&array->high_compare->sk_func,
                    array->high_compare->sk_collation,
                    inc_sk_argument,
                    array->high_compare->sk_argument)))
  {
    /* Keep existing sk_argument after all */
    if (!array->attbyval)
      pfree(DatumGetPointer(inc_sk_argument));

    /* Cannot increment past final array element */
    return false;
  }

  /* Accept value returned by opclass increment callback */
  if (!array->attbyval && skey->sk_argument)
    pfree(DatumGetPointer(skey->sk_argument));
  skey->sk_argument = inc_sk_argument;

  /* Successfully incremented array */
  return true;
}

/*
 * _bt_advance_array_keys_increment() -- Advance to next set of array elements
 *
 * Advances the array keys by a single increment in the current scan
 * direction.  When there are multiple array keys this can roll over from the
 * lowest order array to higher order arrays.
 *
 * Returns true if there is another set of values to consider, false if not.
 * On true result, the scankeys are initialized with the next set of values.
 * On false result, the scankeys stay the same, and the array keys are not
 * advanced (every array remains at its final element for scan direction).
 */
static bool
_bt_advance_array_keys_increment(IndexScanDesc scan, ScanDirection dir,
                 bool *skip_array_set)
{
  Relation  rel = scan->indexRelation;
  BTScanOpaque so = (BTScanOpaque) scan->opaque;

  /*
   * We must advance the last array key most quickly, since it will
   * correspond to the lowest-order index column among the available
   * qualifications
   */
  for (int i = so->numArrayKeys - 1; i >= 0; i--)
  {
    BTArrayKeyInfo *array = &so->arrayKeys[i];
    ScanKey   skey = &so->keyData[array->scan_key];

    if (array->num_elems == -1)
      *skip_array_set = true;

    if (ScanDirectionIsForward(dir))
    {
      if (_bt_array_increment(rel, skey, array))
        return true;
    }
    else
    {
      if (_bt_array_decrement(rel, skey, array))
        return true;
    }

    /*
     * Couldn't increment (or decrement) array.  Handle array roll over.
     *
     * Start over at the array's lowest sorting value (or its highest
     * value, for backward scans)...
     */
    _bt_array_set_low_or_high(rel, skey, array,
                  ScanDirectionIsForward(dir));

    /* ...then increment (or decrement) next most significant array */
  }

  /*
   * The array keys are now exhausted.
   *
   * Restore the array keys to the state they were in immediately before we
   * were called.  This ensures that the arrays only ever ratchet in the
   * current scan direction.
   *
   * Without this, scans could overlook matching tuples when the scan
   * direction gets reversed just before btgettuple runs out of items to
   * return, but just after _bt_readpage prepares all the items from the
   * scan's final page in so->currPos.  When we're on the final page it is
   * typical for so->currPos to get invalidated once btgettuple finally
   * returns false, which'll effectively invalidate the scan's array keys.
   * That hasn't happened yet, though -- and in general it may never happen.
   */
  _bt_start_array_keys(scan, -dir);

  return false;
}

/*
 * _bt_rewind_nonrequired_arrays() -- Rewind SAOP arrays not marked required
 *
 * Called when _bt_advance_array_keys decides to start a new primitive index
 * scan on the basis of the current scan position being before the position
 * that _bt_first is capable of repositioning the scan to by applying an
 * inequality operator required in the opposite-to-scan direction only.
 *
 * Although equality strategy scan keys (for both arrays and non-arrays alike)
 * are either marked required in both directions or in neither direction,
 * there is a sense in which non-required arrays behave like required arrays.
 * With a qual such as "WHERE a IN (100, 200) AND b >= 3 AND c IN (5, 6, 7)",
 * the scan key on "c" is non-required, but nevertheless enables positioning
 * the scan at the first tuple >= "(100, 3, 5)" on the leaf level during the
 * first descent of the tree by _bt_first.  Later on, there could also be a
 * second descent, that places the scan right before tuples >= "(200, 3, 5)".
 * _bt_first must never be allowed to build an insertion scan key whose "c"
 * entry is set to a value other than 5, the "c" array's first element/value.
 * (Actually, it's the first in the current scan direction.  This example uses
 * a forward scan.)
 *
 * Calling here resets the array scan key elements for the scan's non-required
 * arrays.  This is strictly necessary for correctness in a subset of cases
 * involving "required in opposite direction"-triggered primitive index scans.
 * Not all callers are at risk of _bt_first using a non-required array like
 * this, but advancement always resets the arrays when another primitive scan
 * is scheduled, just to keep things simple.  Array advancement even makes
 * sure to reset non-required arrays during scans that have no inequalities.
 * (Advancement still won't call here when there are no inequalities, though
 * that's just because it's all handled indirectly instead.)
 *
 * Note: _bt_verify_arrays_bt_first is called by an assertion to enforce that
 * everybody got this right.
 *
 * Note: In practice almost all SAOP arrays are marked required during
 * preprocessing (if necessary by generating skip arrays).  It is hardly ever
 * truly necessary to call here, but consistently doing so is simpler.
 */
static void
_bt_rewind_nonrequired_arrays(IndexScanDesc scan, ScanDirection dir)
{
  Relation  rel = scan->indexRelation;
  BTScanOpaque so = (BTScanOpaque) scan->opaque;
  int     arrayidx = 0;

  for (int ikey = 0; ikey < so->numberOfKeys; ikey++)
  {
    ScanKey   cur = so->keyData + ikey;
    BTArrayKeyInfo *array = NULL;

    if (!(cur->sk_flags & SK_SEARCHARRAY) ||
      cur->sk_strategy != BTEqualStrategyNumber)
      continue;

    array = &so->arrayKeys[arrayidx++];
    Assert(array->scan_key == ikey);

    if ((cur->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD)))
      continue;

    Assert(array->num_elems != -1); /* No non-required skip arrays */

    _bt_array_set_low_or_high(rel, cur, array,
                  ScanDirectionIsForward(dir));
  }
}

/*
 * _bt_tuple_before_array_skeys() -- too early to advance required arrays?
 *
 * We always compare the tuple using the current array keys (which we assume
 * are already set in so->keyData[]).  readpagetup indicates if tuple is the
 * scan's current _bt_readpage-wise tuple.
 *
 * readpagetup callers must only call here when _bt_check_compare already set
 * continuescan=false.  We help these callers deal with _bt_check_compare's
 * inability to distinguish between the < and > cases (it uses equality
 * operator scan keys, whereas we use 3-way ORDER procs).  These callers pass
 * a _bt_check_compare-set sktrig value that indicates which scan key
 * triggered the call (!readpagetup callers just pass us sktrig=0 instead).
 * This information allows us to avoid wastefully checking earlier scan keys
 * that were already deemed to have been satisfied inside _bt_check_compare.
 *
 * Returns false when caller's tuple is >= the current required equality scan
 * keys (or <=, in the case of backwards scans).  This happens to readpagetup
 * callers when the scan has reached the point of needing its array keys
 * advanced; caller will need to advance required and non-required arrays at
 * scan key offsets >= sktrig, plus scan keys < sktrig iff sktrig rolls over.
 * (When we return false to readpagetup callers, tuple can only be == current
 * required equality scan keys when caller's sktrig indicates that the arrays
 * need to be advanced due to an unsatisfied required inequality key trigger.)
 *
 * Returns true when caller passes a tuple that is < the current set of
 * equality keys for the most significant non-equal required scan key/column
 * (or > the keys, during backwards scans).  This happens to readpagetup
 * callers when tuple is still before the start of matches for the scan's
 * required equality strategy scan keys.  (sktrig can't have indicated that an
 * inequality strategy scan key wasn't satisfied in _bt_check_compare when we
 * return true.  In fact, we automatically return false when passed such an
 * inequality sktrig by readpagetup callers -- _bt_check_compare's initial
 * continuescan=false doesn't really need to be confirmed here by us.)
 *
 * !readpagetup callers optionally pass us *scanBehind, which tracks whether
 * any missing truncated attributes might have affected array advancement
 * (compared to what would happen if it was shown the first non-pivot tuple on
 * the page to the right of caller's finaltup/high key tuple instead).  It's
 * only possible that we'll set *scanBehind to true when caller passes us a
 * pivot tuple (with truncated -inf attributes) that we return false for.
 */
static bool
_bt_tuple_before_array_skeys(IndexScanDesc scan, ScanDirection dir,
               IndexTuple tuple, TupleDesc tupdesc, int tupnatts,
               bool readpagetup, int sktrig, bool *scanBehind)
{
  BTScanOpaque so = (BTScanOpaque) scan->opaque;

  Assert(so->numArrayKeys);
  Assert(so->numberOfKeys);
  Assert(sktrig == 0 || readpagetup);
  Assert(!readpagetup || scanBehind == NULL);

  if (scanBehind)
    *scanBehind = false;

  for (int ikey = sktrig; ikey < so->numberOfKeys; ikey++)
  {
    ScanKey   cur = so->keyData + ikey;
    Datum   tupdatum;
    bool    tupnull;
    int32   result;

    /* readpagetup calls require one ORDER proc comparison (at most) */
    Assert(!readpagetup || ikey == sktrig);

    /*
     * Once we reach a non-required scan key, we're completely done.
     *
     * Note: we deliberately don't consider the scan direction here.
     * _bt_advance_array_keys caller requires that we track *scanBehind
     * without concern for scan direction.
     */
    if ((cur->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD)) == 0)
    {
      Assert(!readpagetup);
      Assert(ikey > sktrig || ikey == 0);
      return false;
    }

    if (cur->sk_attno > tupnatts)
    {
      Assert(!readpagetup);

      /*
       * When we reach a high key's truncated attribute, assume that the
       * tuple attribute's value is >= the scan's equality constraint
       * scan keys (but set *scanBehind to let interested callers know
       * that a truncated attribute might have affected our answer).
       */
      if (scanBehind)
        *scanBehind = true;

      return false;
    }

    /*
     * Deal with inequality strategy scan keys that _bt_check_compare set
     * continuescan=false for
     */
    if (cur->sk_strategy != BTEqualStrategyNumber)
    {
      /*
       * When _bt_check_compare indicated that a required inequality
       * scan key wasn't satisfied, there's no need to verify anything;
       * caller always calls _bt_advance_array_keys with this sktrig.
       */
      if (readpagetup)
        return false;

      /*
       * Otherwise we can't give up, since we must check all required
       * scan keys (required in either direction) in order to correctly
       * track *scanBehind for caller
       */
      continue;
    }

    tupdatum = index_getattr(tuple, cur->sk_attno, tupdesc, &tupnull);

    if (likely(!(cur->sk_flags & (SK_BT_MINVAL | SK_BT_MAXVAL))))
    {
      /* Scankey has a valid/comparable sk_argument value */
      result = _bt_compare_array_skey(&so->orderProcs[ikey],
                      tupdatum, tupnull,
                      cur->sk_argument, cur);

      if (result == 0)
      {
        /*
         * Interpret result in a way that takes NEXT/PRIOR into
         * account
         */
        if (cur->sk_flags & SK_BT_NEXT)
          result = -1;
        else if (cur->sk_flags & SK_BT_PRIOR)
          result = 1;

        Assert(result == 0 || (cur->sk_flags & SK_BT_SKIP));
      }
    }
    else
    {
      BTArrayKeyInfo *array = NULL;

      /*
       * Current array element/array = scan key value is a sentinel
       * value that represents the lowest (or highest) possible value
       * that's still within the range of the array.
       *
       * Like _bt_first, we only see MINVAL keys during forwards scans
       * (and similarly only see MAXVAL keys during backwards scans).
       * Even if the scan's direction changes, we'll stop at some higher
       * order key before we can ever reach any MAXVAL (or MINVAL) keys.
       * (However, unlike _bt_first we _can_ get to keys marked either
       * NEXT or PRIOR, regardless of the scan's current direction.)
       */
      Assert(ScanDirectionIsForward(dir) ?
           !(cur->sk_flags & SK_BT_MAXVAL) :
           !(cur->sk_flags & SK_BT_MINVAL));

