nbtpreprocesskeys.c

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/*-------------------------------------------------------------------------
 *
 * nbtpreprocesskeys.c
 *    Preprocessing for Postgres btree scan keys.
 *
 * Portions Copyright (c) 1996-2025, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *    src/backend/access/nbtree/nbtpreprocesskeys.c
 *
 *-------------------------------------------------------------------------
 */
 
#include "postgres.h"
 
#include "access/nbtree.h"
#include "access/relscan.h"
#include "common/int.h"
#include "lib/qunique.h"
#include "utils/array.h"
#include "utils/lsyscache.h"
#include "utils/memutils.h"
#include "utils/rel.h"
 
typedef struct BTScanKeyPreproc
{
    ScanKey     inkey;
    int         inkeyi;
    int         arrayidx;
} BTScanKeyPreproc;
 
typedef struct BTSortArrayContext
{
    FmgrInfo   *sortproc;
    Oid         collation;
    bool        reverse;
} BTSortArrayContext;
 
static bool _bt_fix_scankey_strategy(ScanKey skey, int16 *indoption);
static void _bt_mark_scankey_required(ScanKey skey);
static bool _bt_compare_scankey_args(IndexScanDesc scan, ScanKey op,
                                     ScanKey leftarg, ScanKey rightarg,
                                     BTArrayKeyInfo *array, FmgrInfo *orderproc,
                                     bool *result);
static bool _bt_compare_array_scankey_args(IndexScanDesc scan,
                                           ScanKey arraysk, ScanKey skey,
                                           FmgrInfo *orderproc, BTArrayKeyInfo *array,
                                           bool *qual_ok);
static bool _bt_saoparray_shrink(IndexScanDesc scan, ScanKey arraysk,
                                 ScanKey skey, FmgrInfo *orderproc,
                                 BTArrayKeyInfo *array, bool *qual_ok);
static bool _bt_skiparray_shrink(IndexScanDesc scan, ScanKey skey,
                                 BTArrayKeyInfo *array, bool *qual_ok);
static void _bt_skiparray_strat_adjust(IndexScanDesc scan, ScanKey arraysk,
                                       BTArrayKeyInfo *array);
static void _bt_skiparray_strat_decrement(IndexScanDesc scan, ScanKey arraysk,
                                          BTArrayKeyInfo *array);
static void _bt_skiparray_strat_increment(IndexScanDesc scan, ScanKey arraysk,
                                          BTArrayKeyInfo *array);
static void _bt_unmark_keys(IndexScanDesc scan, int *keyDataMap);
static int  _bt_reorder_array_cmp(const void *a, const void *b);
static ScanKey _bt_preprocess_array_keys(IndexScanDesc scan, int *new_numberOfKeys);
static void _bt_preprocess_array_keys_final(IndexScanDesc scan, int *keyDataMap);
static int  _bt_num_array_keys(IndexScanDesc scan, Oid *skip_eq_ops_out,
                               int *numSkipArrayKeys_out);
static Datum _bt_find_extreme_element(IndexScanDesc scan, ScanKey skey,
                                      Oid elemtype, StrategyNumber strat,
                                      const Datum *elems, int nelems);
static void _bt_setup_array_cmp(IndexScanDesc scan, ScanKey skey, Oid elemtype,
                                FmgrInfo *orderproc, FmgrInfo **sortprocp);
static int  _bt_sort_array_elements(ScanKey skey, FmgrInfo *sortproc,
                                    bool reverse, Datum *elems, int nelems);
static bool _bt_merge_arrays(IndexScanDesc scan, ScanKey skey,
                             FmgrInfo *sortproc, bool reverse,
                             Oid origelemtype, Oid nextelemtype,
                             Datum *elems_orig, int *nelems_orig,
                             Datum *elems_next, int nelems_next);
static int  _bt_compare_array_elements(const void *a, const void *b, void *arg);
 
 
/*
 *  _bt_preprocess_keys() -- Preprocess scan keys
 *
 * The given search-type keys (taken from scan->keyData[])
 * are copied to so->keyData[] with possible transformation.
 * scan->numberOfKeys is the number of input keys, so->numberOfKeys gets
 * the number of output keys.  Calling here a second or subsequent time
 * (during the same btrescan) is a no-op.
 *
 * The output keys are marked with additional sk_flags bits beyond the
 * system-standard bits supplied by the caller.  The DESC and NULLS_FIRST
 * indoption bits for the relevant index attribute are copied into the flags.
 * Also, for a DESC column, we commute (flip) all the sk_strategy numbers
 * so that the index sorts in the desired direction.
 *
 * One key purpose of this routine is to discover which scan keys must be
 * satisfied to continue the scan.  It also attempts to eliminate redundant
 * keys and detect contradictory keys.  (If the index opfamily provides
 * incomplete sets of cross-type operators, we may fail to detect redundant
 * or contradictory keys, but we can survive that.)
 *
 * Required output keys are sorted by index attribute.  Presently we expect
 * (but verify) that the input keys are already so sorted --- this is done
 * by match_clauses_to_index() in indxpath.c.  Some reordering of the keys
 * within each attribute may be done as a byproduct of the processing here.
 * That process must leave array scan keys (within an attribute) in the same
 * order as corresponding entries from the scan's BTArrayKeyInfo array info.
 * We might also construct skip array scan keys that weren't present in the
 * original input keys; these are also output in standard attribute order.
 *
 * The output keys are marked with flags SK_BT_REQFWD and/or SK_BT_REQBKWD
 * if they must be satisfied in order to continue the scan forward or backward
 * respectively.  _bt_checkkeys uses these flags.  For example, if the quals
 * are "x = 1 AND y < 4 AND z < 5", then _bt_checkkeys will reject a tuple
 * (1,2,7), but we must continue the scan in case there are tuples (1,3,z).
 * But once we reach tuples like (1,4,z) we can stop scanning because no
 * later tuples could match.  This is reflected by marking the x and y keys,
 * but not the z key, with SK_BT_REQFWD.  In general, the keys for leading
 * attributes with "=" keys are marked both SK_BT_REQFWD and SK_BT_REQBKWD.
 * For the first attribute without an "=" key, any "<" and "<=" keys are
 * marked SK_BT_REQFWD while any ">" and ">=" keys are marked SK_BT_REQBKWD.
 * This can be seen to be correct by considering the above example.
 *
 * If we never generated skip array scan keys, it would be possible for "gaps"
 * to appear that make it unsafe to mark any subsequent input scan keys
 * (copied from scan->keyData[]) as required to continue the scan.  Prior to
 * Postgres 18, a qual like "WHERE y = 4" always resulted in a full scan.
 * This qual now becomes "WHERE x = ANY('{every possible x value}') and y = 4"
 * on output.  In other words, preprocessing now adds a skip array on "x".
 * This has the potential to be much more efficient than a full index scan
 * (though it behaves like a full scan when there's many distinct "x" values).
 *
 * Typically, redundant keys are eliminated: we keep only the tightest
 * >/>= bound and the tightest </<= bound, and if there's an = key then
 * that's the only one returned.  (So, we return either a single = key,
 * or one or two boundary-condition keys for each attr.)  However, if we
 * cannot compare two keys for lack of a suitable cross-type operator,
 * we cannot eliminate either key.
 *
 * When all redundant keys could not be eliminated, we'll output a key array
 * that can more or less be treated as if it had no redundant keys.  Suppose
 * we have "x > 4::int AND x > 10::bigint AND x < 70", and we are unable to
 * determine which > key is more restrictive for lack of a suitable cross-type
 * operator.  We'll arbitrarily pick one of the > keys; the other > key won't
 * be marked required.  Obviously, the scan will be less efficient if we
 * choose x > 4 over x > 10 -- but it can still largely proceed as if there
 * was only a single > condition.  "x > 10" will be placed at the end of the
 * so->keyData[] output array.  It'll always be evaluated last, after the keys
 * that could be marked required in the usual way (after "x > 4 AND x < 70").
 * This can sometimes result in so->keyData[] keys that aren't even in index
 * attribute order (if the qual involves multiple attributes).  The scan's
 * required keys will still be in attribute order, though, so it can't matter.
 *
 * This scheme ensures that _bt_first always uses the same set of keys at the
 * start of a forwards scan as those _bt_checkkeys uses to determine when to
 * end a similar backwards scan (and vice-versa).  _bt_advance_array_keys
 * depends on this: it expects to be able to reliably predict what the next
 * _bt_first call will do by testing whether _bt_checkkeys' routines report
 * that the final tuple on the page is past the end of matches for the scan's
 * keys with the scan direction flipped.  If it is (if continuescan=false),
 * then it follows that calling _bt_first will, at a minimum, relocate the
 * scan to the very next leaf page (in the current scan direction).
 *
 * As a byproduct of this work, we can detect contradictory quals such
 * as "x = 1 AND x > 2".  If we see that, we return so->qual_ok = false,
 * indicating the scan need not be run at all since no tuples can match.
 * (In this case we do not bother completing the output key array!)
 * Again, missing cross-type operators might cause us to fail to prove the
 * quals contradictory when they really are, but the scan will work correctly.
 *
 * Skip array = keys will even be generated in the presence of "contradictory"
 * inequality quals when it'll enable marking later input quals as required.
 * We'll merge any such inequalities into the generated skip array by setting
 * its array.low_compare or array.high_compare key field.  The resulting skip
 * array will generate its array elements from a range that's constrained by
 * any merged input inequalities (which won't get output in so->keyData[]).
 *
 * Row comparison keys currently have a couple of notable limitations.
 * Right now we just transfer them into the preprocessed array without any
 * editorialization.  We can treat them the same as an ordinary inequality
 * comparison on the row's first index column, for the purposes of the logic
 * about required keys.  Also, we are unable to merge a row comparison key
 * into a skip array (only ordinary inequalities are merged).  A key that
 * comes after a Row comparison key is therefore never marked as required.
 *
 * Note: the reason we have to copy the preprocessed scan keys into private
 * storage is that we are modifying the array based on comparisons of the
 * key argument values, which could change on a rescan.  Therefore we can't
 * overwrite the source data.
 */
void
_bt_preprocess_keys(IndexScanDesc scan)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    int         numberOfKeys = scan->numberOfKeys;
    int16      *indoption = scan->indexRelation->rd_indoption;
    int         new_numberOfKeys;
    int         numberOfEqualCols;
    ScanKey     inkeys;
    BTScanKeyPreproc xform[BTMaxStrategyNumber];
    bool        test_result,
                redundant_key_kept = false;
    AttrNumber  attno;
    ScanKey     arrayKeyData;
    int        *keyDataMap = NULL;
    int         arrayidx = 0;
 
    if (so->numberOfKeys > 0)
    {
        /*
         * Only need to do preprocessing once per btrescan, at most.  All
         * calls after the first are handled as no-ops.
         */
        return;
    }
 
    /* initialize result variables */
    so->qual_ok = true;
    so->numberOfKeys = 0;
 
    if (numberOfKeys < 1)
        return;                 /* done if qual-less scan */
 
    /* If any keys are SK_SEARCHARRAY type, set up array-key info */
    arrayKeyData = _bt_preprocess_array_keys(scan, &numberOfKeys);
    if (!so->qual_ok)
    {
        /* unmatchable array, so give up */
        return;
    }
 
    /*
     * Treat arrayKeyData[] (a partially preprocessed copy of scan->keyData[])
     * as our input if _bt_preprocess_array_keys just allocated it, else just
     * use scan->keyData[]
     */
    if (arrayKeyData)
    {
        inkeys = arrayKeyData;
 
        /* Also maintain keyDataMap for remapping so->orderProcs[] later */
        keyDataMap = MemoryContextAlloc(so->arrayContext,
                                        numberOfKeys * sizeof(int));
 
        /*
         * Also enlarge output array when it might otherwise not have room for
         * a skip array's scan key
         */
        if (numberOfKeys > scan->numberOfKeys)
            so->keyData = repalloc(so->keyData,
                                   numberOfKeys * sizeof(ScanKeyData));
    }
    else
        inkeys = scan->keyData;
 
    /* we check that input keys are correctly ordered */
    if (inkeys[0].sk_attno < 1)
        elog(ERROR, "btree index keys must be ordered by attribute");
 