      /*
       * There are no valid sk_argument values in MINVAL/MAXVAL keys.
       * Check if tupdatum is within the range of skip array instead.
       */
      for (int arrayidx = 0; arrayidx < so->numArrayKeys; arrayidx++)
      {
        array = &so->arrayKeys[arrayidx];
        if (array->scan_key == ikey)
          break;
      }

      _bt_binsrch_skiparray_skey(false, dir, tupdatum, tupnull,
                     array, cur, &result);

      if (result == 0)
      {
        /*
         * tupdatum satisfies both low_compare and high_compare, so
         * it's time to advance the array keys.
         *
         * Note: It's possible that the skip array will "advance" from
         * its MINVAL (or MAXVAL) representation to an alternative,
         * logically equivalent representation of the same value: a
         * representation where the = key gets a valid datum in its
         * sk_argument.  This is only possible when low_compare uses
         * the >= strategy (or high_compare uses the <= strategy).
         */
        return false;
      }
    }

    /*
     * Does this comparison indicate that caller must _not_ advance the
     * scan's arrays just yet?
     */
    if ((ScanDirectionIsForward(dir) && result < 0) ||
      (ScanDirectionIsBackward(dir) && result > 0))
      return true;

    /*
     * Does this comparison indicate that caller should now advance the
     * scan's arrays?  (Must be if we get here during a readpagetup call.)
     */
    if (readpagetup || result != 0)
    {
      Assert(result != 0);
      return false;
    }

    /*
     * Inconclusive -- need to check later scan keys, too.
     *
     * This must be a finaltup precheck, or a call made from an assertion.
     */
    Assert(result == 0);
  }

  Assert(!readpagetup);

  return false;
}

/*
 * _bt_start_prim_scan() -- start scheduled primitive index scan?
 *
 * Returns true if _bt_checkkeys scheduled another primitive index scan, just
 * as the last one ended.  Otherwise returns false, indicating that the array
 * keys are now fully exhausted.
 *
 * Only call here during scans with one or more equality type array scan keys,
 * after _bt_first or _bt_next return false.
 */
bool
_bt_start_prim_scan(IndexScanDesc scan, ScanDirection dir)
{
  BTScanOpaque so = (BTScanOpaque) scan->opaque;

  Assert(so->numArrayKeys);

  so->scanBehind = so->oppositeDirCheck = false;  /* reset */

  /*
   * Array keys are advanced within _bt_checkkeys when the scan reaches the
   * leaf level (more precisely, they're advanced when the scan reaches the
   * end of each distinct set of array elements).  This process avoids
   * repeat access to leaf pages (across multiple primitive index scans) by
   * advancing the scan's array keys when it allows the primitive index scan
   * to find nearby matching tuples (or when it eliminates ranges of array
   * key space that can't possibly be satisfied by any index tuple).
   *
   * _bt_checkkeys sets a simple flag variable to schedule another primitive
   * index scan.  The flag tells us what to do.
   *
   * We cannot rely on _bt_first always reaching _bt_checkkeys.  There are
   * various cases where that won't happen.  For example, if the index is
   * completely empty, then _bt_first won't call _bt_readpage/_bt_checkkeys.
   * We also don't expect a call to _bt_checkkeys during searches for a
   * non-existent value that happens to be lower/higher than any existing
   * value in the index.
   *
   * We don't require special handling for these cases -- we don't need to
   * be explicitly instructed to _not_ perform another primitive index scan.
   * It's up to code under the control of _bt_first to always set the flag
   * when another primitive index scan will be required.
   *
   * This works correctly, even with the tricky cases listed above, which
   * all involve access to leaf pages "near the boundaries of the key space"
   * (whether it's from a leftmost/rightmost page, or an imaginary empty
   * leaf root page).  If _bt_checkkeys cannot be reached by a primitive
   * index scan for one set of array keys, then it also won't be reached for
   * any later set ("later" in terms of the direction that we scan the index
   * and advance the arrays).  The array keys won't have advanced in these
   * cases, but that's the correct behavior (even _bt_advance_array_keys
   * won't always advance the arrays at the point they become "exhausted").
   */
  if (so->needPrimScan)
  {
    Assert(_bt_verify_arrays_bt_first(scan, dir));

    /*
     * Flag was set -- must call _bt_first again, which will reset the
     * scan's needPrimScan flag
     */
    return true;
  }

  /* The top-level index scan ran out of tuples in this scan direction */
  if (scan->parallel_scan != NULL)
    _bt_parallel_done(scan);

  return false;
}

/*
 * _bt_advance_array_keys() -- Advance array elements using a tuple
 *
 * The scan always gets a new qual as a consequence of calling here (except
 * when we determine that the top-level scan has run out of matching tuples).
 * All later _bt_check_compare calls also use the same new qual that was first
 * used here (at least until the next call here advances the keys once again).
 * It's convenient to structure _bt_check_compare rechecks of caller's tuple
 * (using the new qual) as one the steps of advancing the scan's array keys,
 * so this function works as a wrapper around _bt_check_compare.
 *
 * Like _bt_check_compare, we'll set pstate.continuescan on behalf of the
 * caller, and return a boolean indicating if caller's tuple satisfies the
 * scan's new qual.  But unlike _bt_check_compare, we set so->needPrimScan
 * when we set continuescan=false, indicating if a new primitive index scan
 * has been scheduled (otherwise, the top-level scan has run out of tuples in
 * the current scan direction).
 *
 * Caller must use _bt_tuple_before_array_skeys to determine if the current
 * place in the scan is >= the current array keys _before_ calling here.
 * We're responsible for ensuring that caller's tuple is <= the newly advanced
 * required array keys once we return.  We try to find an exact match, but
 * failing that we'll advance the array keys to whatever set of array elements
 * comes next in the key space for the current scan direction.  Required array
 * keys "ratchet forwards" (or backwards).  They can only advance as the scan
 * itself advances through the index/key space.
 *
 * (The rules are the same for backwards scans, except that the operators are
 * flipped: just replace the precondition's >= operator with a <=, and the
 * postcondition's <= operator with a >=.  In other words, just swap the
 * precondition with the postcondition.)
 *
 * We also deal with "advancing" non-required arrays here (or arrays that are
 * treated as non-required for the duration of a _bt_readpage call).  Callers
 * whose sktrig scan key is non-required specify sktrig_required=false.  These
 * calls are the only exception to the general rule about always advancing the
 * required array keys (the scan may not even have a required array).  These
 * callers should just pass a NULL pstate (since there is never any question
 * of stopping the scan).  No call to _bt_tuple_before_array_skeys is required
 * ahead of these calls (it's already clear that any required scan keys must
 * be satisfied by caller's tuple).
 *
 * Note that we deal with non-array required equality strategy scan keys as
 * degenerate single element arrays here.  Obviously, they can never really
 * advance in the way that real arrays can, but they must still affect how we
 * advance real array scan keys (exactly like true array equality scan keys).
 * We have to keep around a 3-way ORDER proc for these (using the "=" operator
 * won't do), since in general whether the tuple is < or > _any_ unsatisfied
 * required equality key influences how the scan's real arrays must advance.
 *
 * Note also that we may sometimes need to advance the array keys when the
 * existing required array keys (and other required equality keys) are already
 * an exact match for every corresponding value from caller's tuple.  We must
 * do this for inequalities that _bt_check_compare set continuescan=false for.
 * They'll advance the array keys here, just like any other scan key that
 * _bt_check_compare stops on.  (This can even happen _after_ we advance the
 * array keys, in which case we'll advance the array keys a second time.  That
 * way _bt_checkkeys caller always has its required arrays advance to the
 * maximum possible extent that its tuple will allow.)
 */
static bool
_bt_advance_array_keys(IndexScanDesc scan, BTReadPageState *pstate,
             IndexTuple tuple, int tupnatts, TupleDesc tupdesc,
             int sktrig, bool sktrig_required)
{
  BTScanOpaque so = (BTScanOpaque) scan->opaque;
  Relation  rel = scan->indexRelation;
  ScanDirection dir = so->currPos.dir;
  int     arrayidx = 0;
  bool    beyond_end_advance = false,
        skip_array_advanced = false,
        has_required_opposite_direction_only = false,
        all_required_satisfied = true,
        all_satisfied = true;

  Assert(!so->needPrimScan && !so->scanBehind && !so->oppositeDirCheck);
  Assert(_bt_verify_keys_with_arraykeys(scan));

  if (sktrig_required)
  {
    /*
     * Precondition array state assertion
     */
    Assert(!_bt_tuple_before_array_skeys(scan, dir, tuple, tupdesc,
                       tupnatts, false, 0, NULL));

    /*
     * Once we return we'll have a new set of required array keys, so
     * reset state used by "look ahead" optimization
     */
    pstate->rechecks = 0;
    pstate->targetdistance = 0;
  }
  else if (sktrig < so->numberOfKeys - 1 &&
       !(so->keyData[so->numberOfKeys - 1].sk_flags & SK_SEARCHARRAY))
  {
    int     least_sign_ikey = so->numberOfKeys - 1;
    bool    continuescan;

    /*
     * Optimization: perform a precheck of the least significant key
     * during !sktrig_required calls when it isn't already our sktrig
     * (provided the precheck key is not itself an array).
     *
     * When the precheck works out we'll avoid an expensive binary search
     * of sktrig's array (plus any other arrays before least_sign_ikey).
     */
    Assert(so->keyData[sktrig].sk_flags & SK_SEARCHARRAY);
    if (!_bt_check_compare(scan, dir, tuple, tupnatts, tupdesc, false,
                 false, &continuescan,
                 &least_sign_ikey))
      return false;
  }

  for (int ikey = 0; ikey < so->numberOfKeys; ikey++)
  {
    ScanKey   cur = so->keyData + ikey;
    BTArrayKeyInfo *array = NULL;
    Datum   tupdatum;
    bool    required = false,
          required_opposite_direction_only = false,
          tupnull;
    int32   result;
    int     set_elem = 0;

    if (cur->sk_strategy == BTEqualStrategyNumber)
    {
      /* Manage array state */
      if (cur->sk_flags & SK_SEARCHARRAY)
      {
        array = &so->arrayKeys[arrayidx++];
        Assert(array->scan_key == ikey);
      }
    }
    else
    {
      /*
       * Are any inequalities required in the opposite direction only
       * present here?
       */
      if (((ScanDirectionIsForward(dir) &&
          (cur->sk_flags & (SK_BT_REQBKWD))) ||
         (ScanDirectionIsBackward(dir) &&
          (cur->sk_flags & (SK_BT_REQFWD)))))
        has_required_opposite_direction_only =
          required_opposite_direction_only = true;
    }

    /* Optimization: skip over known-satisfied scan keys */
    if (ikey < sktrig)
      continue;

    if (cur->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD))
    {
      required = true;

      if (cur->sk_attno > tupnatts)
      {
        /* Set this just like _bt_tuple_before_array_skeys */
        Assert(sktrig < ikey);
        so->scanBehind = true;
      }
    }

    /*
     * Handle a required non-array scan key that the initial call to
     * _bt_check_compare indicated triggered array advancement, if any.
     *
     * The non-array scan key's strategy will be <, <=, or = during a
     * forwards scan (or any one of =, >=, or > during a backwards scan).
     * It follows that the corresponding tuple attribute's value must now
     * be either > or >= the scan key value (for backwards scans it must
     * be either < or <= that value).
     *
     * If this is a required equality strategy scan key, this is just an
     * optimization; _bt_tuple_before_array_skeys already confirmed that
     * this scan key places us ahead of caller's tuple.  There's no need
     * to repeat that work now.  (The same underlying principle also gets
     * applied by the cur_elem_trig optimization used to speed up searches
     * for the next array element.)
     *
     * If this is a required inequality strategy scan key, we _must_ rely
     * on _bt_check_compare like this; we aren't capable of directly
     * evaluating required inequality strategy scan keys here, on our own.
     */
    if (ikey == sktrig && !array)
    {
      Assert(sktrig_required && required && all_required_satisfied);

      /* Use "beyond end" advancement.  See below for an explanation. */
      beyond_end_advance = true;
      all_satisfied = all_required_satisfied = false;

      continue;
    }

    /*
     * Nothing more for us to do with an inequality strategy scan key that
     * wasn't the one that _bt_check_compare stopped on, though.
     *
     * Note: if our later call to _bt_check_compare (to recheck caller's
     * tuple) sets continuescan=false due to finding this same inequality
     * unsatisfied (possible when it's required in the scan direction),
     * we'll deal with it via a recursive "second pass" call.
     */
    else if (cur->sk_strategy != BTEqualStrategyNumber)
      continue;

    /*
     * Nothing for us to do with an equality strategy scan key that isn't
     * marked required, either -- unless it's a non-required array
     */
    else if (!required && !array)
      continue;

    /*
     * Here we perform steps for all array scan keys after a required
     * array scan key whose binary search triggered "beyond end of array
     * element" array advancement due to encountering a tuple attribute
     * value > the closest matching array key (or < for backwards scans).
     */
    if (beyond_end_advance)
    {
      if (array)
        _bt_array_set_low_or_high(rel, cur, array,
                      ScanDirectionIsBackward(dir));

      continue;
    }

    /*
     * Here we perform steps for all array scan keys after a required
     * array scan key whose tuple attribute was < the closest matching
     * array key when we dealt with it (or > for backwards scans).
     *
     * This earlier required array key already puts us ahead of caller's
     * tuple in the key space (for the current scan direction).  We must
     * make sure that subsequent lower-order array keys do not put us too
     * far ahead (ahead of tuples that have yet to be seen by our caller).
     * For example, when a tuple "(a, b) = (42, 5)" advances the array
     * keys on "a" from 40 to 45, we must also set "b" to whatever the
     * first array element for "b" is.  It would be wrong to allow "b" to
     * be set based on the tuple value.
     *
     * Perform the same steps with truncated high key attributes.  You can
     * think of this as a "binary search" for the element closest to the
     * value -inf.  Again, the arrays must never get ahead of the scan.
     */
    if (!all_required_satisfied || cur->sk_attno > tupnatts)
    {
      if (array)
        _bt_array_set_low_or_high(rel, cur, array,
                      ScanDirectionIsForward(dir));

      continue;
    }

    /*
     * Search in scankey's array for the corresponding tuple attribute
     * value from caller's tuple
     */
    tupdatum = index_getattr(tuple, cur->sk_attno, tupdesc, &tupnull);

    if (array)
    {
      bool    cur_elem_trig = (sktrig_required && ikey == sktrig);

      /*
       * "Binary search" by checking if tupdatum/tupnull are within the
       * range of the skip array
       */
      if (array->num_elems == -1)
        _bt_binsrch_skiparray_skey(cur_elem_trig, dir,
                       tupdatum, tupnull, array, cur,
                       &result);

      /*
       * Binary search for the closest match from the SAOP array
       */
      else
        set_elem = _bt_binsrch_array_skey(&so->orderProcs[ikey],
                          cur_elem_trig, dir,
                          tupdatum, tupnull, array, cur,
                          &result);
    }
    else
    {
      Assert(required);

      /*
       * This is a required non-array equality strategy scan key, which
       * we'll treat as a degenerate single element array.
       *
       * This scan key's imaginary "array" can't really advance, but it
       * can still roll over like any other array.  (Actually, this is
       * no different to real single value arrays, which never advance
       * without rolling over -- they can never truly advance, either.)
       */
      result = _bt_compare_array_skey(&so->orderProcs[ikey],
                      tupdatum, tupnull,
                      cur->sk_argument, cur);
    }

    /*
     * Consider "beyond end of array element" array advancement.
     *
     * When the tuple attribute value is > the closest matching array key
     * (or < in the backwards scan case), we need to ratchet this array
     * forward (backward) by one increment, so that caller's tuple ends up
     * being < final array value instead (or > final array value instead).
     * This process has to work for all of the arrays, not just this one:
     * it must "carry" to higher-order arrays when the set_elem that we
     * just found happens to be the final one for the scan's direction.
     * Incrementing (decrementing) set_elem itself isn't good enough.
     *
     * Our approach is to provisionally use set_elem as if it was an exact
     * match now, then set each later/less significant array to whatever
     * its final element is.  Once outside the loop we'll then "increment
     * this array's set_elem" by calling _bt_advance_array_keys_increment.
     * That way the process rolls over to higher order arrays as needed.
     *
     * Under this scheme any required arrays only ever ratchet forwards
     * (or backwards), and always do so to the maximum possible extent
     * that we can know will be safe without seeing the scan's next tuple.
     * We don't need any special handling for required scan keys that lack
     * a real array to advance, nor for redundant scan keys that couldn't
     * be eliminated by _bt_preprocess_keys.  It won't matter if some of
     * our "true" array scan keys (or even all of them) are non-required.
     */
    if (sktrig_required && required &&
      ((ScanDirectionIsForward(dir) && result > 0) ||
       (ScanDirectionIsBackward(dir) && result < 0)))
      beyond_end_advance = true;

    Assert(all_required_satisfied && all_satisfied);
    if (result != 0)
    {
      /*
       * Track whether caller's tuple satisfies our new post-advancement
       * qual, for required scan keys, as well as for the entire set of
       * interesting scan keys (all required scan keys plus non-required
       * array scan keys are considered interesting.)
       */
      all_satisfied = false;
      if (sktrig_required && required)
        all_required_satisfied = false;
      else
      {
        /*
         * There's no need to advance the arrays using the best
         * available match for a non-required array.  Give up now.
         * (Though note that sktrig_required calls still have to do
         * all the usual post-advancement steps, including the recheck
         * call to _bt_check_compare.)
         */
        break;
      }
    }

    /* Advance array keys, even when we don't have an exact match */
    if (array)
    {
      if (array->num_elems == -1)
      {
        /* Skip array's new element is tupdatum (or MINVAL/MAXVAL) */
        _bt_skiparray_set_element(rel, cur, array, result,
                      tupdatum, tupnull);
        skip_array_advanced = true;
      }
      else if (array->cur_elem != set_elem)
      {
        /* SAOP array's new element is set_elem datum */
        array->cur_elem = set_elem;
        cur->sk_argument = array->elem_values[set_elem];
      }
    }
  }

  /*
   * Advance the array keys incrementally whenever "beyond end of array
   * element" array advancement happens, so that advancement will carry to
   * higher-order arrays (might exhaust all the scan's arrays instead, which
   * ends the top-level scan).
   */
  if (beyond_end_advance &&
    !_bt_advance_array_keys_increment(scan, dir, &skip_array_advanced))
    goto end_toplevel_scan;

  Assert(_bt_verify_keys_with_arraykeys(scan));

  /*
   * Maintain a page-level count of the number of times the scan's array
   * keys advanced in a way that affected at least one skip array
   */
  if (sktrig_required && skip_array_advanced)
    pstate->nskipadvances++;

  /*
   * Does tuple now satisfy our new qual?  Recheck with _bt_check_compare.
   *
   * Calls triggered by an unsatisfied required scan key, whose tuple now
   * satisfies all required scan keys, but not all nonrequired array keys,
   * will still require a recheck call to _bt_check_compare.  They'll still
   * need its "second pass" handling of required inequality scan keys.
   * (Might have missed a still-unsatisfied required inequality scan key
   * that caller didn't detect as the sktrig scan key during its initial
   * _bt_check_compare call that used the old/original qual.)
   *
   * Calls triggered by an unsatisfied nonrequired array scan key never need
   * "second pass" handling of required inequalities (nor any other handling
   * of any required scan key).  All that matters is whether caller's tuple
   * satisfies the new qual, so it's safe to just skip the _bt_check_compare
   * recheck when we've already determined that it can only return 'false'.
   *
   * Note: In practice most scan keys are marked required by preprocessing,
   * if necessary by generating a preceding skip array.  We nevertheless
   * often handle array keys marked required as if they were nonrequired.
   * This behavior is requested by our _bt_check_compare caller, though only
   * when it is passed "forcenonrequired=true" by _bt_checkkeys.
   */
  if ((sktrig_required && all_required_satisfied) ||
    (!sktrig_required && all_satisfied))
  {
    int     nsktrig = sktrig + 1;
    bool    continuescan;

    Assert(all_required_satisfied);

    /* Recheck _bt_check_compare on behalf of caller */
    if (_bt_check_compare(scan, dir, tuple, tupnatts, tupdesc, false,
                !sktrig_required, &continuescan,
                &nsktrig) &&
      !so->scanBehind)
    {
      /* This tuple satisfies the new qual */
      Assert(all_satisfied && continuescan);

      if (pstate)
        pstate->continuescan = true;

      return true;
    }

    /*
     * Consider "second pass" handling of required inequalities.
     *
     * It's possible that our _bt_check_compare call indicated that the
     * scan should end due to some unsatisfied inequality that wasn't
     * initially recognized as such by us.  Handle this by calling
     * ourselves recursively, this time indicating that the trigger is the
     * inequality that we missed first time around (and using a set of
     * required array/equality keys that are now exact matches for tuple).
     *
     * We make a strong, general guarantee that every _bt_checkkeys call
     * here will advance the array keys to the maximum possible extent
     * that we can know to be safe based on caller's tuple alone.  If we
     * didn't perform this step, then that guarantee wouldn't quite hold.
     */
    if (unlikely(!continuescan))
    {
      bool    satisfied PG_USED_FOR_ASSERTS_ONLY;

      Assert(sktrig_required);
      Assert(so->keyData[nsktrig].sk_strategy != BTEqualStrategyNumber);

      /*
       * The tuple must use "beyond end" advancement during the
       * recursive call, so we cannot possibly end up back here when
       * recursing.  We'll consume a small, fixed amount of stack space.
       */
      Assert(!beyond_end_advance);

      /* Advance the array keys a second time using same tuple */
      satisfied = _bt_advance_array_keys(scan, pstate, tuple, tupnatts,
                         tupdesc, nsktrig, true);

      /* This tuple doesn't satisfy the inequality */
      Assert(!satisfied);
      return false;
    }

    /*
     * Some non-required scan key (from new qual) still not satisfied.
     *
     * All scan keys required in the current scan direction must still be
     * satisfied, though, so we can trust all_required_satisfied below.
     */
  }

  /*
   * When we were called just to deal with "advancing" non-required arrays,
   * this is as far as we can go (cannot stop the scan for these callers)
   */
  if (!sktrig_required)
  {
    /* Caller's tuple doesn't match any qual */
    return false;
  }

  /*
   * Postcondition array state assertion (for still-unsatisfied tuples).
   *
   * By here we have established that the scan's required arrays (scan must
   * have at least one required array) advanced, without becoming exhausted.
   *
   * Caller's tuple is now < the newly advanced array keys (or > when this
   * is a backwards scan), except in the case where we only got this far due
   * to an unsatisfied non-required scan key.  Verify that with an assert.
   *
   * Note: we don't just quit at this point when all required scan keys were
   * found to be satisfied because we need to consider edge-cases involving
   * scan keys required in the opposite direction only; those aren't tracked
   * by all_required_satisfied.
   */
  Assert(_bt_tuple_before_array_skeys(scan, dir, tuple, tupdesc, tupnatts,
                    false, 0, NULL) ==
       !all_required_satisfied);

  /*
   * We generally permit primitive index scans to continue onto the next
   * sibling page when the page's finaltup satisfies all required scan keys
   * at the point where we're between pages.
   *
   * If caller's tuple is also the page's finaltup, and we see that required
   * scan keys still aren't satisfied, start a new primitive index scan.
   */
  if (!all_required_satisfied && pstate->finaltup == tuple)
    goto new_prim_scan;

  /*
   * Proactively check finaltup (don't wait until finaltup is reached by the
   * scan) when it might well turn out to not be satisfied later on.
   *
   * Note: if so->scanBehind hasn't already been set for finaltup by us,
   * it'll be set during this call to _bt_tuple_before_array_skeys.  Either
   * way, it'll be set correctly (for the whole page) after this point.
   */
  if (!all_required_satisfied && pstate->finaltup &&
    _bt_tuple_before_array_skeys(scan, dir, pstate->finaltup, tupdesc,
                   BTreeTupleGetNAtts(pstate->finaltup, rel),
                   false, 0, &so->scanBehind))
    goto new_prim_scan;