    /* We can short-circuit most of the work if there's just one key */
    if (numberOfKeys == 1)
    {
        /* Apply indoption to scankey (might change sk_strategy!) */
        if (!_bt_fix_scankey_strategy(&inkeys[0], indoption))
            so->qual_ok = false;
        memcpy(&so->keyData[0], &inkeys[0], sizeof(ScanKeyData));
        so->numberOfKeys = 1;
        /* We can mark the qual as required if it's for first index col */
        if (inkeys[0].sk_attno == 1)
            _bt_mark_scankey_required(&so->keyData[0]);
        if (arrayKeyData)
        {
            /*
             * Don't call _bt_preprocess_array_keys_final in this fast path
             * (we'll miss out on the single value array transformation, but
             * that's not nearly as important when there's only one scan key)
             */
            Assert(so->keyData[0].sk_flags & SK_SEARCHARRAY);
            Assert(so->keyData[0].sk_strategy != BTEqualStrategyNumber ||
                   (so->arrayKeys[0].scan_key == 0 &&
                    !(so->keyData[0].sk_flags & SK_BT_SKIP) &&
                    OidIsValid(so->orderProcs[0].fn_oid)));
        }
 
        return;
    }
 
    /*
     * Otherwise, do the full set of pushups.
     */
    new_numberOfKeys = 0;
    numberOfEqualCols = 0;
 
    /*
     * Initialize for processing of keys for attr 1.
     *
     * xform[i] points to the currently best scan key of strategy type i+1; it
     * is NULL if we haven't yet found such a key for this attr.
     */
    attno = 1;
    memset(xform, 0, sizeof(xform));
 
    /*
     * Loop iterates from 0 to numberOfKeys inclusive; we use the last pass to
     * handle after-last-key processing.  Actual exit from the loop is at the
     * "break" statement below.
     */
    for (int i = 0;; i++)
    {
        ScanKey     inkey = inkeys + i;
        int         j;
 
        if (i < numberOfKeys)
        {
            /* Apply indoption to scankey (might change sk_strategy!) */
            if (!_bt_fix_scankey_strategy(inkey, indoption))
            {
                /* NULL can't be matched, so give up */
                so->qual_ok = false;
                return;
            }
        }
 
        /*
         * If we are at the end of the keys for a particular attr, finish up
         * processing and emit the cleaned-up keys.
         */
        if (i == numberOfKeys || inkey->sk_attno != attno)
        {
            int         priorNumberOfEqualCols = numberOfEqualCols;
 
            /* check input keys are correctly ordered */
            if (i < numberOfKeys && inkey->sk_attno < attno)
                elog(ERROR, "btree index keys must be ordered by attribute");
 
            /*
             * If = has been specified, all other keys can be eliminated as
             * redundant.  Note that this is no less true if the = key is
             * SEARCHARRAY; the only real difference is that the inequality
             * key _becomes_ redundant by making _bt_compare_scankey_args
             * eliminate the subset of elements that won't need to be matched
             * (with SAOP arrays and skip arrays alike).
             *
             * If we have a case like "key = 1 AND key > 2", we set qual_ok to
             * false and abandon further processing.  We'll do the same thing
             * given a case like "key IN (0, 1) AND key > 2".
             *
             * We also have to deal with the case of "key IS NULL", which is
             * unsatisfiable in combination with any other index condition. By
             * the time we get here, that's been classified as an equality
             * check, and we've rejected any combination of it with a regular
             * equality condition; but not with other types of conditions.
             */
            if (xform[BTEqualStrategyNumber - 1].inkey)
            {
                ScanKey     eq = xform[BTEqualStrategyNumber - 1].inkey;
                BTArrayKeyInfo *array = NULL;
                FmgrInfo   *orderproc = NULL;
 
                if (arrayKeyData && (eq->sk_flags & SK_SEARCHARRAY))
                {
                    int         eq_in_ikey,
                                eq_arrayidx;
 
                    eq_in_ikey = xform[BTEqualStrategyNumber - 1].inkeyi;
                    eq_arrayidx = xform[BTEqualStrategyNumber - 1].arrayidx;
                    array = &so->arrayKeys[eq_arrayidx - 1];
                    orderproc = so->orderProcs + eq_in_ikey;
 
                    Assert(array->scan_key == eq_in_ikey);
                    Assert(OidIsValid(orderproc->fn_oid));
                }
 
                for (j = BTMaxStrategyNumber; --j >= 0;)
                {
                    ScanKey     chk = xform[j].inkey;
 
                    if (!chk || j == (BTEqualStrategyNumber - 1))
                        continue;
 
                    if (eq->sk_flags & SK_SEARCHNULL)
                    {
                        /* IS NULL is contradictory to anything else */
                        so->qual_ok = false;
                        return;
                    }
 
                    if (_bt_compare_scankey_args(scan, chk, eq, chk,
                                                 array, orderproc,
                                                 &test_result))
                    {
                        if (!test_result)
                        {
                            /* keys proven mutually contradictory */
                            so->qual_ok = false;
                            return;
                        }
                        /* else discard the redundant non-equality key */
                        xform[j].inkey = NULL;
                        xform[j].inkeyi = -1;
                    }
                    else
                        redundant_key_kept = true;
                }
                /* track number of attrs for which we have "=" keys */
                numberOfEqualCols++;
            }
 
            /* try to keep only one of <, <= */
            if (xform[BTLessStrategyNumber - 1].inkey &&
                xform[BTLessEqualStrategyNumber - 1].inkey)
            {
                ScanKey     lt = xform[BTLessStrategyNumber - 1].inkey;
                ScanKey     le = xform[BTLessEqualStrategyNumber - 1].inkey;
 
                if (_bt_compare_scankey_args(scan, le, lt, le, NULL, NULL,
                                             &test_result))
                {
                    if (test_result)
                        xform[BTLessEqualStrategyNumber - 1].inkey = NULL;
                    else
                        xform[BTLessStrategyNumber - 1].inkey = NULL;
                }
                else
                    redundant_key_kept = true;
            }
 
            /* try to keep only one of >, >= */
            if (xform[BTGreaterStrategyNumber - 1].inkey &&
                xform[BTGreaterEqualStrategyNumber - 1].inkey)
            {
                ScanKey     gt = xform[BTGreaterStrategyNumber - 1].inkey;
                ScanKey     ge = xform[BTGreaterEqualStrategyNumber - 1].inkey;
 
                if (_bt_compare_scankey_args(scan, ge, gt, ge, NULL, NULL,
                                             &test_result))
                {
                    if (test_result)
                        xform[BTGreaterEqualStrategyNumber - 1].inkey = NULL;
                    else
                        xform[BTGreaterStrategyNumber - 1].inkey = NULL;
                }
                else
                    redundant_key_kept = true;
            }
 
            /*
             * Emit the cleaned-up keys into the so->keyData[] array, and then
             * mark them if they are required.  They are required (possibly
             * only in one direction) if all attrs before this one had "=".
             *
             * In practice we'll rarely output non-required scan keys here;
             * typically, _bt_preprocess_array_keys has already added "=" keys
             * sufficient to form an unbroken series of "=" constraints on all
             * attrs prior to the attr from the final scan->keyData[] key.
             */
            for (j = BTMaxStrategyNumber; --j >= 0;)
            {
                if (xform[j].inkey)
                {
                    ScanKey     outkey = &so->keyData[new_numberOfKeys++];
 
                    memcpy(outkey, xform[j].inkey, sizeof(ScanKeyData));
                    if (arrayKeyData)
                        keyDataMap[new_numberOfKeys - 1] = xform[j].inkeyi;
                    if (priorNumberOfEqualCols == attno - 1)
                        _bt_mark_scankey_required(outkey);
                }
            }
 
            /*
             * Exit loop here if done.
             */
            if (i == numberOfKeys)
                break;
 
            /* Re-initialize for new attno */
            attno = inkey->sk_attno;
            memset(xform, 0, sizeof(xform));
        }
 
        /* check strategy this key's operator corresponds to */
        j = inkey->sk_strategy - 1;
 
        if (inkey->sk_strategy == BTEqualStrategyNumber &&
            (inkey->sk_flags & SK_SEARCHARRAY))
        {
            /* must track how input scan keys map to arrays */
            Assert(arrayKeyData);
            arrayidx++;
        }
 
        /*
         * have we seen a scan key for this same attribute and using this same
         * operator strategy before now?
         */
        if (xform[j].inkey == NULL)
        {
            /* nope, so this scan key wins by default (at least for now) */
            xform[j].inkey = inkey;
            xform[j].inkeyi = i;
            xform[j].arrayidx = arrayidx;
        }
        else
        {
            FmgrInfo   *orderproc = NULL;
            BTArrayKeyInfo *array = NULL;
 
            /*
             * Seen one of these before, so keep only the more restrictive key
             * if possible
             */
            if (j == (BTEqualStrategyNumber - 1) && arrayKeyData)
            {
                /*
                 * Have to set up array keys
                 */
                if (inkey->sk_flags & SK_SEARCHARRAY)
                {
                    array = &so->arrayKeys[arrayidx - 1];
                    orderproc = so->orderProcs + i;
 
                    Assert(array->scan_key == i);
                    Assert(OidIsValid(orderproc->fn_oid));
                    Assert(!(inkey->sk_flags & SK_BT_SKIP));
                }
                else if (xform[j].inkey->sk_flags & SK_SEARCHARRAY)
                {
                    array = &so->arrayKeys[xform[j].arrayidx - 1];
                    orderproc = so->orderProcs + xform[j].inkeyi;
 
                    Assert(array->scan_key == xform[j].inkeyi);
                    Assert(OidIsValid(orderproc->fn_oid));
                    Assert(!(xform[j].inkey->sk_flags & SK_BT_SKIP));
                }
 
                /*
                 * Both scan keys might have arrays, in which case we'll
                 * arbitrarily pass only one of the arrays.  That won't
                 * matter, since _bt_compare_scankey_args is aware that two
                 * SEARCHARRAY scan keys mean that _bt_preprocess_array_keys
                 * failed to eliminate redundant arrays through array merging.
                 * _bt_compare_scankey_args just returns false when it sees
                 * this; it won't even try to examine either array.
                 */
            }
 
            if (_bt_compare_scankey_args(scan, inkey, inkey, xform[j].inkey,
                                         array, orderproc, &test_result))
            {
                /* Have all we need to determine redundancy */
                if (test_result)
                {
                    /*
                     * New key is more restrictive, and so replaces old key...
                     */
                    if (j != (BTEqualStrategyNumber - 1) ||
                        !(xform[j].inkey->sk_flags & SK_SEARCHARRAY))
                    {
                        xform[j].inkey = inkey;
                        xform[j].inkeyi = i;
                        xform[j].arrayidx = arrayidx;
                    }
                    else
                    {
                        /*
                         * ...unless we have to keep the old key because it's
                         * an array that rendered the new key redundant.  We
                         * need to make sure that we don't throw away an array
                         * scan key.  _bt_preprocess_array_keys_final expects
                         * us to keep all of the arrays that weren't already
                         * eliminated by _bt_preprocess_array_keys earlier on.
                         */
                        Assert(!(inkey->sk_flags & SK_SEARCHARRAY));
                    }
                }
                else if (j == (BTEqualStrategyNumber - 1))
                {
                    /* key == a && key == b, but a != b */
                    so->qual_ok = false;
                    return;
                }
                /* else old key is more restrictive, keep it */
            }
            else
            {
                /*
                 * We can't determine which key is more restrictive.  Push
                 * xform[j] directly to the output array, then set xform[j] to
                 * the new scan key.
                 *
                 * Note: We do things this way around so that our arrays are
                 * always in the same order as their corresponding scan keys.
                 * _bt_preprocess_array_keys_final expects this.
                 */
                ScanKey     outkey = &so->keyData[new_numberOfKeys++];
 
                memcpy(outkey, xform[j].inkey, sizeof(ScanKeyData));
                if (arrayKeyData)
                    keyDataMap[new_numberOfKeys - 1] = xform[j].inkeyi;
                if (numberOfEqualCols == attno - 1)
                    _bt_mark_scankey_required(outkey);
                xform[j].inkey = inkey;
                xform[j].inkeyi = i;
                xform[j].arrayidx = arrayidx;
                redundant_key_kept = true;
            }
        }
    }
 
    so->numberOfKeys = new_numberOfKeys;
 