  /*
   * When we encounter a truncated finaltup high key attribute, we're
   * optimistic about the chances of its corresponding required scan key
   * being satisfied when we go on to recheck it against tuples from this
   * page's right sibling leaf page.  We consider truncated attributes to be
   * satisfied by required scan keys, which allows the primitive index scan
   * to continue to the next leaf page.  We must set so->scanBehind to true
   * to remember that the last page's finaltup had "satisfied" required scan
   * keys for one or more truncated attribute values (scan keys required in
   * _either_ scan direction).
   *
   * There is a chance that _bt_readpage (which checks so->scanBehind) will
   * find that even the sibling leaf page's finaltup is < the new array
   * keys.  When that happens, our optimistic policy will have incurred a
   * single extra leaf page access that could have been avoided.
   *
   * A pessimistic policy would give backward scans a gratuitous advantage
   * over forward scans.  We'd punish forward scans for applying more
   * accurate information from the high key, rather than just using the
   * final non-pivot tuple as finaltup, in the style of backward scans.
   * Being pessimistic would also give some scans with non-required arrays a
   * perverse advantage over similar scans that use required arrays instead.
   *
   * This is similar to our scan-level heuristics, below.  They also set
   * scanBehind to speculatively continue the primscan onto the next page.
   */
  if (so->scanBehind)
  {
    /* Truncated high key -- _bt_scanbehind_checkkeys recheck scheduled */
  }

  /*
   * Handle inequalities marked required in the opposite scan direction.
   * They can also signal that we should start a new primitive index scan.
   *
   * It's possible that the scan is now positioned where "matching" tuples
   * begin, and that caller's tuple satisfies all scan keys required in the
   * current scan direction.  But if caller's tuple still doesn't satisfy
   * other scan keys that are required in the opposite scan direction only
   * (e.g., a required >= strategy scan key when scan direction is forward),
   * it's still possible that there are many leaf pages before the page that
   * _bt_first could skip straight to.  Groveling through all those pages
   * will always give correct answers, but it can be very inefficient.  We
   * must avoid needlessly scanning extra pages.
   *
   * Separately, it's possible that _bt_check_compare set continuescan=false
   * for a scan key that's required in the opposite direction only.  This is
   * a special case, that happens only when _bt_check_compare sees that the
   * inequality encountered a NULL value.  This signals the end of non-NULL
   * values in the current scan direction, which is reason enough to end the
   * (primitive) scan.  If this happens at the start of a large group of
   * NULL values, then we shouldn't expect to be called again until after
   * the scan has already read indefinitely-many leaf pages full of tuples
   * with NULL suffix values.  (_bt_first is expected to skip over the group
   * of NULLs by applying a similar "deduce NOT NULL" rule of its own, which
   * involves consing up an explicit SK_SEARCHNOTNULL key.)
   *
   * Apply a test against finaltup to detect and recover from the problem:
   * if even finaltup doesn't satisfy such an inequality, we just skip by
   * starting a new primitive index scan.  When we skip, we know for sure
   * that all of the tuples on the current page following caller's tuple are
   * also before the _bt_first-wise start of tuples for our new qual.  That
   * at least suggests many more skippable pages beyond the current page.
   * (when so->scanBehind and so->oppositeDirCheck are set, this'll happen
   * when we test the next page's finaltup/high key instead.)
   */
  else if (has_required_opposite_direction_only && pstate->finaltup &&
       unlikely(!_bt_oppodir_checkkeys(scan, dir, pstate->finaltup)))
  {
    /*
     * Make sure that any SAOP arrays that were not marked required by
     * preprocessing are reset to their first element for this direction
     */
    _bt_rewind_nonrequired_arrays(scan, dir);
    goto new_prim_scan;
  }

continue_scan:

  /*
   * Stick with the ongoing primitive index scan for now.
   *
   * It's possible that later tuples will also turn out to have values that
   * are still < the now-current array keys (or > the current array keys).
   * Our caller will handle this by performing what amounts to a linear
   * search of the page, implemented by calling _bt_check_compare and then
   * _bt_tuple_before_array_skeys for each tuple.
   *
   * This approach has various advantages over a binary search of the page.
   * Repeated binary searches of the page (one binary search for every array
   * advancement) won't outperform a continuous linear search.  While there
   * are workloads that a naive linear search won't handle well, our caller
   * has a "look ahead" fallback mechanism to deal with that problem.
   */
  pstate->continuescan = true;  /* Override _bt_check_compare */
  so->needPrimScan = false; /* _bt_readpage has more tuples to check */

  if (so->scanBehind)
  {
    /*
     * Remember if recheck needs to call _bt_oppodir_checkkeys for next
     * page's finaltup (see above comments about "Handle inequalities
     * marked required in the opposite scan direction" for why).
     */
    so->oppositeDirCheck = has_required_opposite_direction_only;

    _bt_rewind_nonrequired_arrays(scan, dir);

    /*
     * skip by setting "look ahead" mechanism's offnum for forwards scans
     * (backwards scans check scanBehind flag directly instead)
     */
    if (ScanDirectionIsForward(dir))
      pstate->skip = pstate->maxoff + 1;
  }

  /* Caller's tuple doesn't match the new qual */
  return false;

new_prim_scan:

  Assert(pstate->finaltup); /* not on rightmost/leftmost page */

  /*
   * Looks like another primitive index scan is required.  But consider
   * continuing the current primscan based on scan-level heuristics.
   *
   * Continue the ongoing primitive scan (and schedule a recheck for when
   * the scan arrives on the next sibling leaf page) when it has already
   * read at least one leaf page before the one we're reading now.  This
   * makes primscan scheduling more efficient when scanning subsets of an
   * index with many distinct attribute values matching many array elements.
   * It encourages fewer, larger primitive scans where that makes sense.
   * This will in turn encourage _bt_readpage to apply the pstate.startikey
   * optimization more often.
   *
   * Also continue the ongoing primitive index scan when it is still on the
   * first page if there have been more than NSKIPADVANCES_THRESHOLD calls
   * here that each advanced at least one of the scan's skip arrays
   * (deliberately ignore advancements that only affected SAOP arrays here).
   * A page that cycles through this many skip array elements is quite
   * likely to neighbor similar pages, that we'll also need to read.
   *
   * Note: These heuristics aren't as aggressive as you might think.  We're
   * conservative about allowing a primitive scan to step from the first
   * leaf page it reads to the page's sibling page (we only allow it on
   * first pages whose finaltup strongly suggests that it'll work out, as
   * well as first pages that have a large number of skip array advances).
   * Clearing this first page finaltup hurdle is a strong signal in itself.
   *
   * Note: The NSKIPADVANCES_THRESHOLD heuristic exists only to avoid
   * pathological cases.  Specifically, cases where a skip scan should just
   * behave like a traditional full index scan, but ends up "skipping" again
   * and again, descending to the prior leaf page's direct sibling leaf page
   * each time.  This misbehavior would otherwise be possible during scans
   * that never quite manage to "clear the first page finaltup hurdle".
   */
  if (!pstate->firstpage || pstate->nskipadvances > NSKIPADVANCES_THRESHOLD)
  {
    /* Schedule a recheck once on the next (or previous) page */
    so->scanBehind = true;

    /* Continue the current primitive scan after all */
    goto continue_scan;
  }

  /*
   * End this primitive index scan, but schedule another.
   *
   * Note: We make a soft assumption that the current scan direction will
   * also be used within _bt_next, when it is asked to step off this page.
   * It is up to _bt_next to cancel this scheduled primitive index scan
   * whenever it steps to a page in the direction opposite currPos.dir.
   */
  pstate->continuescan = false; /* Tell _bt_readpage we're done... */
  so->needPrimScan = true;  /* ...but call _bt_first again */

  if (scan->parallel_scan)
    _bt_parallel_primscan_schedule(scan, so->currPos.currPage);

  /* Caller's tuple doesn't match the new qual */
  return false;

end_toplevel_scan:

  /*
   * End the current primitive index scan, but don't schedule another.
   *
   * This ends the entire top-level scan in the current scan direction.
   *
   * Note: The scan's arrays (including any non-required arrays) are now in
   * their final positions for the current scan direction.  If the scan
   * direction happens to change, then the arrays will already be in their
   * first positions for what will then be the current scan direction.
   */
  pstate->continuescan = false; /* Tell _bt_readpage we're done... */
  so->needPrimScan = false; /* ...and don't call _bt_first again */

  /* Caller's tuple doesn't match any qual */
  return false;
}

#ifdef USE_ASSERT_CHECKING
/*
 * Verify that the scan's qual state matches what we expect at the point that
 * _bt_start_prim_scan is about to start a just-scheduled new primitive scan.
 *
 * We enforce a rule against non-required array scan keys: they must start out
 * with whatever element is the first for the scan's current scan direction.
 * See _bt_rewind_nonrequired_arrays comments for an explanation.
 */
static bool
_bt_verify_arrays_bt_first(IndexScanDesc scan, ScanDirection dir)
{
  BTScanOpaque so = (BTScanOpaque) scan->opaque;
  int     arrayidx = 0;

  for (int ikey = 0; ikey < so->numberOfKeys; ikey++)
  {
    ScanKey   cur = so->keyData + ikey;
    BTArrayKeyInfo *array = NULL;
    int     first_elem_dir;

    if (!(cur->sk_flags & SK_SEARCHARRAY) ||
      cur->sk_strategy != BTEqualStrategyNumber)
      continue;

    array = &so->arrayKeys[arrayidx++];

    if (((cur->sk_flags & SK_BT_REQFWD) && ScanDirectionIsForward(dir)) ||
      ((cur->sk_flags & SK_BT_REQBKWD) && ScanDirectionIsBackward(dir)))
      continue;

    if (ScanDirectionIsForward(dir))
      first_elem_dir = 0;
    else
      first_elem_dir = array->num_elems - 1;

    if (array->cur_elem != first_elem_dir)
      return false;
  }

  return _bt_verify_keys_with_arraykeys(scan);
}

/*
 * Verify that the scan's "so->keyData[]" scan keys are in agreement with
 * its array key state
 */
static bool
_bt_verify_keys_with_arraykeys(IndexScanDesc scan)
{
  BTScanOpaque so = (BTScanOpaque) scan->opaque;
  int     last_sk_attno = InvalidAttrNumber,
        arrayidx = 0;

  if (!so->qual_ok)
    return false;

  for (int ikey = 0; ikey < so->numberOfKeys; ikey++)
  {
    ScanKey   cur = so->keyData + ikey;
    BTArrayKeyInfo *array;

    if (cur->sk_strategy != BTEqualStrategyNumber ||
      !(cur->sk_flags & SK_SEARCHARRAY))
      continue;

    array = &so->arrayKeys[arrayidx++];
    if (array->scan_key != ikey)
      return false;

    if (array->num_elems == 0 || array->num_elems < -1)
      return false;

    if (array->num_elems != -1 &&
      cur->sk_argument != array->elem_values[array->cur_elem])
      return false;
    if (last_sk_attno > cur->sk_attno)
      return false;
    last_sk_attno = cur->sk_attno;
  }

  if (arrayidx != so->numArrayKeys)
    return false;

  return true;
}
#endif

/*
 * Test whether an indextuple satisfies all the scankey conditions.
 *
 * Return true if so, false if not.  If the tuple fails to pass the qual,
 * we also determine whether there's any need to continue the scan beyond
 * this tuple, and set pstate.continuescan accordingly.  See comments for
 * _bt_preprocess_keys() about how this is done.
 *
 * Forward scan callers can pass a high key tuple in the hopes of having
 * us set *continuescan to false, and avoiding an unnecessary visit to
 * the page to the right.
 *
 * Advances the scan's array keys when necessary for arrayKeys=true callers.
 * Scans without any array keys must always pass arrayKeys=false.
 *
 * Also stops and starts primitive index scans for arrayKeys=true callers.
 * Scans with array keys are required to set up page state that helps us with
 * this.  The page's finaltup tuple (the page high key for a forward scan, or
 * the page's first non-pivot tuple for a backward scan) must be set in
 * pstate.finaltup ahead of the first call here for the page.  Set this to
 * NULL for rightmost page (or the leftmost page for backwards scans).
 *
 * scan: index scan descriptor (containing a search-type scankey)
 * pstate: page level input and output parameters
 * arrayKeys: should we advance the scan's array keys if necessary?
 * tuple: index tuple to test
 * tupnatts: number of attributes in tupnatts (high key may be truncated)
 */
bool
_bt_checkkeys(IndexScanDesc scan, BTReadPageState *pstate, bool arrayKeys,
        IndexTuple tuple, int tupnatts)
{
  TupleDesc tupdesc = RelationGetDescr(scan->indexRelation);
  BTScanOpaque so = (BTScanOpaque) scan->opaque;
  ScanDirection dir = so->currPos.dir;
  int     ikey = pstate->startikey;
  bool    res;

  Assert(BTreeTupleGetNAtts(tuple, scan->indexRelation) == tupnatts);
  Assert(!so->needPrimScan && !so->scanBehind && !so->oppositeDirCheck);
  Assert(arrayKeys || so->numArrayKeys == 0);

  res = _bt_check_compare(scan, dir, tuple, tupnatts, tupdesc, arrayKeys,
              pstate->forcenonrequired, &pstate->continuescan,
              &ikey);

  /*
   * If _bt_check_compare relied on the pstate.startikey optimization, call
   * again (in assert-enabled builds) to verify it didn't affect our answer.
   *
   * Note: we can't do this when !pstate.forcenonrequired, since any arrays
   * before pstate.startikey won't have advanced on this page at all.
   */
  Assert(!pstate->forcenonrequired || arrayKeys);
#ifdef USE_ASSERT_CHECKING
  if (pstate->startikey > 0 && !pstate->forcenonrequired)
  {
    bool    dres,
          dcontinuescan;
    int     dikey = 0;

    /* Pass arrayKeys=false to avoid array side-effects */
    dres = _bt_check_compare(scan, dir, tuple, tupnatts, tupdesc, false,
                 pstate->forcenonrequired, &dcontinuescan,
                 &dikey);
    Assert(res == dres);
    Assert(pstate->continuescan == dcontinuescan);

    /*
     * Should also get the same ikey result.  We need a slightly weaker
     * assertion during arrayKeys calls, since they might be using an
     * array that couldn't be marked required during preprocessing.
     */
    Assert(arrayKeys || ikey == dikey);
    Assert(ikey <= dikey);
  }
#endif

  /*
   * Only one _bt_check_compare call is required in the common case where
   * there are no equality strategy array scan keys.  Otherwise we can only
   * accept _bt_check_compare's answer unreservedly when it didn't set
   * pstate.continuescan=false.
   */
  if (!arrayKeys || pstate->continuescan)
    return res;

  /*
   * _bt_check_compare call set continuescan=false in the presence of
   * equality type array keys.  This could mean that the tuple is just past
   * the end of matches for the current array keys.
   *
   * It's also possible that the scan is still _before_ the _start_ of
   * tuples matching the current set of array keys.  Check for that first.
   */
  Assert(!pstate->forcenonrequired);
  if (_bt_tuple_before_array_skeys(scan, dir, tuple, tupdesc, tupnatts, true,
                   ikey, NULL))
  {
    /* Override _bt_check_compare, continue primitive scan */
    pstate->continuescan = true;

    /*
     * We will end up here repeatedly given a group of tuples > the
     * previous array keys and < the now-current keys (for a backwards
     * scan it's just the same, though the operators swap positions).
     *
     * We must avoid allowing this linear search process to scan very many
     * tuples from well before the start of tuples matching the current
     * array keys (or from well before the point where we'll once again
     * have to advance the scan's array keys).
     *
     * We keep the overhead under control by speculatively "looking ahead"
     * to later still-unscanned items from this same leaf page.  We'll
     * only attempt this once the number of tuples that the linear search
     * process has examined starts to get out of hand.
     */
    pstate->rechecks++;
    if (pstate->rechecks >= LOOK_AHEAD_REQUIRED_RECHECKS)
    {
      /* See if we should skip ahead within the current leaf page */
      _bt_checkkeys_look_ahead(scan, pstate, tupnatts, tupdesc);

      /*
       * Might have set pstate.skip to a later page offset.  When that
       * happens then _bt_readpage caller will inexpensively skip ahead
       * to a later tuple from the same page (the one just after the
       * tuple we successfully "looked ahead" to).
       */
    }

    /* This indextuple doesn't match the current qual, in any case */
    return false;
  }

  /*
   * Caller's tuple is >= the current set of array keys and other equality
   * constraint scan keys (or <= if this is a backwards scan).  It's now
   * clear that we _must_ advance any required array keys in lockstep with
   * the scan.
   */
  return _bt_advance_array_keys(scan, pstate, tuple, tupnatts, tupdesc,
                  ikey, true);
}

/*
 * Test whether caller's finaltup tuple is still before the start of matches
 * for the current array keys.
 *
 * Called at the start of reading a page during a scan with array keys, though
 * only when the so->scanBehind flag was set on the scan's prior page.
 *
 * Returns false if the tuple is still before the start of matches.  When that
 * happens, caller should cut its losses and start a new primitive index scan.
 * Otherwise returns true.
 */
bool
_bt_scanbehind_checkkeys(IndexScanDesc scan, ScanDirection dir,
             IndexTuple finaltup)
{
  Relation  rel = scan->indexRelation;
  TupleDesc tupdesc = RelationGetDescr(rel);
  BTScanOpaque so = (BTScanOpaque) scan->opaque;
  int     nfinaltupatts = BTreeTupleGetNAtts(finaltup, rel);
  bool    scanBehind;

  Assert(so->numArrayKeys);

  if (_bt_tuple_before_array_skeys(scan, dir, finaltup, tupdesc,
                   nfinaltupatts, false, 0, &scanBehind))
    return false;

  /*
   * If scanBehind was set, all of the untruncated attribute values from
   * finaltup that correspond to an array match the array's current element,
   * but there are other keys associated with truncated suffix attributes.
   * Array advancement must have incremented the scan's arrays on the
   * previous page, resulting in a set of array keys that happen to be an
   * exact match for the current page high key's untruncated prefix values.
   *
   * This page definitely doesn't contain tuples that the scan will need to
   * return.  The next page may or may not contain relevant tuples.  Handle
   * this by cutting our losses and starting a new primscan.
   */
  if (scanBehind)
    return false;

  if (!so->oppositeDirCheck)
    return true;

  return _bt_oppodir_checkkeys(scan, dir, finaltup);
}

/*
 * Test whether an indextuple fails to satisfy an inequality required in the
 * opposite direction only.
 *
 * Caller's finaltup tuple is the page high key (for forwards scans), or the
 * first non-pivot tuple (for backwards scans).  Called during scans with
 * required array keys and required opposite-direction inequalities.
 *
 * Returns false if an inequality scan key required in the opposite direction
 * only isn't satisfied (and any earlier required scan keys are satisfied).
 * Otherwise returns true.
 *
 * An unsatisfied inequality required in the opposite direction only might
 * well enable skipping over many leaf pages, provided another _bt_first call
 * takes place.  This type of unsatisfied inequality won't usually cause
 * _bt_checkkeys to stop the scan to consider array advancement/starting a new
 * primitive index scan.
 */
static bool
_bt_oppodir_checkkeys(IndexScanDesc scan, ScanDirection dir,
            IndexTuple finaltup)
{
  Relation  rel = scan->indexRelation;
  TupleDesc tupdesc = RelationGetDescr(rel);
  BTScanOpaque so = (BTScanOpaque) scan->opaque;
  int     nfinaltupatts = BTreeTupleGetNAtts(finaltup, rel);
  bool    continuescan;
  ScanDirection flipped = -dir;
  int     ikey = 0;

  Assert(so->numArrayKeys);

  _bt_check_compare(scan, flipped, finaltup, nfinaltupatts, tupdesc, false,
            false, &continuescan,
            &ikey);

  if (!continuescan && so->keyData[ikey].sk_strategy != BTEqualStrategyNumber)
    return false;

  return true;
}

/*
 * Determines an offset to the first scan key (an so->keyData[]-wise offset)
 * that is _not_ guaranteed to be satisfied by every tuple from pstate.page,
 * which is set in pstate.startikey for _bt_checkkeys calls for the page.
 * This allows caller to save cycles on comparisons of a prefix of keys while
 * reading pstate.page.
 *
 * Also determines if later calls to _bt_checkkeys (for pstate.page) should be
 * forced to treat all required scan keys >= pstate.startikey as nonrequired
 * (that is, if they're to be treated as if any SK_BT_REQFWD/SK_BT_REQBKWD
 * markings that were set by preprocessing were not set at all, for the
 * duration of _bt_checkkeys calls prior to the call for pstate.finaltup).
 * This is indicated to caller by setting pstate.forcenonrequired.
 *
 * Call here at the start of reading a leaf page beyond the first one for the
 * primitive index scan.  We consider all non-pivot tuples, so it doesn't make
 * sense to call here when only a subset of those tuples can ever be read.
 * This is also a good idea on performance grounds; not calling here when on
 * the first page (first for the current primitive scan) avoids wasting cycles
 * during selective point queries.  They typically don't stand to gain as much
 * when we can set pstate.startikey, and are likely to notice the overhead of
 * calling here.  (Also, allowing pstate.forcenonrequired to be set on a
 * primscan's first page would mislead _bt_advance_array_keys, which expects
 * pstate.nskipadvances to be representative of every first page's key space.)
 *
 * Caller must call _bt_start_array_keys and reset startikey/forcenonrequired
 * ahead of the finaltup _bt_checkkeys call when we set forcenonrequired=true.
 * This will give _bt_checkkeys the opportunity to call _bt_advance_array_keys
 * with sktrig_required=true, restoring the invariant that the scan's required
 * arrays always track the scan's progress through the index's key space.
 * Caller won't need to do this on the rightmost/leftmost page in the index
 * (where pstate.finaltup isn't ever set), since forcenonrequired will never
 * be set here in the first place.
 */
void
_bt_set_startikey(IndexScanDesc scan, BTReadPageState *pstate)
{
  BTScanOpaque so = (BTScanOpaque) scan->opaque;
  Relation  rel = scan->indexRelation;
  TupleDesc tupdesc = RelationGetDescr(rel);
  ItemId    iid;
  IndexTuple  firsttup,
        lasttup;
  int     startikey = 0,
        arrayidx = 0,
        firstchangingattnum;
  bool    start_past_saop_eq = false;

  Assert(!so->scanBehind);
  Assert(pstate->minoff < pstate->maxoff);
  Assert(!pstate->firstpage);
  Assert(pstate->startikey == 0);
  Assert(!so->numArrayKeys || pstate->finaltup ||
       P_RIGHTMOST(BTPageGetOpaque(pstate->page)) ||
       P_LEFTMOST(BTPageGetOpaque(pstate->page)));

  if (so->numberOfKeys == 0)
    return;

  /* minoff is an offset to the lowest non-pivot tuple on the page */
  iid = PageGetItemId(pstate->page, pstate->minoff);
  firsttup = (IndexTuple) PageGetItem(pstate->page, iid);

  /* maxoff is an offset to the highest non-pivot tuple on the page */
  iid = PageGetItemId(pstate->page, pstate->maxoff);
  lasttup = (IndexTuple) PageGetItem(pstate->page, iid);

  /* Determine the first attribute whose values change on caller's page */
  firstchangingattnum = _bt_keep_natts_fast(rel, firsttup, lasttup);

  for (; startikey < so->numberOfKeys; startikey++)
  {
    ScanKey   key = so->keyData + startikey;
    BTArrayKeyInfo *array;
    Datum   firstdatum,
          lastdatum;
    bool    firstnull,
          lastnull;
    int32   result;