    /*
     * Now that we've built a temporary mapping from so->keyData[] (output
     * scan keys) to arrayKeyData[] (our input scan keys), fix array->scan_key
     * references.  Also consolidate the so->orderProcs[] array such that it
     * can be subscripted using so->keyData[]-wise offsets.
     */
    if (arrayKeyData)
        _bt_preprocess_array_keys_final(scan, keyDataMap);
 
    /*
     * If there are remaining redundant inequality keys, we must make sure
     * that each index attribute has no more than one required >/>= key, and
     * no more than one required </<= key.  Attributes that have one or more
     * required = keys now must keep only one required key (the first = key).
     */
    if (unlikely(redundant_key_kept) && so->qual_ok)
        _bt_unmark_keys(scan, keyDataMap);
 
    /* Could pfree arrayKeyData/keyDataMap now, but not worth the cycles */
}
 
/*
 * Adjust a scankey's strategy and flags setting as needed for indoptions.
 *
 * We copy the appropriate indoption value into the scankey sk_flags
 * (shifting to avoid clobbering system-defined flag bits).  Also, if
 * the DESC option is set, commute (flip) the operator strategy number.
 *
 * A secondary purpose is to check for IS NULL/NOT NULL scankeys and set up
 * the strategy field correctly for them.
 *
 * Lastly, for ordinary scankeys (not IS NULL/NOT NULL), we check for a
 * NULL comparison value.  Since all btree operators are assumed strict,
 * a NULL means that the qual cannot be satisfied.  We return true if the
 * comparison value isn't NULL, or false if the scan should be abandoned.
 *
 * This function is applied to the *input* scankey structure; therefore
 * on a rescan we will be looking at already-processed scankeys.  Hence
 * we have to be careful not to re-commute the strategy if we already did it.
 * It's a bit ugly to modify the caller's copy of the scankey but in practice
 * there shouldn't be any problem, since the index's indoptions are certainly
 * not going to change while the scankey survives.
 */
static bool
_bt_fix_scankey_strategy(ScanKey skey, int16 *indoption)
{
    int         addflags;
 
    addflags = indoption[skey->sk_attno - 1] << SK_BT_INDOPTION_SHIFT;
 
    /*
     * We treat all btree operators as strict (even if they're not so marked
     * in pg_proc). This means that it is impossible for an operator condition
     * with a NULL comparison constant to succeed, and we can reject it right
     * away.
     *
     * However, we now also support "x IS NULL" clauses as search conditions,
     * so in that case keep going. The planner has not filled in any
     * particular strategy in this case, so set it to BTEqualStrategyNumber
     * --- we can treat IS NULL as an equality operator for purposes of search
     * strategy.
     *
     * Likewise, "x IS NOT NULL" is supported.  We treat that as either "less
     * than NULL" in a NULLS LAST index, or "greater than NULL" in a NULLS
     * FIRST index.
     *
     * Note: someday we might have to fill in sk_collation from the index
     * column's collation.  At the moment this is a non-issue because we'll
     * never actually call the comparison operator on a NULL.
     */
    if (skey->sk_flags & SK_ISNULL)
    {
        /* SK_ISNULL shouldn't be set in a row header scankey */
        Assert(!(skey->sk_flags & SK_ROW_HEADER));
 
        /* Set indoption flags in scankey (might be done already) */
        skey->sk_flags |= addflags;
 
        /* Set correct strategy for IS NULL or NOT NULL search */
        if (skey->sk_flags & SK_SEARCHNULL)
        {
            skey->sk_strategy = BTEqualStrategyNumber;
            skey->sk_subtype = InvalidOid;
            skey->sk_collation = InvalidOid;
        }
        else if (skey->sk_flags & SK_SEARCHNOTNULL)
        {
            if (skey->sk_flags & SK_BT_NULLS_FIRST)
                skey->sk_strategy = BTGreaterStrategyNumber;
            else
                skey->sk_strategy = BTLessStrategyNumber;
            skey->sk_subtype = InvalidOid;
            skey->sk_collation = InvalidOid;
        }
        else
        {
            /* regular qual, so it cannot be satisfied */
            return false;
        }
 
        /* Needn't do the rest */
        return true;
    }
 
    /* Adjust strategy for DESC, if we didn't already */
    if ((addflags & SK_BT_DESC) && !(skey->sk_flags & SK_BT_DESC))
        skey->sk_strategy = BTCommuteStrategyNumber(skey->sk_strategy);
    skey->sk_flags |= addflags;
 
    /* If it's a row header, fix row member flags and strategies similarly */
    if (skey->sk_flags & SK_ROW_HEADER)
    {
        ScanKey     subkey = (ScanKey) DatumGetPointer(skey->sk_argument);
 
        if (subkey->sk_flags & SK_ISNULL)
        {
            /* First row member is NULL, so RowCompare is unsatisfiable */
            Assert(subkey->sk_flags & SK_ROW_MEMBER);
            return false;
        }
 
        for (;;)
        {
            Assert(subkey->sk_flags & SK_ROW_MEMBER);
            addflags = indoption[subkey->sk_attno - 1] << SK_BT_INDOPTION_SHIFT;
            if ((addflags & SK_BT_DESC) && !(subkey->sk_flags & SK_BT_DESC))
                subkey->sk_strategy = BTCommuteStrategyNumber(subkey->sk_strategy);
            subkey->sk_flags |= addflags;
            if (subkey->sk_flags & SK_ROW_END)
                break;
            subkey++;
        }
    }
 
    return true;
}
 
/*
 * Mark a scankey as "required to continue the scan".
 *
 * Depending on the operator type, the key may be required for both scan
 * directions or just one.  Also, if the key is a row comparison header,
 * we have to mark the appropriate subsidiary ScanKeys as required.  In such
 * cases, the first subsidiary key is required, but subsequent ones are
 * required only as long as they correspond to successive index columns and
 * match the leading column as to sort direction.  Otherwise the row
 * comparison ordering is different from the index ordering and so we can't
 * stop the scan on the basis of those lower-order columns.
 *
 * Note: when we set required-key flag bits in a subsidiary scankey, we are
 * scribbling on a data structure belonging to the index AM's caller, not on
 * our private copy.  This should be OK because the marking will not change
 * from scan to scan within a query, and so we'd just re-mark the same way
 * anyway on a rescan.  Something to keep an eye on though.
 */
static void
_bt_mark_scankey_required(ScanKey skey)
{
    int         addflags;
 
    switch (skey->sk_strategy)
    {
        case BTLessStrategyNumber:
        case BTLessEqualStrategyNumber:
            addflags = SK_BT_REQFWD;
            break;
        case BTEqualStrategyNumber:
            addflags = SK_BT_REQFWD | SK_BT_REQBKWD;
            break;
        case BTGreaterEqualStrategyNumber:
        case BTGreaterStrategyNumber:
            addflags = SK_BT_REQBKWD;
            break;
        default:
            elog(ERROR, "unrecognized StrategyNumber: %d",
                 (int) skey->sk_strategy);
            addflags = 0;       /* keep compiler quiet */
            break;
    }
 
    skey->sk_flags |= addflags;
 
    if (skey->sk_flags & SK_ROW_HEADER)
    {
        ScanKey     subkey = (ScanKey) DatumGetPointer(skey->sk_argument);
        AttrNumber  attno = skey->sk_attno;
 
        /* First subkey should be same column/operator as the header */
        Assert(subkey->sk_attno == attno);
        Assert(subkey->sk_strategy == skey->sk_strategy);
 
        for (;;)
        {
            Assert(subkey->sk_flags & SK_ROW_MEMBER);
            if (subkey->sk_attno != attno)
                break;          /* non-adjacent key, so not required */
            if (subkey->sk_strategy != skey->sk_strategy)
                break;          /* wrong direction, so not required */
            subkey->sk_flags |= addflags;
            if (subkey->sk_flags & SK_ROW_END)
                break;
            subkey++;
            attno++;
        }
    }
}
 
/*
 * Compare two scankey values using a specified operator.
 *
 * The test we want to perform is logically "leftarg op rightarg", where
 * leftarg and rightarg are the sk_argument values in those ScanKeys, and
 * the comparison operator is the one in the op ScanKey.  However, in
 * cross-data-type situations we may need to look up the correct operator in
 * the index's opfamily: it is the one having amopstrategy = op->sk_strategy
 * and amoplefttype/amoprighttype equal to the two argument datatypes.
 *
 * If the opfamily doesn't supply a complete set of cross-type operators we
 * may not be able to make the comparison.  If we can make the comparison
 * we store the operator result in *result and return true.  We return false
 * if the comparison could not be made.
 *
 * If either leftarg or rightarg are an array, we'll apply array-specific
 * rules to determine which array elements are redundant on behalf of caller.
 * It is up to our caller to save whichever of the two scan keys is the array,
 * and discard the non-array scan key (the non-array scan key is guaranteed to
 * be redundant with any complete opfamily).  Caller isn't expected to call
 * here with a pair of array scan keys provided we're dealing with a complete
 * opfamily (_bt_preprocess_array_keys will merge array keys together to make
 * sure of that).
 *
 * Note: we'll also shrink caller's array as needed to eliminate redundant
 * array elements.  One reason why caller should prefer to discard non-array
 * scan keys is so that we'll have the opportunity to shrink the array
 * multiple times, in multiple calls (for each of several other scan keys on
 * the same index attribute).
 *
 * Note: op always points at the same ScanKey as either leftarg or rightarg.
 * Since we don't scribble on the scankeys themselves, this aliasing should
 * cause no trouble.
 *
 * Note: this routine needs to be insensitive to any DESC option applied
 * to the index column.  For example, "x < 4" is a tighter constraint than
 * "x < 5" regardless of which way the index is sorted.
 */
static bool
_bt_compare_scankey_args(IndexScanDesc scan, ScanKey op,
                         ScanKey leftarg, ScanKey rightarg,
                         BTArrayKeyInfo *array, FmgrInfo *orderproc,
                         bool *result)
{
    Relation    rel = scan->indexRelation;
    Oid         lefttype,
                righttype,
                optype,
                opcintype,
                cmp_op;
    StrategyNumber strat;
 
    Assert(!((leftarg->sk_flags | rightarg->sk_flags) & SK_ROW_MEMBER));
 
    /*
     * First, deal with cases where one or both args are NULL.  This should
     * only happen when the scankeys represent IS NULL/NOT NULL conditions.
     */
    if ((leftarg->sk_flags | rightarg->sk_flags) & SK_ISNULL)
    {
        bool        leftnull,
                    rightnull;
 
        /* Handle skip array comparison with IS NOT NULL scan key */
        if ((leftarg->sk_flags | rightarg->sk_flags) & SK_BT_SKIP)
        {
            /* Shouldn't generate skip array in presence of IS NULL key */
            Assert(!((leftarg->sk_flags | rightarg->sk_flags) & SK_SEARCHNULL));
            Assert((leftarg->sk_flags | rightarg->sk_flags) & SK_SEARCHNOTNULL);
 
            /* Skip array will have no NULL element/IS NULL scan key */
            Assert(array->num_elems == -1);
            array->null_elem = false;
 
            /* IS NOT NULL key (could be leftarg or rightarg) now redundant */
            *result = true;
            return true;
        }
 
        if (leftarg->sk_flags & SK_ISNULL)
        {
            Assert(leftarg->sk_flags & (SK_SEARCHNULL | SK_SEARCHNOTNULL));
            leftnull = true;
        }
        else
            leftnull = false;
        if (rightarg->sk_flags & SK_ISNULL)
        {
            Assert(rightarg->sk_flags & (SK_SEARCHNULL | SK_SEARCHNOTNULL));
            rightnull = true;
        }
        else
            rightnull = false;
 
        /*
         * We treat NULL as either greater than or less than all other values.
         * Since true > false, the tests below work correctly for NULLS LAST
         * logic.  If the index is NULLS FIRST, we need to flip the strategy.
         */
        strat = op->sk_strategy;
        if (op->sk_flags & SK_BT_NULLS_FIRST)
            strat = BTCommuteStrategyNumber(strat);
 
        switch (strat)
        {
            case BTLessStrategyNumber:
                *result = (leftnull < rightnull);
                break;
            case BTLessEqualStrategyNumber:
                *result = (leftnull <= rightnull);
                break;
            case BTEqualStrategyNumber:
                *result = (leftnull == rightnull);
                break;
            case BTGreaterEqualStrategyNumber:
                *result = (leftnull >= rightnull);
                break;
            case BTGreaterStrategyNumber:
                *result = (leftnull > rightnull);
                break;
            default:
                elog(ERROR, "unrecognized StrategyNumber: %d", (int) strat);
                *result = false;    /* keep compiler quiet */
                break;
        }
        return true;
    }
 
    /*
     * We don't yet know how to determine redundancy when it involves a row
     * compare key (barring simple cases involving IS NULL/IS NOT NULL)
     */
    if ((leftarg->sk_flags | rightarg->sk_flags) & SK_ROW_HEADER)
    {
        Assert(!((leftarg->sk_flags | rightarg->sk_flags) & SK_BT_SKIP));
        return false;
    }
 
    /*
     * If either leftarg or rightarg are equality-type array scankeys, we need
     * specialized handling (since by now we know that IS NULL wasn't used)
     */
    if (array)
    {
        bool        leftarray,
                    rightarray;
 
        leftarray = ((leftarg->sk_flags & SK_SEARCHARRAY) &&
                     leftarg->sk_strategy == BTEqualStrategyNumber);
        rightarray = ((rightarg->sk_flags & SK_SEARCHARRAY) &&
                      rightarg->sk_strategy == BTEqualStrategyNumber);
 
        /*
         * _bt_preprocess_array_keys is responsible for merging together array
         * scan keys, and will do so whenever the opfamily has the required
         * cross-type support.  If it failed to do that, we handle it just
         * like the case where we can't make the comparison ourselves.
         */
        if (leftarray && rightarray)
        {
            /* Can't make the comparison */
            *result = false;    /* suppress compiler warnings */
            Assert(!((leftarg->sk_flags | rightarg->sk_flags) & SK_BT_SKIP));
            return false;
        }
 
        /*
         * Otherwise we need to determine if either one of leftarg or rightarg
         * uses an array, then pass this through to a dedicated helper
         * function.
         */
        if (leftarray)
            return _bt_compare_array_scankey_args(scan, leftarg, rightarg,
                                                  orderproc, array, result);
        else if (rightarray)
            return _bt_compare_array_scankey_args(scan, rightarg, leftarg,
                                                  orderproc, array, result);
 
        /* FALL THRU */
    }
 
    /*
     * The opfamily we need to worry about is identified by the index column.
     */
    Assert(leftarg->sk_attno == rightarg->sk_attno);
 
    opcintype = rel->rd_opcintype[leftarg->sk_attno - 1];
 
    /*
     * Determine the actual datatypes of the ScanKey arguments.  We have to
     * support the convention that sk_subtype == InvalidOid means the opclass
     * input type; this is a hack to simplify life for ScanKeyInit().
     */
    lefttype = leftarg->sk_subtype;
    if (lefttype == InvalidOid)
        lefttype = opcintype;
    righttype = rightarg->sk_subtype;
    if (righttype == InvalidOid)
        righttype = opcintype;
    optype = op->sk_subtype;
    if (optype == InvalidOid)
        optype = opcintype;
 
    /*
     * If leftarg and rightarg match the types expected for the "op" scankey,
     * we can use its already-looked-up comparison function.
     */
    if (lefttype == opcintype && righttype == optype)
    {
        *result = DatumGetBool(FunctionCall2Coll(&op->sk_func,
                                                 op->sk_collation,
                                                 leftarg->sk_argument,
                                                 rightarg->sk_argument));
        return true;
    }
 
    /*
     * Otherwise, we need to go to the syscache to find the appropriate
     * operator.  (This cannot result in infinite recursion, since no
     * indexscan initiated by syscache lookup will use cross-data-type
     * operators.)
     *
     * If the sk_strategy was flipped by _bt_fix_scankey_strategy, we have to
     * un-flip it to get the correct opfamily member.
     */
    strat = op->sk_strategy;
    if (op->sk_flags & SK_BT_DESC)
        strat = BTCommuteStrategyNumber(strat);
 
    cmp_op = get_opfamily_member(rel->rd_opfamily[leftarg->sk_attno - 1],
                                 lefttype,
                                 righttype,
                                 strat);
    if (OidIsValid(cmp_op))
    {
        RegProcedure cmp_proc = get_opcode(cmp_op);
 
        if (RegProcedureIsValid(cmp_proc))
        {
            *result = DatumGetBool(OidFunctionCall2Coll(cmp_proc,
                                                        op->sk_collation,
                                                        leftarg->sk_argument,
                                                        rightarg->sk_argument));
            return true;
        }
    }
 
    /* Can't make the comparison */
    *result = false;            /* suppress compiler warnings */
    return false;
}
 
/*
 * Compare an array scan key to a scalar scan key, eliminating contradictory
 * array elements such that the scalar scan key becomes redundant.
 *
 * If the opfamily is incomplete we may not be able to determine which
 * elements are contradictory.  When we return true we'll have validly set
 * *qual_ok, guaranteeing that at least the scalar scan key can be considered
 * redundant.  We return false if the comparison could not be made (caller
 * must keep both scan keys when this happens).
 *
 * Note: it's up to caller to deal with IS [NOT] NULL scan keys, as well as
 * row comparison scan keys.  We only deal with scalar scan keys.
 */
static bool
_bt_compare_array_scankey_args(IndexScanDesc scan, ScanKey arraysk, ScanKey skey,
                               FmgrInfo *orderproc, BTArrayKeyInfo *array,
                               bool *qual_ok)
{
    Assert(arraysk->sk_attno == skey->sk_attno);
    Assert(!(arraysk->sk_flags & (SK_ISNULL | SK_ROW_HEADER | SK_ROW_MEMBER)));
    Assert((arraysk->sk_flags & SK_SEARCHARRAY) &&
           arraysk->sk_strategy == BTEqualStrategyNumber);
    /* don't expect to have to deal with NULLs/row comparison scan keys */
    Assert(!(skey->sk_flags & (SK_ISNULL | SK_ROW_HEADER | SK_ROW_MEMBER)));
    Assert(!(skey->sk_flags & SK_SEARCHARRAY) ||
           skey->sk_strategy != BTEqualStrategyNumber);
 
    /*
     * Just call the appropriate helper function based on whether it's a SAOP
     * array or a skip array.  Both helpers will set *qual_ok in passing.
     */
    if (array->num_elems != -1)
        return _bt_saoparray_shrink(scan, arraysk, skey, orderproc, array,
                                    qual_ok);
    else
        return _bt_skiparray_shrink(scan, skey, array, qual_ok);
}
 
/*
 * Preprocessing of SAOP array scan key, used to determine which array
 * elements are eliminated as contradictory by a non-array scalar key.
 *
 * _bt_compare_array_scankey_args helper function.
 *
 * Array elements can be eliminated as contradictory when excluded by some
 * other operator on the same attribute.  For example, with an index scan qual
 * "WHERE a IN (1, 2, 3) AND a < 2", all array elements except the value "1"
 * are eliminated, and the < scan key is eliminated as redundant.  Cases where
 * every array element is eliminated by a redundant scalar scan key have an
 * unsatisfiable qual, which we handle by setting *qual_ok=false for caller.
 */
static bool
_bt_saoparray_shrink(IndexScanDesc scan, ScanKey arraysk, ScanKey skey,
                     FmgrInfo *orderproc, BTArrayKeyInfo *array, bool *qual_ok)
{
    Relation    rel = scan->indexRelation;
    Oid         opcintype = rel->rd_opcintype[arraysk->sk_attno - 1];
    int         cmpresult = 0,
                cmpexact = 0,
                matchelem,
                new_nelems = 0;
    FmgrInfo    crosstypeproc;
    FmgrInfo   *orderprocp = orderproc;
 
    Assert(array->num_elems > 0);
    Assert(!(arraysk->sk_flags & SK_BT_SKIP));
 
    /*
     * _bt_binsrch_array_skey searches an array for the entry best matching a
     * datum of opclass input type for the index's attribute (on-disk type).
     * We can reuse the array's ORDER proc whenever the non-array scan key's
     * type is a match for the corresponding attribute's input opclass type.
     * Otherwise, we have to do another ORDER proc lookup so that our call to
     * _bt_binsrch_array_skey applies the correct comparator.
     *
     * Note: we have to support the convention that sk_subtype == InvalidOid
     * means the opclass input type; this is a hack to simplify life for
     * ScanKeyInit().
     */
    if (skey->sk_subtype != opcintype && skey->sk_subtype != InvalidOid)
    {
        RegProcedure cmp_proc;
        Oid         arraysk_elemtype;
 
        /*
         * Need an ORDER proc lookup to detect redundancy/contradictoriness
         * with this pair of scankeys.
         *
         * Scalar scan key's argument will be passed to _bt_compare_array_skey
         * as its tupdatum/lefthand argument (rhs arg is for array elements).
         */
        arraysk_elemtype = arraysk->sk_subtype;
        if (arraysk_elemtype == InvalidOid)
            arraysk_elemtype = rel->rd_opcintype[arraysk->sk_attno - 1];
        cmp_proc = get_opfamily_proc(rel->rd_opfamily[arraysk->sk_attno - 1],
                                     skey->sk_subtype, arraysk_elemtype,
                                     BTORDER_PROC);
        if (!RegProcedureIsValid(cmp_proc))
        {
            /* Can't make the comparison */
            *qual_ok = false;   /* suppress compiler warnings */
            return false;
        }
 
        /* We have all we need to determine redundancy/contradictoriness */
        orderprocp = &crosstypeproc;
        fmgr_info(cmp_proc, orderprocp);
    }
 
    matchelem = _bt_binsrch_array_skey(orderprocp, false,
                                       NoMovementScanDirection,
                                       skey->sk_argument, false, array,
                                       arraysk, &cmpresult);
 
    switch (skey->sk_strategy)
    {
        case BTLessStrategyNumber:
            cmpexact = 1;       /* exclude exact match, if any */
            /* FALL THRU */
        case BTLessEqualStrategyNumber:
            if (cmpresult >= cmpexact)
                matchelem++;
            /* Resize, keeping elements from the start of the array */
            new_nelems = matchelem;
            break;
        case BTEqualStrategyNumber:
            if (cmpresult != 0)
            {
                /* qual is unsatisfiable */
                new_nelems = 0;
            }
            else
            {
                /* Shift matching element to the start of the array, resize */
                array->elem_values[0] = array->elem_values[matchelem];
                new_nelems = 1;
            }
            break;
        case BTGreaterEqualStrategyNumber:
            cmpexact = 1;       /* include exact match, if any */
            /* FALL THRU */
        case BTGreaterStrategyNumber:
            if (cmpresult >= cmpexact)
                matchelem++;
            /* Shift matching elements to the start of the array, resize */
            new_nelems = array->num_elems - matchelem;
            memmove(array->elem_values, array->elem_values + matchelem,
                    sizeof(Datum) * new_nelems);
            break;
        default:
            elog(ERROR, "unrecognized StrategyNumber: %d",
                 (int) skey->sk_strategy);
            break;
    }
 
    Assert(new_nelems >= 0);
    Assert(new_nelems <= array->num_elems);
 
    array->num_elems = new_nelems;
    *qual_ok = new_nelems > 0;
 
    return true;
}
 
/*
 * Preprocessing of skip array scan key, used to determine redundancy against
 * a non-array scalar scan key (must be an inequality).
 *
 * _bt_compare_array_scankey_args helper function.
 *
 * Skip arrays work by procedurally generating their elements as needed, so we
 * just store the inequality as the skip array's low_compare or high_compare
 * (except when there's already a more restrictive low_compare/high_compare).
 * The array's final elements are the range of values that still satisfy the
 * array's final low_compare and high_compare.
 */
static bool
_bt_skiparray_shrink(IndexScanDesc scan, ScanKey skey, BTArrayKeyInfo *array,
                     bool *qual_ok)
{
    bool        test_result;
 
    Assert(array->num_elems == -1);
 
    /*
     * Array's index attribute will be constrained by a strict operator/key.
     * Array must not "contain a NULL element" (i.e. the scan must not apply
     * "IS NULL" qual when it reaches the end of the index that stores NULLs).
     */
    array->null_elem = false;
    *qual_ok = true;
 