    /*
     * Determine if it's safe to set pstate.startikey to an offset to a
     * key that comes after this key, by examining this key
     */
    if (!(key->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD)))
    {
      /* Scan key isn't marked required (corner case) */
      Assert(!(key->sk_flags & SK_ROW_HEADER));
      break;        /* unsafe */
    }
    if (key->sk_flags & SK_ROW_HEADER)
    {
      /*
       * RowCompare inequality.
       *
       * Only the first subkey from a RowCompare can ever be marked
       * required (that happens when the row header is marked required).
       * There is no simple, general way for us to transitively deduce
       * whether or not every tuple on the page satisfies a RowCompare
       * key based only on firsttup and lasttup -- so we just give up.
       */
      if (!start_past_saop_eq && !so->skipScan)
        break;     /* unsafe to go further */

      /*
       * We have to be even more careful with RowCompares that come
       * after an array: we assume it's unsafe to even bypass the array.
       * Calling _bt_start_array_keys to recover the scan's arrays
       * following use of forcenonrequired mode isn't compatible with
       * _bt_check_rowcompare's continuescan=false behavior with NULL
       * row compare members.  _bt_advance_array_keys must not make a
       * decision on the basis of a key not being satisfied in the
       * opposite-to-scan direction until the scan reaches a leaf page
       * where the same key begins to be satisfied in scan direction.
       * The _bt_first !used_all_subkeys behavior makes this limitation
       * hard to work around some other way.
       */
      return;       /* completely unsafe to set pstate.startikey */
    }
    if (key->sk_strategy != BTEqualStrategyNumber)
    {
      /*
       * Scalar inequality key.
       *
       * It's definitely safe for _bt_checkkeys to avoid assessing this
       * inequality when the page's first and last non-pivot tuples both
       * satisfy the inequality (since the same must also be true of all
       * the tuples in between these two).
       *
       * Unlike the "=" case, it doesn't matter if this attribute has
       * more than one distinct value (though it _is_ necessary for any
       * and all _prior_ attributes to contain no more than one distinct
       * value amongst all of the tuples from pstate.page).
       */
      if (key->sk_attno > firstchangingattnum) /* >, not >= */
        break;     /* unsafe, preceding attr has multiple
                 * distinct values */

      firstdatum = index_getattr(firsttup, key->sk_attno, tupdesc, &firstnull);
      lastdatum = index_getattr(lasttup, key->sk_attno, tupdesc, &lastnull);

      if (key->sk_flags & SK_ISNULL)
      {
        /* IS NOT NULL key */
        Assert(key->sk_flags & SK_SEARCHNOTNULL);

        if (firstnull || lastnull)
          break;   /* unsafe */

        /* Safe, IS NOT NULL key satisfied by every tuple */
        continue;
      }

      /* Test firsttup */
      if (firstnull ||
        !DatumGetBool(FunctionCall2Coll(&key->sk_func,
                        key->sk_collation, firstdatum,
                        key->sk_argument)))
        break;     /* unsafe */

      /* Test lasttup */
      if (lastnull ||
        !DatumGetBool(FunctionCall2Coll(&key->sk_func,
                        key->sk_collation, lastdatum,
                        key->sk_argument)))
        break;     /* unsafe */

      /* Safe, scalar inequality satisfied by every tuple */
      continue;
    }

    /* Some = key (could be a scalar = key, could be an array = key) */
    Assert(key->sk_strategy == BTEqualStrategyNumber);

    if (!(key->sk_flags & SK_SEARCHARRAY))
    {
      /*
       * Scalar = key (possibly an IS NULL key).
       *
       * It is unsafe to set pstate.startikey to an ikey beyond this
       * key, unless the = key is satisfied by every possible tuple on
       * the page (possible only when attribute has just one distinct
       * value among all tuples on the page).
       */
      if (key->sk_attno >= firstchangingattnum)
        break;     /* unsafe, multiple distinct attr values */

      firstdatum = index_getattr(firsttup, key->sk_attno, tupdesc,
                     &firstnull);
      if (key->sk_flags & SK_ISNULL)
      {
        /* IS NULL key */
        Assert(key->sk_flags & SK_SEARCHNULL);

        if (!firstnull)
          break;   /* unsafe */

        /* Safe, IS NULL key satisfied by every tuple */
        continue;
      }
      if (firstnull ||
        !DatumGetBool(FunctionCall2Coll(&key->sk_func,
                        key->sk_collation, firstdatum,
                        key->sk_argument)))
        break;     /* unsafe */

      /* Safe, scalar = key satisfied by every tuple */
      continue;
    }

    /* = array key (could be a SAOP array, could be a skip array) */
    array = &so->arrayKeys[arrayidx++];
    Assert(array->scan_key == startikey);
    if (array->num_elems != -1)
    {
      /*
       * SAOP array = key.
       *
       * Handle this like we handle scalar = keys (though binary search
       * for a matching element, to avoid relying on key's sk_argument).
       */
      if (key->sk_attno >= firstchangingattnum)
        break;     /* unsafe, multiple distinct attr values */

      firstdatum = index_getattr(firsttup, key->sk_attno, tupdesc,
                     &firstnull);
      _bt_binsrch_array_skey(&so->orderProcs[startikey],
                   false, NoMovementScanDirection,
                   firstdatum, firstnull, array, key,
                   &result);
      if (result != 0)
        break;     /* unsafe */

      /* Safe, SAOP = key satisfied by every tuple */
      start_past_saop_eq = true;
      continue;
    }

    /*
     * Skip array = key
     */
    Assert(key->sk_flags & SK_BT_SKIP);
    if (array->null_elem)
    {
      /*
       * Non-range skip array = key.
       *
       * Safe, non-range skip array "satisfied" by every tuple on page
       * (safe even when "key->sk_attno > firstchangingattnum").
       */
      continue;
    }

    /*
     * Range skip array = key.
     *
     * Handle this like we handle scalar inequality keys (but avoid using
     * key's sk_argument directly, as in the SAOP array case).
     */
    if (key->sk_attno > firstchangingattnum) /* >, not >= */
      break;       /* unsafe, preceding attr has multiple
                 * distinct values */

    firstdatum = index_getattr(firsttup, key->sk_attno, tupdesc, &firstnull);
    lastdatum = index_getattr(lasttup, key->sk_attno, tupdesc, &lastnull);

    /* Test firsttup */
    _bt_binsrch_skiparray_skey(false, ForwardScanDirection,
                   firstdatum, firstnull, array, key,
                   &result);
    if (result != 0)
      break;       /* unsafe */

    /* Test lasttup */
    _bt_binsrch_skiparray_skey(false, ForwardScanDirection,
                   lastdatum, lastnull, array, key,
                   &result);
    if (result != 0)
      break;       /* unsafe */

    /* Safe, range skip array satisfied by every tuple on page */
  }

  /*
   * Use of forcenonrequired is typically undesirable, since it'll force
   * _bt_readpage caller to read every tuple on the page -- even though, in
   * general, it might well be possible to end the scan on an earlier tuple.
   * However, caller must use forcenonrequired when start_past_saop_eq=true,
   * since the usual required array behavior might fail to roll over to the
   * SAOP array.
   *
   * We always prefer forcenonrequired=true during scans with skip arrays
   * (except on the first page of each primitive index scan), though -- even
   * when "startikey == 0".  That way, _bt_advance_array_keys's low-order
   * key precheck optimization can always be used (unless on the first page
   * of the scan).  It seems slightly preferable to check more tuples when
   * that allows us to do significantly less skip array maintenance.
   */
  pstate->forcenonrequired = (start_past_saop_eq || so->skipScan);
  pstate->startikey = startikey;

  /*
   * _bt_readpage caller is required to call _bt_checkkeys against page's
   * finaltup with forcenonrequired=false whenever we initially set
   * forcenonrequired=true.  That way the scan's arrays will reliably track
   * its progress through the index's key space.
   *
   * We don't expect this when _bt_readpage caller has no finaltup due to
   * its page being the rightmost (or the leftmost, during backwards scans).
   * When we see that _bt_readpage has no finaltup, back out of everything.
   */
  Assert(!pstate->forcenonrequired || so->numArrayKeys);
  if (pstate->forcenonrequired && !pstate->finaltup)
  {
    pstate->forcenonrequired = false;
    pstate->startikey = 0;
  }
}

/*
 * Test whether an indextuple satisfies current scan condition.
 *
 * Return true if so, false if not.  If not, also sets *continuescan to false
 * when it's also not possible for any later tuples to pass the current qual
 * (with the scan's current set of array keys, in the current scan direction),
 * in addition to setting *ikey to the so->keyData[] subscript/offset for the
 * unsatisfied scan key (needed when caller must consider advancing the scan's
 * array keys).
 *
 * This is a subroutine for _bt_checkkeys.  We provisionally assume that
 * reaching the end of the current set of required keys (in particular the
 * current required array keys) ends the ongoing (primitive) index scan.
 * Callers without array keys should just end the scan right away when they
 * find that continuescan has been set to false here by us.  Things are more
 * complicated for callers with array keys.
 *
 * Callers with array keys must first consider advancing the arrays when
 * continuescan has been set to false here by us.  They must then consider if
 * it really does make sense to end the current (primitive) index scan, in
 * light of everything that is known at that point.  (In general when we set
 * continuescan=false for these callers it must be treated as provisional.)
 *
 * We deal with advancing unsatisfied non-required arrays directly, though.
 * This is safe, since by definition non-required keys can't end the scan.
 * This is just how we determine if non-required arrays are just unsatisfied
 * by the current array key, or if they're truly unsatisfied (that is, if
 * they're unsatisfied by every possible array key).
 *
 * Pass advancenonrequired=false to avoid all array related side effects.
 * This allows _bt_advance_array_keys caller to avoid infinite recursion.
 *
 * Pass forcenonrequired=true to instruct us to treat all keys as nonrequired.
 * This is used to make it safe to temporarily stop properly maintaining the
 * scan's required arrays.  _bt_checkkeys caller (_bt_readpage, actually)
 * determines a prefix of keys that must satisfy every possible corresponding
 * index attribute value from its page, which is passed to us via *ikey arg
 * (this is the first key that might be unsatisfied by tuples on the page).
 * Obviously, we won't maintain any array keys from before *ikey, so it's
 * quite possible for such arrays to "fall behind" the index's keyspace.
 * Caller will need to "catch up" by passing forcenonrequired=true (alongside
 * an *ikey=0) once the page's finaltup is reached.
 *
 * Note: it's safe to pass an *ikey > 0 with forcenonrequired=false, but only
 * when caller determines that it won't affect array maintenance.
 */
static bool
_bt_check_compare(IndexScanDesc scan, ScanDirection dir,
          IndexTuple tuple, int tupnatts, TupleDesc tupdesc,
          bool advancenonrequired, bool forcenonrequired,
          bool *continuescan, int *ikey)
{
  BTScanOpaque so = (BTScanOpaque) scan->opaque;

  *continuescan = true;   /* default assumption */

  for (; *ikey < so->numberOfKeys; (*ikey)++)
  {
    ScanKey   key = so->keyData + *ikey;
    Datum   datum;
    bool    isNull;
    bool    requiredSameDir = false,
          requiredOppositeDirOnly = false;

    /*
     * Check if the key is required in the current scan direction, in the
     * opposite scan direction _only_, or in neither direction (except
     * when we're forced to treat all scan keys as nonrequired)
     */
    if (forcenonrequired)
    {
      /* treating scan's keys as non-required */
    }
    else if (((key->sk_flags & SK_BT_REQFWD) && ScanDirectionIsForward(dir)) ||
         ((key->sk_flags & SK_BT_REQBKWD) && ScanDirectionIsBackward(dir)))
      requiredSameDir = true;
    else if (((key->sk_flags & SK_BT_REQFWD) && ScanDirectionIsBackward(dir)) ||
         ((key->sk_flags & SK_BT_REQBKWD) && ScanDirectionIsForward(dir)))
      requiredOppositeDirOnly = true;

    if (key->sk_attno > tupnatts)
    {
      /*
       * This attribute is truncated (must be high key).  The value for
       * this attribute in the first non-pivot tuple on the page to the
       * right could be any possible value.  Assume that truncated
       * attribute passes the qual.
       */
      Assert(BTreeTupleIsPivot(tuple));
      continue;
    }