    /*
     * Consider if we should treat caller's scalar scan key as the skip
     * array's high_compare or low_compare.
     *
     * In general the current array element must either be a copy of a value
     * taken from an index tuple, or a derivative value generated by opclass's
     * skip support function.  That way the scan can always safely assume that
     * it's okay to use the only-input-opclass-type proc from so->orderProcs[]
     * (they can be cross-type with SAOP arrays, but never with skip arrays).
     *
     * This approach is enabled by MINVAL/MAXVAL sentinel key markings, which
     * can be thought of as representing either the lowest or highest matching
     * array element (excluding the NULL element, where applicable, though as
     * just discussed it isn't applicable to this range skip array anyway).
     * Array keys marked MINVAL/MAXVAL never have a valid datum in their
     * sk_argument field.  The scan directly applies the array's low_compare
     * key when it encounters MINVAL in the array key proper (just as it
     * applies high_compare when it sees MAXVAL set in the array key proper).
     * The scan must never use the array's so->orderProcs[] proc against
     * low_compare's/high_compare's sk_argument, either (so->orderProcs[] is
     * only intended to be used with rhs datums from the array proper/index).
     */
    switch (skey->sk_strategy)
    {
        case BTLessStrategyNumber:
        case BTLessEqualStrategyNumber:
            if (array->high_compare)
            {
                /* replace existing high_compare with caller's key? */
                if (!_bt_compare_scankey_args(scan, array->high_compare, skey,
                                              array->high_compare, NULL, NULL,
                                              &test_result))
                    return false;   /* can't determine more restrictive key */
 
                if (!test_result)
                    return true;    /* no, just discard caller's key */
 
                /* yes, replace existing high_compare with caller's key */
            }
 
            /* caller's key becomes skip array's high_compare */
            array->high_compare = skey;
            break;
        case BTGreaterEqualStrategyNumber:
        case BTGreaterStrategyNumber:
            if (array->low_compare)
            {
                /* replace existing low_compare with caller's key? */
                if (!_bt_compare_scankey_args(scan, array->low_compare, skey,
                                              array->low_compare, NULL, NULL,
                                              &test_result))
                    return false;   /* can't determine more restrictive key */
 
                if (!test_result)
                    return true;    /* no, just discard caller's key */
 
                /* yes, replace existing low_compare with caller's key */
            }
 
            /* caller's key becomes skip array's low_compare */
            array->low_compare = skey;
            break;
        case BTEqualStrategyNumber:
        default:
            elog(ERROR, "unrecognized StrategyNumber: %d",
                 (int) skey->sk_strategy);
            break;
    }
 
    return true;
}
 
/*
 * Applies the opfamily's skip support routine to convert the skip array's >
 * low_compare key (if any) into a >= key, and to convert its < high_compare
 * key (if any) into a <= key.  Decrements the high_compare key's sk_argument,
 * and/or increments the low_compare key's sk_argument (also adjusts their
 * operator strategies, while changing the operator as appropriate).
 *
 * This optional optimization reduces the number of descents required within
 * _bt_first.  Whenever _bt_first is called with a skip array whose current
 * array element is the sentinel value MINVAL, using a transformed >= key
 * instead of using the original > key makes it safe to include lower-order
 * scan keys in the insertion scan key (there must be lower-order scan keys
 * after the skip array).  We will avoid an extra _bt_first to find the first
 * value in the index > sk_argument -- at least when the first real matching
 * value in the index happens to be an exact match for the sk_argument value
 * that we produced here by incrementing the original input key's sk_argument.
 * (Backwards scans derive the same benefit when they encounter the sentinel
 * value MAXVAL, by converting the high_compare key from < to <=.)
 *
 * Note: The transformation is only correct when it cannot allow the scan to
 * overlook matching tuples, but we don't have enough semantic information to
 * safely make sure that can't happen during scans with cross-type operators.
 * That's why we'll never apply the transformation in cross-type scenarios.
 * For example, if we attempted to convert "sales_ts > '2024-01-01'::date"
 * into "sales_ts >= '2024-01-02'::date" given a "sales_ts" attribute whose
 * input opclass is timestamp_ops, the scan would overlook almost all (or all)
 * tuples for sales that fell on '2024-01-01'.
 *
 * Note: We can safely modify array->low_compare/array->high_compare in place
 * because they just point to copies of our scan->keyData[] input scan keys
 * (namely the copies returned by _bt_preprocess_array_keys to be used as
 * input into the standard preprocessing steps in _bt_preprocess_keys).
 * Everything will be reset if there's a rescan.
 */
static void
_bt_skiparray_strat_adjust(IndexScanDesc scan, ScanKey arraysk,
                           BTArrayKeyInfo *array)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    MemoryContext oldContext;
 
    /*
     * Called last among all preprocessing steps, when the skip array's final
     * low_compare and high_compare have both been chosen
     */
    Assert(arraysk->sk_flags & SK_BT_SKIP);
    Assert(array->num_elems == -1 && !array->null_elem && array->sksup);
 
    oldContext = MemoryContextSwitchTo(so->arrayContext);
 
    if (array->high_compare &&
        array->high_compare->sk_strategy == BTLessStrategyNumber)
        _bt_skiparray_strat_decrement(scan, arraysk, array);
 
    if (array->low_compare &&
        array->low_compare->sk_strategy == BTGreaterStrategyNumber)
        _bt_skiparray_strat_increment(scan, arraysk, array);
 
    MemoryContextSwitchTo(oldContext);
}
 
/*
 * Convert skip array's > low_compare key into a >= key
 */
static void
_bt_skiparray_strat_decrement(IndexScanDesc scan, ScanKey arraysk,
                              BTArrayKeyInfo *array)
{
    Relation    rel = scan->indexRelation;
    Oid         opfamily = rel->rd_opfamily[arraysk->sk_attno - 1],
                opcintype = rel->rd_opcintype[arraysk->sk_attno - 1],
                leop;
    RegProcedure cmp_proc;
    ScanKey     high_compare = array->high_compare;
    Datum       orig_sk_argument = high_compare->sk_argument,
                new_sk_argument;
    bool        uflow;
    int16       lookupstrat;
 
    Assert(high_compare->sk_strategy == BTLessStrategyNumber);
 
    /*
     * Only perform the transformation when the operator type matches the
     * index attribute's input opclass type
     */
    if (high_compare->sk_subtype != opcintype &&
        high_compare->sk_subtype != InvalidOid)
        return;
 
    /* Decrement, handling underflow by marking the qual unsatisfiable */
    new_sk_argument = array->sksup->decrement(rel, orig_sk_argument, &uflow);
    if (uflow)
    {
        BTScanOpaque so = (BTScanOpaque) scan->opaque;
 
        so->qual_ok = false;
        return;
    }
 
    /*
     * Look up <= operator (might fail), accounting for the fact that a
     * high_compare on a DESC column already had its strategy commuted
     */
    lookupstrat = BTLessEqualStrategyNumber;
    if (high_compare->sk_flags & SK_BT_DESC)
        lookupstrat = BTGreaterEqualStrategyNumber; /* commute this too */
    leop = get_opfamily_member(opfamily, opcintype, opcintype, lookupstrat);
    if (!OidIsValid(leop))
        return;
    cmp_proc = get_opcode(leop);
    if (RegProcedureIsValid(cmp_proc))
    {
        /* Transform < high_compare key into <= key */
        fmgr_info(cmp_proc, &high_compare->sk_func);
        high_compare->sk_argument = new_sk_argument;
        high_compare->sk_strategy = BTLessEqualStrategyNumber;
    }
}
 
/*
 * Convert skip array's < low_compare key into a <= key
 */
static void
_bt_skiparray_strat_increment(IndexScanDesc scan, ScanKey arraysk,
                              BTArrayKeyInfo *array)
{
    Relation    rel = scan->indexRelation;
    Oid         opfamily = rel->rd_opfamily[arraysk->sk_attno - 1],
                opcintype = rel->rd_opcintype[arraysk->sk_attno - 1],
                geop;
    RegProcedure cmp_proc;
    ScanKey     low_compare = array->low_compare;
    Datum       orig_sk_argument = low_compare->sk_argument,
                new_sk_argument;
    bool        oflow;
    int16       lookupstrat;
 
    Assert(low_compare->sk_strategy == BTGreaterStrategyNumber);
 
    /*
     * Only perform the transformation when the operator type matches the
     * index attribute's input opclass type
     */
    if (low_compare->sk_subtype != opcintype &&
        low_compare->sk_subtype != InvalidOid)
        return;
 
    /* Increment, handling overflow by marking the qual unsatisfiable */
    new_sk_argument = array->sksup->increment(rel, orig_sk_argument, &oflow);
    if (oflow)
    {
        BTScanOpaque so = (BTScanOpaque) scan->opaque;
 
        so->qual_ok = false;
        return;
    }
 
    /*
     * Look up >= operator (might fail), accounting for the fact that a
     * low_compare on a DESC column already had its strategy commuted
     */
    lookupstrat = BTGreaterEqualStrategyNumber;
    if (low_compare->sk_flags & SK_BT_DESC)
        lookupstrat = BTLessEqualStrategyNumber;    /* commute this too */
    geop = get_opfamily_member(opfamily, opcintype, opcintype, lookupstrat);
    if (!OidIsValid(geop))
        return;
    cmp_proc = get_opcode(geop);
    if (RegProcedureIsValid(cmp_proc))
    {
        /* Transform > low_compare key into >= key */
        fmgr_info(cmp_proc, &low_compare->sk_func);
        low_compare->sk_argument = new_sk_argument;
        low_compare->sk_strategy = BTGreaterEqualStrategyNumber;
    }
}
 
/*
 *  _bt_unmark_keys() -- make superfluous required keys nonrequired after all
 *
 * When _bt_preprocess_keys fails to eliminate one or more redundant keys, it
 * calls here to make sure that no index attribute has more than one > or >=
 * key marked required, and no more than one required < or <= key.  Attributes
 * with = keys will always get one = key as their required key.  All other
 * keys that were initially marked required get "unmarked" here.  That way,
 * _bt_first and _bt_checkkeys will reliably agree on which keys to use to
 * start and/or to end the scan.
 *
 * We also relocate keys that become/started out nonrequired to the end of
 * so->keyData[].  That way, _bt_first and _bt_checkkeys cannot fail to reach
 * a required key due to some earlier nonrequired key getting in the way.
 *
 * Only call here when _bt_compare_scankey_args returned false at least once
 * (otherwise, calling here will just waste cycles).
 */
static void
_bt_unmark_keys(IndexScanDesc scan, int *keyDataMap)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    AttrNumber  attno;
    bool       *unmarkikey;
    int         nunmark,
                nunmarked,
                nkept,
                firsti;
    ScanKey     keepKeys,
                unmarkKeys;
    FmgrInfo   *keepOrderProcs = NULL,
               *unmarkOrderProcs = NULL;
    bool        haveReqEquals,
                haveReqForward,
                haveReqBackward;
 
    /*
     * Do an initial pass over so->keyData[] that determines which keys to
     * keep as required.  We expect so->keyData[] to still be in attribute
     * order when we're called (though we don't expect any particular order
     * among each attribute's keys).
     *
     * When both equality and inequality keys remain on a single attribute, we
     * *must* make sure that exactly one of the equalities remains required.
     * Any requiredness markings that we might leave on later keys/attributes
     * are predicated on there being required = keys on all prior columns.
     */
    unmarkikey = palloc0(so->numberOfKeys * sizeof(bool));
    nunmark = 0;
 
    /* Set things up for first key's attribute */
    attno = so->keyData[0].sk_attno;
    firsti = 0;
    haveReqEquals = false;
    haveReqForward = false;
    haveReqBackward = false;
    for (int i = 0; i < so->numberOfKeys; i++)
    {
        ScanKey     origkey = &so->keyData[i];
 
        if (origkey->sk_attno != attno)
        {
            /* Reset for next attribute */
            attno = origkey->sk_attno;
            firsti = i;
 
            haveReqEquals = false;
            haveReqForward = false;
            haveReqBackward = false;
        }
 
        /* Equalities get priority over inequalities */
        if (haveReqEquals)
        {
            /*
             * We already found the first "=" key for this attribute.  We've
             * already decided that all its other keys will be unmarked.
             */
            Assert(!(origkey->sk_flags & SK_SEARCHNULL));
            unmarkikey[i] = true;
            nunmark++;
            continue;
        }
        else if ((origkey->sk_flags & SK_BT_REQFWD) &&
                 (origkey->sk_flags & SK_BT_REQBKWD))
        {
            /*
             * Found the first "=" key for attno.  All other attno keys will
             * be unmarked.
             */
            Assert(origkey->sk_strategy == BTEqualStrategyNumber);
 
            haveReqEquals = true;
            for (int j = firsti; j < i; j++)
            {
                /* Unmark any prior inequality keys on attno after all */
                if (!unmarkikey[j])
                {
                    unmarkikey[j] = true;
                    nunmark++;
                }
            }
            continue;
        }
 
        /* Deal with inequalities next */
        if ((origkey->sk_flags & SK_BT_REQFWD) && !haveReqForward)
        {
            haveReqForward = true;
            continue;
        }
        else if ((origkey->sk_flags & SK_BT_REQBKWD) && !haveReqBackward)
        {
            haveReqBackward = true;
            continue;
        }
 
        /*
         * We have either a redundant inequality key that will be unmarked, or
         * we have a key that wasn't marked required in the first place
         */
        unmarkikey[i] = true;
        nunmark++;
    }
 
    /* Should only be called when _bt_compare_scankey_args reported failure */
    Assert(nunmark > 0);
 
    /*
     * Next, allocate temp arrays: one for required keys that'll remain
     * required, the other for all remaining keys
     */
    unmarkKeys = palloc(nunmark * sizeof(ScanKeyData));
    keepKeys = palloc((so->numberOfKeys - nunmark) * sizeof(ScanKeyData));
    nunmarked = 0;
    nkept = 0;
    if (so->numArrayKeys)
    {
        unmarkOrderProcs = palloc(nunmark * sizeof(FmgrInfo));
        keepOrderProcs = palloc((so->numberOfKeys - nunmark) * sizeof(FmgrInfo));
    }
 
    /*
     * Next, copy the contents of so->keyData[] into the appropriate temp
     * array.
     *
     * Scans with = array keys need us to maintain invariants around the order
     * of so->orderProcs[] and so->arrayKeys[] relative to so->keyData[].  See
     * _bt_preprocess_array_keys_final for a full explanation.
     */
    for (int i = 0; i < so->numberOfKeys; i++)
    {
        ScanKey     origkey = &so->keyData[i];
        ScanKey     unmark;
 
        if (!unmarkikey[i])
        {
            /*
             * Key gets to keep its original requiredness markings.
             *
             * Key will stay in its original position, unless we're going to
             * unmark an earlier key (in which case this key gets moved back).
             */
            memcpy(keepKeys + nkept, origkey, sizeof(ScanKeyData));
 
            if (so->numArrayKeys)
            {
                keyDataMap[i] = nkept;
                memcpy(keepOrderProcs + nkept, &so->orderProcs[i],
                       sizeof(FmgrInfo));
            }
 
            nkept++;
            continue;
        }
 
        /*
         * Key will be unmarked as needed, and moved to the end of the array,
         * next to other keys that will become (or always were) nonrequired
         */
        unmark = unmarkKeys + nunmarked;
        memcpy(unmark, origkey, sizeof(ScanKeyData));
 
        if (so->numArrayKeys)
        {
            keyDataMap[i] = (so->numberOfKeys - nunmark) + nunmarked;
            memcpy(&unmarkOrderProcs[nunmarked], &so->orderProcs[i],
                   sizeof(FmgrInfo));
        }
 
        /*
         * Preprocessing only generates skip arrays when it knows that they'll
         * be the only required = key on the attr.  We'll never unmark them.
         */
        Assert(!(unmark->sk_flags & SK_BT_SKIP));
 
        /*
         * Also shouldn't have to unmark an IS NULL or an IS NOT NULL key.
         * They aren't cross-type, so an incomplete opfamily can't matter.
         */
        Assert(!(unmark->sk_flags & SK_ISNULL) ||
               !(unmark->sk_flags & (SK_BT_REQFWD | SK_BT_REQBKWD)));
 
        /* Clear requiredness flags on redundant key (and on any subkeys) */
        unmark->sk_flags &= ~(SK_BT_REQFWD | SK_BT_REQBKWD);
        if (unmark->sk_flags & SK_ROW_HEADER)
        {
            ScanKey     subkey = (ScanKey) DatumGetPointer(unmark->sk_argument);
 
            Assert(subkey->sk_strategy == unmark->sk_strategy);
            for (;;)
            {
                Assert(subkey->sk_flags & SK_ROW_MEMBER);
                subkey->sk_flags &= ~(SK_BT_REQFWD | SK_BT_REQBKWD);
                if (subkey->sk_flags & SK_ROW_END)
                    break;
                subkey++;
            }
        }
 
        nunmarked++;
    }
 
    /* Copy both temp arrays back into so->keyData[] to reorder */
    Assert(nkept == so->numberOfKeys - nunmark);
    Assert(nunmarked == nunmark);
    memcpy(so->keyData, keepKeys, sizeof(ScanKeyData) * nkept);
    memcpy(so->keyData + nkept, unmarkKeys, sizeof(ScanKeyData) * nunmarked);
 
    /* Done with temp arrays */
    pfree(unmarkikey);
    pfree(keepKeys);
    pfree(unmarkKeys);
 
    /*
     * Now copy so->orderProcs[] temp entries needed by scans with = array
     * keys back (just like with the so->keyData[] temp arrays)
     */
    if (so->numArrayKeys)
    {
        memcpy(so->orderProcs, keepOrderProcs, sizeof(FmgrInfo) * nkept);
        memcpy(so->orderProcs + nkept, unmarkOrderProcs,
               sizeof(FmgrInfo) * nunmarked);
 
        /* Also fix-up array->scan_key references */
        for (int arridx = 0; arridx < so->numArrayKeys; arridx++)
        {
            BTArrayKeyInfo *array = &so->arrayKeys[arridx];
 
            array->scan_key = keyDataMap[array->scan_key];
        }
 
        /*
         * Sort so->arrayKeys[] based on its new BTArrayKeyInfo.scan_key
         * offsets, so that its order matches so->keyData[] order as expected
         */
        qsort(so->arrayKeys, so->numArrayKeys, sizeof(BTArrayKeyInfo),
              _bt_reorder_array_cmp);
 
        /* Done with temp arrays */
        pfree(unmarkOrderProcs);
        pfree(keepOrderProcs);
    }
}
 
/*
 * qsort comparator for reordering so->arrayKeys[] BTArrayKeyInfo entries
 */
static int
_bt_reorder_array_cmp(const void *a, const void *b)
{
    BTArrayKeyInfo *arraya = (BTArrayKeyInfo *) a;
    BTArrayKeyInfo *arrayb = (BTArrayKeyInfo *) b;
 
    return pg_cmp_s32(arraya->scan_key, arrayb->scan_key);
}
 
/*
 *  _bt_preprocess_array_keys() -- Preprocess SK_SEARCHARRAY scan keys
 *
 * If there are any SK_SEARCHARRAY scan keys, deconstruct the array(s) and
 * set up BTArrayKeyInfo info for each one that is an equality-type key.
 * Returns modified scan keys as input for further, standard preprocessing.
 *
 * Currently we perform two kinds of preprocessing to deal with redundancies.
 * For inequality array keys, it's sufficient to find the extreme element
 * value and replace the whole array with that scalar value.  This eliminates
 * all but one array element as redundant.  Similarly, we are capable of
 * "merging together" multiple equality array keys (from two or more input
 * scan keys) into a single output scan key containing only the intersecting
 * array elements.  This can eliminate many redundant array elements, as well
 * as eliminating whole array scan keys as redundant.  It can also allow us to
 * detect contradictory quals.
 *
 * Caller must pass *new_numberOfKeys to give us a way to change the number of
 * scan keys that caller treats as input to standard preprocessing steps.  The
 * returned array is smaller than scan->keyData[] when we could eliminate a
 * redundant array scan key (redundant with another array scan key).  It is
 * convenient for _bt_preprocess_keys caller to have to deal with no more than
 * one equality strategy array scan key per index attribute.  We'll always be
 * able to set things up that way when complete opfamilies are used.
 *
 * We're also responsible for generating skip arrays (and their associated
 * scan keys) here.  This enables skip scan.  We do this for index attributes
 * that initially lacked an equality condition within scan->keyData[], iff
 * doing so allows a later scan key (that was passed to us in scan->keyData[])
 * to be marked required by our _bt_preprocess_keys caller.
 *
 * We set the scan key references from the scan's BTArrayKeyInfo info array to
 * offsets into the temp modified input array returned to caller.  Scans that
 * have array keys should call _bt_preprocess_array_keys_final when standard
 * preprocessing steps are complete.  This will convert the scan key offset
 * references into references to the scan's so->keyData[] output scan keys.
 *
 * Note: the reason we need to return a temp scan key array, rather than just
 * modifying scan->keyData[], is that callers are permitted to call btrescan
 * without supplying a new set of scankey data.  Certain other preprocessing
 * routines (e.g., _bt_fix_scankey_strategy) _can_ modify scan->keyData[], but
 * we can't make that work here because our modifications are non-idempotent.
 */
static ScanKey
_bt_preprocess_array_keys(IndexScanDesc scan, int *new_numberOfKeys)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    Relation    rel = scan->indexRelation;
    int16      *indoption = rel->rd_indoption;
    Oid         skip_eq_ops[INDEX_MAX_KEYS];
    int         numArrayKeys,
                numSkipArrayKeys,
                numArrayKeyData;
    AttrNumber  attno_skip = 1;
    int         origarrayatt = InvalidAttrNumber,
                origarraykey = -1;
    Oid         origelemtype = InvalidOid;
    MemoryContext oldContext;
    ScanKey     arrayKeyData;   /* modified copy of scan->keyData */
 
    /*
     * Check the number of input array keys within scan->keyData[] input keys
     * (also checks if we should add extra skip arrays based on input keys)
     */
    numArrayKeys = _bt_num_array_keys(scan, skip_eq_ops, &numSkipArrayKeys);
    so->skipScan = (numSkipArrayKeys > 0);
 
    /* Quit if nothing to do. */
    if (numArrayKeys == 0)
        return NULL;
 
    /*
     * Estimated final size of arrayKeyData[] array we'll return to our caller
     * is the size of the original scan->keyData[] input array, plus space for
     * any additional skip array scan keys we'll need to generate below
     */
    numArrayKeyData = scan->numberOfKeys + numSkipArrayKeys;
 
    /*
     * Make a scan-lifespan context to hold array-associated data, or reset it
     * if we already have one from a previous rescan cycle.
     */
    if (so->arrayContext == NULL)
        so->arrayContext = AllocSetContextCreate(CurrentMemoryContext,
                                                 "BTree array context",
                                                 ALLOCSET_SMALL_SIZES);
    else
        MemoryContextReset(so->arrayContext);
 
    oldContext = MemoryContextSwitchTo(so->arrayContext);
 
    /* Create output scan keys in the workspace context */
    arrayKeyData = (ScanKey) palloc(numArrayKeyData * sizeof(ScanKeyData));
 
    /* Allocate space for per-array data in the workspace context */
    so->arrayKeys = (BTArrayKeyInfo *) palloc(numArrayKeys * sizeof(BTArrayKeyInfo));
 
    /* Allocate space for ORDER procs used to help _bt_checkkeys */
    so->orderProcs = (FmgrInfo *) palloc(numArrayKeyData * sizeof(FmgrInfo));
 
    numArrayKeys = 0;
    numArrayKeyData = 0;
    for (int input_ikey = 0; input_ikey < scan->numberOfKeys; input_ikey++)
    {
        ScanKey     inkey = scan->keyData + input_ikey,
                    cur;
        FmgrInfo    sortproc;
        FmgrInfo   *sortprocp = &sortproc;
        Oid         elemtype;
        bool        reverse;
        ArrayType  *arrayval;
        int16       elmlen;
        bool        elmbyval;
        char        elmalign;
        int         num_elems;
        Datum      *elem_values;
        bool       *elem_nulls;
        int         num_nonnulls;
 