    /*
     * A skip array scan key uses one of several sentinel values.  We just
     * fall back on _bt_tuple_before_array_skeys when we see such a value.
     */
    if (key->sk_flags & (SK_BT_MINVAL | SK_BT_MAXVAL |
               SK_BT_NEXT | SK_BT_PRIOR))
    {
      Assert(key->sk_flags & SK_SEARCHARRAY);
      Assert(key->sk_flags & SK_BT_SKIP);
      Assert(requiredSameDir || forcenonrequired);

      /*
       * Cannot fall back on _bt_tuple_before_array_skeys when we're
       * treating the scan's keys as nonrequired, though.  Just handle
       * this like any other non-required equality-type array key.
       */
      if (forcenonrequired)
        return _bt_advance_array_keys(scan, NULL, tuple, tupnatts,
                        tupdesc, *ikey, false);

      *continuescan = false;
      return false;
    }

    /* row-comparison keys need special processing */
    if (key->sk_flags & SK_ROW_HEADER)
    {
      if (_bt_check_rowcompare(key, tuple, tupnatts, tupdesc, dir,
                   forcenonrequired, continuescan))
        continue;
      return false;
    }

    datum = index_getattr(tuple,
                key->sk_attno,
                tupdesc,
                &isNull);

    if (key->sk_flags & SK_ISNULL)
    {
      /* Handle IS NULL/NOT NULL tests */
      if (key->sk_flags & SK_SEARCHNULL)
      {
        if (isNull)
          continue; /* tuple satisfies this qual */
      }
      else
      {
        Assert(key->sk_flags & SK_SEARCHNOTNULL);
        Assert(!(key->sk_flags & SK_BT_SKIP));
        if (!isNull)
          continue; /* tuple satisfies this qual */
      }

      /*
       * Tuple fails this qual.  If it's a required qual for the current
       * scan direction, then we can conclude no further tuples will
       * pass, either.
       */
      if (requiredSameDir)
        *continuescan = false;
      else if (unlikely(key->sk_flags & SK_BT_SKIP))
      {
        /*
         * If we're treating scan keys as nonrequired, and encounter a
         * skip array scan key whose current element is NULL, then it
         * must be a non-range skip array.  It must be satisfied, so
         * there's no need to call _bt_advance_array_keys to check.
         */
        Assert(forcenonrequired && *ikey > 0);
        continue;
      }

      /*
       * This indextuple doesn't match the qual.
       */
      return false;
    }

    if (isNull)
    {
      /*
       * Scalar scan key isn't satisfied by NULL tuple value.
       *
       * If we're treating scan keys as nonrequired, and key is for a
       * skip array, then we must attempt to advance the array to NULL
       * (if we're successful then the tuple might match the qual).
       */
      if (unlikely(forcenonrequired && key->sk_flags & SK_BT_SKIP))
        return _bt_advance_array_keys(scan, NULL, tuple, tupnatts,
                        tupdesc, *ikey, false);

      if (key->sk_flags & SK_BT_NULLS_FIRST)
      {
        /*
         * Since NULLs are sorted before non-NULLs, we know we have
         * reached the lower limit of the range of values for this
         * index attr.  On a backward scan, we can stop if this qual
         * is one of the "must match" subset.  We can stop regardless
         * of whether the qual is > or <, so long as it's required,
         * because it's not possible for any future tuples to pass. On
         * a forward scan, however, we must keep going, because we may
         * have initially positioned to the start of the index.
         * (_bt_advance_array_keys also relies on this behavior during
         * forward scans.)
         */
        if ((requiredSameDir || requiredOppositeDirOnly) &&
          ScanDirectionIsBackward(dir))
          *continuescan = false;
      }
      else
      {
        /*
         * Since NULLs are sorted after non-NULLs, we know we have
         * reached the upper limit of the range of values for this
         * index attr.  On a forward scan, we can stop if this qual is
         * one of the "must match" subset.  We can stop regardless of
         * whether the qual is > or <, so long as it's required,
         * because it's not possible for any future tuples to pass. On
         * a backward scan, however, we must keep going, because we
         * may have initially positioned to the end of the index.
         * (_bt_advance_array_keys also relies on this behavior during
         * backward scans.)
         */
        if ((requiredSameDir || requiredOppositeDirOnly) &&
          ScanDirectionIsForward(dir))
          *continuescan = false;
      }

      /*
       * This indextuple doesn't match the qual.
       */
      return false;
    }

    if (!DatumGetBool(FunctionCall2Coll(&key->sk_func, key->sk_collation,
                      datum, key->sk_argument)))
    {
      /*
       * Tuple fails this qual.  If it's a required qual for the current
       * scan direction, then we can conclude no further tuples will
       * pass, either.
       *
       * Note: because we stop the scan as soon as any required equality
       * qual fails, it is critical that equality quals be used for the
       * initial positioning in _bt_first() when they are available. See
       * comments in _bt_first().
       */
      if (requiredSameDir)
        *continuescan = false;

      /*
       * If this is a non-required equality-type array key, the tuple
       * needs to be checked against every possible array key.  Handle
       * this by "advancing" the scan key's array to a matching value
       * (if we're successful then the tuple might match the qual).
       */
      else if (advancenonrequired &&
           key->sk_strategy == BTEqualStrategyNumber &&
           (key->sk_flags & SK_SEARCHARRAY))
        return _bt_advance_array_keys(scan, NULL, tuple, tupnatts,
                        tupdesc, *ikey, false);

      /*
       * This indextuple doesn't match the qual.
       */
      return false;
    }
  }

  /* If we get here, the tuple passes all index quals. */
  return true;
}

/*
 * Test whether an indextuple satisfies a row-comparison scan condition.
 *
 * Return true if so, false if not.  If not, also clear *continuescan if
 * it's not possible for any future tuples in the current scan direction
 * to pass the qual.
 *
 * This is a subroutine for _bt_checkkeys/_bt_check_compare.
 */
static bool
_bt_check_rowcompare(ScanKey skey, IndexTuple tuple, int tupnatts,
           TupleDesc tupdesc, ScanDirection dir,
           bool forcenonrequired, bool *continuescan)
{
  ScanKey   subkey = (ScanKey) DatumGetPointer(skey->sk_argument);
  int32   cmpresult = 0;
  bool    result;

  /* First subkey should be same as the header says */
  Assert(subkey->sk_attno == skey->sk_attno);

  /* Loop over columns of the row condition */
  for (;;)
  {
    Datum   datum;
    bool    isNull;

    Assert(subkey->sk_flags & SK_ROW_MEMBER);

    if (subkey->sk_attno > tupnatts)
    {
      /*
       * This attribute is truncated (must be high key).  The value for
       * this attribute in the first non-pivot tuple on the page to the
       * right could be any possible value.  Assume that truncated
       * attribute passes the qual.
       */
      Assert(BTreeTupleIsPivot(tuple));
      cmpresult = 0;
      if (subkey->sk_flags & SK_ROW_END)
        break;
      subkey++;
      continue;
    }

    datum = index_getattr(tuple,
                subkey->sk_attno,
                tupdesc,
                &isNull);

    if (isNull)
    {
      if (forcenonrequired)
      {
        /* treating scan's keys as non-required */
      }
      else if (subkey->sk_flags & SK_BT_NULLS_FIRST)
      {
        /*
         * Since NULLs are sorted before non-NULLs, we know we have
         * reached the lower limit of the range of values for this
         * index attr.  On a backward scan, we can stop if this qual
         * is one of the "must match" subset.  We can stop regardless
         * of whether the qual is > or <, so long as it's required,
         * because it's not possible for any future tuples to pass. On
         * a forward scan, however, we must keep going, because we may
         * have initially positioned to the start of the index.
         * (_bt_advance_array_keys also relies on this behavior during
         * forward scans.)
         */
        if ((subkey->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD)) &&
          ScanDirectionIsBackward(dir))
          *continuescan = false;
      }
      else
      {
        /*
         * Since NULLs are sorted after non-NULLs, we know we have
         * reached the upper limit of the range of values for this
         * index attr.  On a forward scan, we can stop if this qual is
         * one of the "must match" subset.  We can stop regardless of
         * whether the qual is > or <, so long as it's required,
         * because it's not possible for any future tuples to pass. On
         * a backward scan, however, we must keep going, because we
         * may have initially positioned to the end of the index.
         * (_bt_advance_array_keys also relies on this behavior during
         * backward scans.)
         */
        if ((subkey->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD)) &&
          ScanDirectionIsForward(dir))
          *continuescan = false;
      }

      /*
       * In any case, this indextuple doesn't match the qual.
       */
      return false;
    }

    if (subkey->sk_flags & SK_ISNULL)
    {
      /*
       * Unlike the simple-scankey case, this isn't a disallowed case
       * (except when it's the first row element that has the NULL arg).
       * But it can never match.  If all the earlier row comparison
       * columns are required for the scan direction, we can stop the
       * scan, because there can't be another tuple that will succeed.
       */
      Assert(subkey != (ScanKey) DatumGetPointer(skey->sk_argument));
      subkey--;
      if (forcenonrequired)
      {
        /* treating scan's keys as non-required */
      }
      else if ((subkey->sk_flags & SK_BT_REQFWD) &&
           ScanDirectionIsForward(dir))
        *continuescan = false;
      else if ((subkey->sk_flags & SK_BT_REQBKWD) &&
           ScanDirectionIsBackward(dir))
        *continuescan = false;
      return false;
    }

    /* 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, "unexpected strategy number %d", subkey->sk_strategy);
      result = 0;     /* keep compiler quiet */
      break;
  }

  if (!result && !forcenonrequired)
  {
    /*
     * Tuple fails this qual.  If it's a required qual for the current
     * scan direction, then we can conclude no further tuples will pass,
     * either.  Note we have to look at the deciding column, not
     * necessarily the first or last column of the row condition.
     */
    if ((subkey->sk_flags & SK_BT_REQFWD) &&
      ScanDirectionIsForward(dir))
      *continuescan = false;
    else if ((subkey->sk_flags & SK_BT_REQBKWD) &&
         ScanDirectionIsBackward(dir))
      *continuescan = false;
  }

  return result;
}

/*
 * Determine if a scan with array keys should skip over uninteresting tuples.
 *
 * This is a subroutine for _bt_checkkeys.  Called when _bt_readpage's linear
 * search process (started after it finishes reading an initial group of
 * matching tuples, used to locate the start of the next group of tuples
 * matching the next set of required array keys) has already scanned an
 * excessive number of tuples whose key space is "between arrays".
 *
 * When we perform look ahead successfully, we'll sets pstate.skip, which
 * instructs _bt_readpage to skip ahead to that tuple next (could be past the
 * end of the scan's leaf page).  Pages where the optimization is effective
 * will generally still need to skip several times.  Each call here performs
 * only a single "look ahead" comparison of a later tuple, whose distance from
 * the current tuple's offset number is determined by applying heuristics.
 */
static void
_bt_checkkeys_look_ahead(IndexScanDesc scan, BTReadPageState *pstate,
             int tupnatts, TupleDesc tupdesc)
{
  BTScanOpaque so = (BTScanOpaque) scan->opaque;
  ScanDirection dir = so->currPos.dir;
  OffsetNumber aheadoffnum;
  IndexTuple  ahead;

  Assert(!pstate->forcenonrequired);

  /* Avoid looking ahead when comparing the page high key */
  if (pstate->offnum < pstate->minoff)
    return;

  /*
   * Don't look ahead when there aren't enough tuples remaining on the page
   * (in the current scan direction) for it to be worth our while
   */
  if (ScanDirectionIsForward(dir) &&
    pstate->offnum >= pstate->maxoff - LOOK_AHEAD_DEFAULT_DISTANCE)
    return;
  else if (ScanDirectionIsBackward(dir) &&
       pstate->offnum <= pstate->minoff + LOOK_AHEAD_DEFAULT_DISTANCE)
    return;

  /*
   * The look ahead distance starts small, and ramps up as each call here
   * allows _bt_readpage to skip over more tuples
   */
  if (!pstate->targetdistance)
    pstate->targetdistance = LOOK_AHEAD_DEFAULT_DISTANCE;
  else if (pstate->targetdistance < MaxIndexTuplesPerPage / 2)
    pstate->targetdistance *= 2;