        /* set up next output scan key */
        cur = &arrayKeyData[numArrayKeyData];
 
        /* Backfill skip arrays for attrs < or <= input key's attr? */
        while (numSkipArrayKeys && attno_skip <= inkey->sk_attno)
        {
            Oid         opfamily = rel->rd_opfamily[attno_skip - 1];
            Oid         opcintype = rel->rd_opcintype[attno_skip - 1];
            Oid         collation = rel->rd_indcollation[attno_skip - 1];
            Oid         eq_op = skip_eq_ops[attno_skip - 1];
            CompactAttribute *attr;
            RegProcedure cmp_proc;
 
            if (!OidIsValid(eq_op))
            {
                /*
                 * Attribute already has an = input key, so don't output a
                 * skip array for attno_skip.  Just copy attribute's = input
                 * key into arrayKeyData[] once outside this inner loop.
                 *
                 * Note: When we get here there must be a later attribute that
                 * lacks an equality input key, and still needs a skip array
                 * (if there wasn't then numSkipArrayKeys would be 0 by now).
                 */
                Assert(attno_skip == inkey->sk_attno);
                /* inkey can't be last input key to be marked required: */
                Assert(input_ikey < scan->numberOfKeys - 1);
#if 0
                /* Could be a redundant input scan key, so can't do this: */
                Assert(inkey->sk_strategy == BTEqualStrategyNumber ||
                       (inkey->sk_flags & SK_SEARCHNULL));
#endif
 
                attno_skip++;
                break;
            }
 
            cmp_proc = get_opcode(eq_op);
            if (!RegProcedureIsValid(cmp_proc))
                elog(ERROR, "missing oprcode for skipping equals operator %u", eq_op);
 
            ScanKeyEntryInitialize(cur,
                                   SK_SEARCHARRAY | SK_BT_SKIP, /* flags */
                                   attno_skip,  /* skipped att number */
                                   BTEqualStrategyNumber,   /* equality strategy */
                                   InvalidOid,  /* opclass input subtype */
                                   collation,   /* index column's collation */
                                   cmp_proc,    /* equality operator's proc */
                                   (Datum) 0);  /* constant */
 
            /* Initialize generic BTArrayKeyInfo fields */
            so->arrayKeys[numArrayKeys].scan_key = numArrayKeyData;
            so->arrayKeys[numArrayKeys].num_elems = -1;
 
            /* Initialize skip array specific BTArrayKeyInfo fields */
            attr = TupleDescCompactAttr(RelationGetDescr(rel), attno_skip - 1);
            reverse = (indoption[attno_skip - 1] & INDOPTION_DESC) != 0;
            so->arrayKeys[numArrayKeys].attlen = attr->attlen;
            so->arrayKeys[numArrayKeys].attbyval = attr->attbyval;
            so->arrayKeys[numArrayKeys].null_elem = true;   /* for now */
            so->arrayKeys[numArrayKeys].sksup =
                PrepareSkipSupportFromOpclass(opfamily, opcintype, reverse);
            so->arrayKeys[numArrayKeys].low_compare = NULL; /* for now */
            so->arrayKeys[numArrayKeys].high_compare = NULL;    /* for now */
 
            /*
             * We'll need a 3-way ORDER proc.  Set that up now.
             */
            _bt_setup_array_cmp(scan, cur, opcintype,
                                &so->orderProcs[numArrayKeyData], NULL);
 
            numArrayKeys++;
            numArrayKeyData++;  /* keep this scan key/array */
 
            /* set up next output scan key */
            cur = &arrayKeyData[numArrayKeyData];
 
            /* remember having output this skip array and scan key */
            numSkipArrayKeys--;
            attno_skip++;
        }
 
        /*
         * Provisionally copy scan key into arrayKeyData[] array we'll return
         * to _bt_preprocess_keys caller
         */
        *cur = *inkey;
 
        if (!(cur->sk_flags & SK_SEARCHARRAY))
        {
            numArrayKeyData++;  /* keep this non-array scan key */
            continue;
        }
 
        /*
         * Process SAOP array scan key
         */
        Assert(!(cur->sk_flags & (SK_ROW_HEADER | SK_SEARCHNULL | SK_SEARCHNOTNULL)));
 
        /* If array is null as a whole, the scan qual is unsatisfiable */
        if (cur->sk_flags & SK_ISNULL)
        {
            so->qual_ok = false;
            break;
        }
 
        /*
         * Deconstruct the array into elements
         */
        arrayval = DatumGetArrayTypeP(cur->sk_argument);
        /* We could cache this data, but not clear it's worth it */
        get_typlenbyvalalign(ARR_ELEMTYPE(arrayval),
                             &elmlen, &elmbyval, &elmalign);
        deconstruct_array(arrayval,
                          ARR_ELEMTYPE(arrayval),
                          elmlen, elmbyval, elmalign,
                          &elem_values, &elem_nulls, &num_elems);
 
        /*
         * Compress out any null elements.  We can ignore them since we assume
         * all btree operators are strict.
         */
        num_nonnulls = 0;
        for (int j = 0; j < num_elems; j++)
        {
            if (!elem_nulls[j])
                elem_values[num_nonnulls++] = elem_values[j];
        }
 
        /* We could pfree(elem_nulls) now, but not worth the cycles */
 
        /* If there's no non-nulls, the scan qual is unsatisfiable */
        if (num_nonnulls == 0)
        {
            so->qual_ok = false;
            break;
        }
 
        /*
         * Determine the nominal datatype of the array elements.  We have to
         * support the convention that sk_subtype == InvalidOid means the
         * opclass input type; this is a hack to simplify life for
         * ScanKeyInit().
         */
        elemtype = cur->sk_subtype;
        if (elemtype == InvalidOid)
            elemtype = rel->rd_opcintype[cur->sk_attno - 1];
 
        /*
         * If the comparison operator is not equality, then the array qual
         * degenerates to a simple comparison against the smallest or largest
         * non-null array element, as appropriate.
         */
        switch (cur->sk_strategy)
        {
            case BTLessStrategyNumber:
            case BTLessEqualStrategyNumber:
                cur->sk_argument =
                    _bt_find_extreme_element(scan, cur, elemtype,
                                             BTGreaterStrategyNumber,
                                             elem_values, num_nonnulls);
                numArrayKeyData++;  /* keep this transformed scan key */
                continue;
            case BTEqualStrategyNumber:
                /* proceed with rest of loop */
                break;
            case BTGreaterEqualStrategyNumber:
            case BTGreaterStrategyNumber:
                cur->sk_argument =
                    _bt_find_extreme_element(scan, cur, elemtype,
                                             BTLessStrategyNumber,
                                             elem_values, num_nonnulls);
                numArrayKeyData++;  /* keep this transformed scan key */
                continue;
            default:
                elog(ERROR, "unrecognized StrategyNumber: %d",
                     (int) cur->sk_strategy);
                break;
        }
 
        /*
         * We'll need a 3-way ORDER proc to perform binary searches for the
         * next matching array element.  Set that up now.
         *
         * Array scan keys with cross-type equality operators will require a
         * separate same-type ORDER proc for sorting their array.  Otherwise,
         * sortproc just points to the same proc used during binary searches.
         */
        _bt_setup_array_cmp(scan, cur, elemtype,
                            &so->orderProcs[numArrayKeyData], &sortprocp);
 
        /*
         * Sort the non-null elements and eliminate any duplicates.  We must
         * sort in the same ordering used by the index column, so that the
         * arrays can be advanced in lockstep with the scan's progress through
         * the index's key space.
         */
        reverse = (indoption[cur->sk_attno - 1] & INDOPTION_DESC) != 0;
        num_elems = _bt_sort_array_elements(cur, sortprocp, reverse,
                                            elem_values, num_nonnulls);
 
        if (origarrayatt == cur->sk_attno)
        {
            BTArrayKeyInfo *orig = &so->arrayKeys[origarraykey];
 
            /*
             * This array scan key is redundant with a previous equality
             * operator array scan key.  Merge the two arrays together to
             * eliminate contradictory non-intersecting elements (or try to).
             *
             * We merge this next array back into attribute's original array.
             */
            Assert(arrayKeyData[orig->scan_key].sk_attno == cur->sk_attno);
            Assert(arrayKeyData[orig->scan_key].sk_collation ==
                   cur->sk_collation);
            if (_bt_merge_arrays(scan, cur, sortprocp, reverse,
                                 origelemtype, elemtype,
                                 orig->elem_values, &orig->num_elems,
                                 elem_values, num_elems))
            {
                /* Successfully eliminated this array */
                pfree(elem_values);
 
                /*
                 * If no intersecting elements remain in the original array,
                 * the scan qual is unsatisfiable
                 */
                if (orig->num_elems == 0)
                {
                    so->qual_ok = false;
                    break;
                }
 
                /* Throw away this scan key/array */
                continue;
            }
 
            /*
             * Unable to merge this array with previous array due to a lack of
             * suitable cross-type opfamily support.  Will need to keep both
             * scan keys/arrays.
             */
        }
        else
        {
            /*
             * This array is the first for current index attribute.
             *
             * If it turns out to not be the last array (that is, if the next
             * array is redundantly applied to this same index attribute),
             * we'll then treat this array as the attribute's "original" array
             * when merging.
             */
            origarrayatt = cur->sk_attno;
            origarraykey = numArrayKeys;
            origelemtype = elemtype;
        }
 
        /* Initialize generic BTArrayKeyInfo fields */
        so->arrayKeys[numArrayKeys].scan_key = numArrayKeyData;
        so->arrayKeys[numArrayKeys].num_elems = num_elems;
 
        /* Initialize SAOP array specific BTArrayKeyInfo fields */
        so->arrayKeys[numArrayKeys].elem_values = elem_values;
        so->arrayKeys[numArrayKeys].cur_elem = -1;  /* i.e. invalid */
 
        numArrayKeys++;
        numArrayKeyData++;      /* keep this scan key/array */
    }
 
    Assert(numSkipArrayKeys == 0 || !so->qual_ok);
 
    /* Set final number of equality-type array keys */
    so->numArrayKeys = numArrayKeys;
    /* Set number of scan keys in arrayKeyData[] */
    *new_numberOfKeys = numArrayKeyData;
 
    MemoryContextSwitchTo(oldContext);
 
    return arrayKeyData;
}
 
/*
 *  _bt_preprocess_array_keys_final() -- fix up array scan key references
 *
 * When _bt_preprocess_array_keys performed initial array preprocessing, it
 * set each array's array->scan_key to its scankey's arrayKeyData[] offset.
 * This function handles translation of the scan key references from the
 * BTArrayKeyInfo info array, from input scan key references (to the keys in
 * arrayKeyData[]), into output references (to the keys in so->keyData[]).
 * Caller's keyDataMap[] array tells us how to perform this remapping.
 *
 * Also finalizes so->orderProcs[] for the scan.  Arrays already have an ORDER
 * proc, which might need to be repositioned to its so->keyData[]-wise offset
 * (very much like the remapping that we apply to array->scan_key references).
 * Non-array equality strategy scan keys (that survived preprocessing) don't
 * yet have an so->orderProcs[] entry, so we set one for them here.
 *
 * Also converts single-element array scan keys into equivalent non-array
 * equality scan keys, which decrements so->numArrayKeys.  It's possible that
 * this will leave this new btrescan without any arrays at all.  This isn't
 * necessary for correctness; it's just an optimization.  Non-array equality
 * scan keys are slightly faster than equivalent array scan keys at runtime.
 */
static void
_bt_preprocess_array_keys_final(IndexScanDesc scan, int *keyDataMap)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    Relation    rel = scan->indexRelation;
    int         arrayidx = 0;
    int         last_equal_output_ikey PG_USED_FOR_ASSERTS_ONLY = -1;
 
    Assert(so->qual_ok);
 
    /*
     * Nothing for us to do when _bt_preprocess_array_keys only had to deal
     * with array inequalities
     */
    if (so->numArrayKeys == 0)
        return;
 
    for (int output_ikey = 0; output_ikey < so->numberOfKeys; output_ikey++)
    {
        ScanKey     outkey = so->keyData + output_ikey;
        int         input_ikey;
        bool        found PG_USED_FOR_ASSERTS_ONLY = false;
 