  /* Don't read past the end (or before the start) of the page, though */
  if (ScanDirectionIsForward(dir))
    aheadoffnum = Min((int) pstate->maxoff,
              (int) pstate->offnum + pstate->targetdistance);
  else
    aheadoffnum = Max((int) pstate->minoff,
              (int) pstate->offnum - pstate->targetdistance);

  ahead = (IndexTuple) PageGetItem(pstate->page,
                   PageGetItemId(pstate->page, aheadoffnum));
  if (_bt_tuple_before_array_skeys(scan, dir, ahead, tupdesc, tupnatts,
                   false, 0, NULL))
  {
    /*
     * Success -- instruct _bt_readpage to skip ahead to very next tuple
     * after the one we determined was still before the current array keys
     */
    if (ScanDirectionIsForward(dir))
      pstate->skip = aheadoffnum + 1;
    else
      pstate->skip = aheadoffnum - 1;
  }
  else
  {
    /*
     * Failure -- "ahead" tuple is too far ahead (we were too aggressive).
     *
     * Reset the number of rechecks, and aggressively reduce the target
     * distance (we're much more aggressive here than we were when the
     * distance was initially ramped up).
     */
    pstate->rechecks = 0;
    pstate->targetdistance = Max(pstate->targetdistance / 8, 1);
  }
}

/*
 * _bt_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).
 *
 * Caller should not have a lock on the so->currPos page, but must hold a
 * buffer pin when !so->dropPin.  When we return, it still won't be locked.
 * It'll continue to hold whatever pins were held before calling here.
 *
 * We match items by heap TID before assuming they are the right ones to set
 * LP_DEAD.  If the scan is one that holds a buffer pin on the target page
 * continuously from initially reading the items until applying this function
 * (if it is a !so->dropPin scan), VACUUM cannot have deleted any items on the
 * page, so the page's TIDs can't have been recycled by now.  There's no risk
 * that we'll confuse a new index tuple that happens to use a recycled TID
 * with a now-removed tuple with the same TID (that used to be on this same
 * page).  We can't rely on that during scans that drop buffer pins eagerly
 * (so->dropPin scans), though, so we must condition setting LP_DEAD bits on
 * the page LSN having not changed since back when _bt_readpage saw the page.
 * We totally give up on setting LP_DEAD bits when the page LSN changed.
 *
 * We give up much less often during !so->dropPin scans, but it still happens.
 * 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 just give up on it.
 */
void
_bt_killitems(IndexScanDesc scan)
{
  Relation  rel = scan->indexRelation;
  BTScanOpaque so = (BTScanOpaque) scan->opaque;
  Page    page;
  BTPageOpaque opaque;
  OffsetNumber minoff;
  OffsetNumber maxoff;
  int     numKilled = so->numKilled;
  bool    killedsomething = false;
  Buffer    buf;

  Assert(numKilled > 0);
  Assert(BTScanPosIsValid(so->currPos));
  Assert(scan->heapRelation != NULL); /* can't be a bitmap index scan */

  /* Always invalidate so->killedItems[] before leaving so->currPos */
  so->numKilled = 0;

  if (!so->dropPin)
  {
    /*
     * 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
     * concurrent VACUUMs from recycling any of the TIDs on the page.
     */
    Assert(BTScanPosIsPinned(so->currPos));
    buf = so->currPos.buf;
    _bt_lockbuf(rel, buf, BT_READ);
  }
  else
  {
    XLogRecPtr  latestlsn;

    Assert(!BTScanPosIsPinned(so->currPos));
    Assert(RelationNeedsWAL(rel));
    buf = _bt_getbuf(rel, so->currPos.currPage, BT_READ);

    latestlsn = BufferGetLSNAtomic(buf);
    Assert(!XLogRecPtrIsInvalid(so->currPos.lsn));
    Assert(so->currPos.lsn <= latestlsn);
    if (so->currPos.lsn != latestlsn)
    {
      /* Modified, give up on hinting */
      _bt_relbuf(rel, buf);
      return;
    }

    /* Unmodified, hinting is safe */
  }

  page = BufferGetPage(buf);
  opaque = BTPageGetOpaque(page);
  minoff = P_FIRSTDATAKEY(opaque);
  maxoff = PageGetMaxOffsetNumber(page);

  for (int 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 !so->dropPin 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 || !so->dropPin);

          /*
           * 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(buf, true);
  }

  if (!so->dropPin)
    _bt_unlockbuf(rel, buf);
  else
    _bt_relbuf(rel, 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;
    CompactAttribute *att;

    datum1 = index_getattr(lastleft, attnum, itupdesc, &isNull1);
    datum2 = index_getattr(firstright, attnum, itupdesc, &isNull2);
    att = TupleDescCompactAttr(itupdesc, attnum - 1);

    if (isNull1 != isNull2)
      break;

    if (!isNull1 &&
      !datum_image_eq(datum1, datum2, att->attbyval, att->attlen))
      break;

    keepnatts++;
  }

  return keepnatts;
}

/*
 *  _bt_check_natts() -- Verify tuple has expected number of attributes.
 *
 * Returns value indicating if the expected number of attributes were found
 * for a particular offset on page.  This can be used as a general purpose
 * sanity check.
 *
 * Testing a tuple directly with BTreeTupleGetNAtts() should generally be
 * preferred to calling here.  That's usually more convenient, and is always
 * more explicit.  Call here instead when offnum's tuple may be a negative
 * infinity tuple that uses the pre-v11 on-disk representation, or when a low
 * context check is appropriate.  This routine is as strict as possible about
 * what is expected on each version of btree.
 */
bool
_bt_check_natts(Relation rel, bool heapkeyspace, Page page, OffsetNumber offnum)
{
  int16   natts = IndexRelationGetNumberOfAttributes(rel);
  int16   nkeyatts = IndexRelationGetNumberOfKeyAttributes(rel);
  BTPageOpaque opaque = BTPageGetOpaque(page);
  IndexTuple  itup;
  int     tupnatts;

  /*
   * We cannot reliably test a deleted or half-dead page, since they have
   * dummy high keys
   */
  if (P_IGNORE(opaque))
    return true;

  Assert(offnum >= FirstOffsetNumber &&
       offnum <= PageGetMaxOffsetNumber(page));

  itup = (IndexTuple) PageGetItem(page, PageGetItemId(page, offnum));
  tupnatts = BTreeTupleGetNAtts(itup, rel);

  /* !heapkeyspace indexes do not support deduplication */
  if (!heapkeyspace && BTreeTupleIsPosting(itup))
    return false;

  /* Posting list tuples should never have "pivot heap TID" bit set */
  if (BTreeTupleIsPosting(itup) &&
    (ItemPointerGetOffsetNumberNoCheck(&itup->t_tid) &
     BT_PIVOT_HEAP_TID_ATTR) != 0)
    return false;

  /* INCLUDE indexes do not support deduplication */
  if (natts != nkeyatts && BTreeTupleIsPosting(itup))
    return false;

  if (P_ISLEAF(opaque))
  {
    if (offnum >= P_FIRSTDATAKEY(opaque))
    {
      /*
       * Non-pivot tuple should never be explicitly marked as a pivot
       * tuple
       */
      if (BTreeTupleIsPivot(itup))
        return false;

      /*
       * Leaf tuples that are not the page high key (non-pivot tuples)
       * should never be truncated.  (Note that tupnatts must have been
       * inferred, even with a posting list tuple, because only pivot
       * tuples store tupnatts directly.)
       */
      return tupnatts == natts;
    }
    else
    {
      /*
       * Rightmost page doesn't contain a page high key, so tuple was
       * checked above as ordinary leaf tuple
       */
      Assert(!P_RIGHTMOST(opaque));

      /*
       * !heapkeyspace high key tuple contains only key attributes. Note
       * that tupnatts will only have been explicitly represented in
       * !heapkeyspace indexes that happen to have non-key attributes.
       */
      if (!heapkeyspace)
        return tupnatts == nkeyatts;

      /* Use generic heapkeyspace pivot tuple handling */
    }
  }
  else            /* !P_ISLEAF(opaque) */
  {
    if (offnum == P_FIRSTDATAKEY(opaque))
    {
      /*
       * The first tuple on any internal page (possibly the first after
       * its high key) is its negative infinity tuple.  Negative
       * infinity tuples are always truncated to zero attributes.  They
       * are a particular kind of pivot tuple.
       */
      if (heapkeyspace)
        return tupnatts == 0;

      /*
       * The number of attributes won't be explicitly represented if the
       * negative infinity tuple was generated during a page split that
       * occurred with a version of Postgres before v11.  There must be
       * a problem when there is an explicit representation that is
       * non-zero, or when there is no explicit representation and the
       * tuple is evidently not a pre-pg_upgrade tuple.
       *
       * Prior to v11, downlinks always had P_HIKEY as their offset.
       * Accept that as an alternative indication of a valid
       * !heapkeyspace negative infinity tuple.
       */
      return tupnatts == 0 ||
        ItemPointerGetOffsetNumber(&(itup->t_tid)) == P_HIKEY;
    }
    else
    {
      /*
       * !heapkeyspace downlink tuple with separator key contains only
       * key attributes.  Note that tupnatts will only have been
       * explicitly represented in !heapkeyspace indexes that happen to
       * have non-key attributes.
       */
      if (!heapkeyspace)
        return tupnatts == nkeyatts;

      /* Use generic heapkeyspace pivot tuple handling */
    }
  }

  /* Handle heapkeyspace pivot tuples (excluding minus infinity items) */
  Assert(heapkeyspace);

  /*
   * Explicit representation of the number of attributes is mandatory with
   * heapkeyspace index pivot tuples, regardless of whether or not there are
   * non-key attributes.
   */
  if (!BTreeTupleIsPivot(itup))
    return false;

  /* Pivot tuple should not use posting list representation (redundant) */
  if (BTreeTupleIsPosting(itup))
    return false;

  /*
   * Heap TID is a tiebreaker key attribute, so it cannot be untruncated
   * when any other key attribute is truncated
   */
  if (BTreeTupleGetHeapTID(itup) != NULL && tupnatts != nkeyatts)
    return false;

  /*
   * Pivot tuple must have at least one untruncated key attribute (minus
   * infinity pivot tuples are the only exception).  Pivot tuples can never
   * represent that there is a value present for a key attribute that
   * exceeds pg_index.indnkeyatts for the index.
   */
  return tupnatts > 0 && tupnatts <= nkeyatts;
}

/*
 *
 *  _bt_check_third_page() -- check whether tuple fits on a btree page at all.
 *
 * We actually need to be able to fit three items on every page, so restrict
 * any one item to 1/3 the per-page available space.  Note that itemsz should
 * not include the ItemId overhead.
 *
 * It might be useful to apply TOAST methods rather than throw an error here.
 * Using out of line storage would break assumptions made by suffix truncation
 * and by contrib/amcheck, though.
 */
void
_bt_check_third_page(Relation rel, Relation heap, bool needheaptidspace,
           Page page, IndexTuple newtup)
{
  Size    itemsz;
  BTPageOpaque opaque;

  itemsz = MAXALIGN(IndexTupleSize(newtup));

  /* Double check item size against limit */
  if (itemsz <= BTMaxItemSize)
    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)
    return;

  /*
   * Internal page insertions cannot fail here, because that would mean that
   * an earlier leaf level insertion that should have failed didn't
   */
  opaque = BTPageGetOpaque(page);
  if (!P_ISLEAF(opaque))
    elog(ERROR, "cannot insert oversized tuple of size %zu on internal page of index \"%s\"",
       itemsz, RelationGetRelationName(rel));

  ereport(ERROR,
      (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
       errmsg("index row size %zu exceeds btree version %u maximum %zu for index \"%s\"",
          itemsz,
          needheaptidspace ? BTREE_VERSION : BTREE_NOVAC_VERSION,
          needheaptidspace ? BTMaxItemSize : BTMaxItemSizeNoHeapTid,
          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;
}

Coverage Report

Created: 2025-06-13 06:06