        Assert(outkey->sk_strategy != InvalidStrategy);
 
        if (outkey->sk_strategy != BTEqualStrategyNumber)
            continue;
 
        input_ikey = keyDataMap[output_ikey];
 
        Assert(last_equal_output_ikey < output_ikey);
        Assert(last_equal_output_ikey < input_ikey);
        last_equal_output_ikey = output_ikey;
 
        /*
         * We're lazy about looking up ORDER procs for non-array keys, since
         * not all input keys become output keys.  Take care of it now.
         */
        if (!(outkey->sk_flags & SK_SEARCHARRAY))
        {
            Oid         elemtype;
 
            /* No need for an ORDER proc given an IS NULL scan key */
            if (outkey->sk_flags & SK_SEARCHNULL)
                continue;
 
            /*
             * A non-required scan key doesn't need an ORDER proc, either
             * (unless it's associated with an array, which this one isn't)
             */
            if (!(outkey->sk_flags & SK_BT_REQFWD))
                continue;
 
            elemtype = outkey->sk_subtype;
            if (elemtype == InvalidOid)
                elemtype = rel->rd_opcintype[outkey->sk_attno - 1];
 
            _bt_setup_array_cmp(scan, outkey, elemtype,
                                &so->orderProcs[output_ikey], NULL);
            continue;
        }
 
        /*
         * Reorder existing array scan key so->orderProcs[] entries.
         *
         * Doing this in-place is safe because preprocessing is required to
         * output all equality strategy scan keys in original input order
         * (among each group of entries against the same index attribute).
         * This is also the order that the arrays themselves appear in.
         */
        so->orderProcs[output_ikey] = so->orderProcs[input_ikey];
 
        /* Fix-up array->scan_key references for arrays */
        for (; arrayidx < so->numArrayKeys; arrayidx++)
        {
            BTArrayKeyInfo *array = &so->arrayKeys[arrayidx];
 
            /*
             * All skip arrays must be marked required, and final column can
             * never have a skip array
             */
            Assert(array->num_elems > 0 || array->num_elems == -1);
            Assert(array->num_elems != -1 || outkey->sk_flags & SK_BT_REQFWD);
            Assert(array->num_elems != -1 ||
                   outkey->sk_attno < IndexRelationGetNumberOfKeyAttributes(rel));
 
            if (array->scan_key == input_ikey)
            {
                /* found it */
                array->scan_key = output_ikey;
                found = true;
 
                /*
                 * Transform array scan keys that have exactly 1 element
                 * remaining (following all prior preprocessing) into
                 * equivalent non-array scan keys.
                 */
                if (array->num_elems == 1)
                {
                    outkey->sk_flags &= ~SK_SEARCHARRAY;
                    outkey->sk_argument = array->elem_values[0];
                    so->numArrayKeys--;
 
                    /* If we're out of array keys, we can quit right away */
                    if (so->numArrayKeys == 0)
                        return;
 
                    /* Shift other arrays forward */
                    memmove(array, array + 1,
                            sizeof(BTArrayKeyInfo) *
                            (so->numArrayKeys - arrayidx));
 
                    /*
                     * Don't increment arrayidx (there was an entry that was
                     * just shifted forward to the offset at arrayidx, which
                     * will still need to be matched)
                     */
                }
                else
                {
                    /*
                     * Any skip array low_compare and high_compare scan keys
                     * are now final.  Transform the array's > low_compare key
                     * into a >= key (and < high_compare keys into a <= key).
                     */
                    if (array->num_elems == -1 && array->sksup &&
                        !array->null_elem)
                        _bt_skiparray_strat_adjust(scan, outkey, array);
 
                    /* Match found, so done with this array */
                    arrayidx++;
                }
 
                break;
            }
        }
 
        Assert(found);
    }
 
    /*
     * Parallel index scans require space in shared memory to store the
     * current array elements (for arrays kept by preprocessing) to schedule
     * the next primitive index scan.  The underlying structure is protected
     * using an LWLock, so defensively limit its size.  In practice this can
     * only affect parallel scans that use an incomplete opfamily.
     */
    if (scan->parallel_scan && so->numArrayKeys > INDEX_MAX_KEYS)
        ereport(ERROR,
                (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
                 errmsg_internal("number of array scan keys left by preprocessing (%d) exceeds the maximum allowed by parallel btree index scans (%d)",
                                 so->numArrayKeys, INDEX_MAX_KEYS)));
}
 
/*
 *  _bt_num_array_keys() -- determine # of BTArrayKeyInfo entries
 *
 * _bt_preprocess_array_keys helper function.  Returns the estimated size of
 * the scan's BTArrayKeyInfo array, which is guaranteed to be large enough to
 * fit every so->arrayKeys[] entry.
 *
 * Also sets *numSkipArrayKeys_out to the number of skip arrays caller must
 * add to the scan keys it'll output.  Caller must add this many skip arrays:
 * one array for each of the most significant attributes that lack a = input
 * key (IS NULL keys count as = input keys here).  The specific attributes
 * that need skip arrays are indicated by initializing skip_eq_ops_out[] arg
 * 0-based attribute offset to a valid = op strategy Oid.  We'll only ever set
 * skip_eq_ops_out[] entries to InvalidOid for attributes that already have an
 * equality key in scan->keyData[] input keys -- and only when there's some
 * later "attribute gap" for us to "fill-in" with a skip array.
 *
 * We're optimistic about skipping working out: we always add exactly the skip
 * arrays needed to maximize the number of input scan keys that can ultimately
 * be marked as required to continue the scan (but no more).  Given a
 * multi-column index on (a, b, c, d), we add skip arrays as follows:
 *
 * Input keys                       Output keys (after all preprocessing)
 * ----------                       -------------------------------------
 * a = 1                            a = 1 (no skip arrays)
 * b = 42                           skip a AND b = 42
 * a = 1 AND b = 42                 a = 1 AND b = 42 (no skip arrays)
 * a >= 1 AND b = 42                range skip a AND b = 42
 * a = 1 AND b > 42                 a = 1 AND b > 42 (no skip arrays)
 * a >= 1 AND a <= 3 AND b = 42     range skip a AND b = 42
 * a = 1 AND c <= 27                a = 1 AND skip b AND c <= 27
 * a = 1 AND d >= 1                 a = 1 AND skip b AND skip c AND d >= 1
 * a = 1 AND b >= 42 AND d > 1      a = 1 AND range skip b AND skip c AND d > 1
 */
static int
_bt_num_array_keys(IndexScanDesc scan, Oid *skip_eq_ops_out,
                   int *numSkipArrayKeys_out)
{
    Relation    rel = scan->indexRelation;
    AttrNumber  attno_skip = 1,
                attno_inkey = 1;
    bool        attno_has_equal = false,
                attno_has_rowcompare = false;
    int         numSAOPArrayKeys,
                numSkipArrayKeys,
                prev_numSkipArrayKeys;
 
    Assert(scan->numberOfKeys);
 
    /* Initial pass over input scan keys counts the number of SAOP arrays */
    numSAOPArrayKeys = 0;
    *numSkipArrayKeys_out = prev_numSkipArrayKeys = numSkipArrayKeys = 0;
    for (int i = 0; i < scan->numberOfKeys; i++)
    {
        ScanKey     inkey = scan->keyData + i;
 
        if (inkey->sk_flags & SK_SEARCHARRAY)
            numSAOPArrayKeys++;
    }
 
#ifdef DEBUG_DISABLE_SKIP_SCAN
    /* don't attempt to add skip arrays */
    return numSAOPArrayKeys;
#endif
 
    for (int i = 0;; i++)
    {
        ScanKey     inkey = scan->keyData + i;
 
        /*
         * Backfill skip arrays for any wholly omitted attributes prior to
         * attno_inkey
         */
        while (attno_skip < attno_inkey)
        {
            Oid         opfamily = rel->rd_opfamily[attno_skip - 1];
            Oid         opcintype = rel->rd_opcintype[attno_skip - 1];
 
            /* Look up input opclass's equality operator (might fail) */
            skip_eq_ops_out[attno_skip - 1] =
                get_opfamily_member(opfamily, opcintype, opcintype,
                                    BTEqualStrategyNumber);
            if (!OidIsValid(skip_eq_ops_out[attno_skip - 1]))
            {
                /*
                 * Cannot generate a skip array for this or later attributes
                 * (input opclass lacks an equality strategy operator)
                 */
                *numSkipArrayKeys_out = prev_numSkipArrayKeys;
                return numSAOPArrayKeys + prev_numSkipArrayKeys;
            }
 
            /* plan on adding a backfill skip array for this attribute */
            numSkipArrayKeys++;
            attno_skip++;
        }
 
        prev_numSkipArrayKeys = numSkipArrayKeys;
 
        /*
         * Stop once past the final input scan key.  We deliberately never add
         * a skip array for the last input scan key's attribute -- even when
         * there are only inequality keys on that attribute.
         */
        if (i == scan->numberOfKeys)
            break;
 
        /*
         * Later preprocessing steps cannot merge a RowCompare into a skip
         * array, so stop adding skip arrays once we see one.  (Note that we
         * can backfill skip arrays before a RowCompare, which will allow keys
         * up to and including the RowCompare to be marked required.)
         *
         * Skip arrays work by maintaining a current array element value,
         * which anchors lower-order keys via an implied equality constraint.
         * This is incompatible with the current nbtree row comparison design,
         * which compares all columns together, as an indivisible group.
         * Alternative designs that can be used alongside skip arrays are
         * possible, but it's not clear that they're really worth pursuing.
         *
         * A RowCompare qual "(a, b, c) > (10, 'foo', 42)" is equivalent to
         * "(a=10 AND b='foo' AND c>42) OR (a=10 AND b>'foo') OR (a>10)".
         * Decomposing this RowCompare into these 3 disjuncts allows each
         * disjunct to be executed as a separate "single value" index scan.
         * That'll give all 3 scans the ability to add skip arrays in the
         * usual way (when there are any scalar keys after the RowCompare).
         * Under this scheme, a qual "(a, b, c) > (10, 'foo', 42) AND d = 99"
         * performs 3 separate scans, each of which can mark keys up to and
         * including its "d = 99" key as required to continue the scan.
         */
        if (attno_has_rowcompare)
            break;
 
        /*
         * Now consider next attno_inkey (or keep going if this is an
         * additional scan key against the same attribute)
         */
        if (attno_inkey < inkey->sk_attno)
        {
            /*
             * Now add skip array for previous scan key's attribute, though
             * only if the attribute has no equality strategy scan keys
             */
            if (attno_has_equal)
            {
                /* Attributes with an = key must have InvalidOid eq_op set */
                skip_eq_ops_out[attno_skip - 1] = InvalidOid;
            }
            else
            {
                Oid         opfamily = rel->rd_opfamily[attno_skip - 1];
                Oid         opcintype = rel->rd_opcintype[attno_skip - 1];
 
                /* Look up input opclass's equality operator (might fail) */
                skip_eq_ops_out[attno_skip - 1] =
                    get_opfamily_member(opfamily, opcintype, opcintype,
                                        BTEqualStrategyNumber);
 
                if (!OidIsValid(skip_eq_ops_out[attno_skip - 1]))
                {
                    /*
                     * Input opclass lacks an equality strategy operator, so
                     * don't generate a skip array that definitely won't work
                     */
                    break;
                }
 
                /* plan on adding a backfill skip array for this attribute */
                numSkipArrayKeys++;
            }
 
            /* Set things up for this new attribute */
            attno_skip++;
            attno_inkey = inkey->sk_attno;
            attno_has_equal = false;
        }
 
        /*
         * Track if this attribute's scan keys include any equality strategy
         * scan keys (IS NULL keys count as equality keys here).  Also track
         * if it has any RowCompare keys.
         */
        if (inkey->sk_strategy == BTEqualStrategyNumber ||
            (inkey->sk_flags & SK_SEARCHNULL))
            attno_has_equal = true;
        if (inkey->sk_flags & SK_ROW_HEADER)
            attno_has_rowcompare = true;
    }
 
    *numSkipArrayKeys_out = numSkipArrayKeys;
    return numSAOPArrayKeys + numSkipArrayKeys;
}
 
/*
 * _bt_find_extreme_element() -- get least or greatest array element
 *
 * scan and skey identify the index column, whose opfamily determines the
 * comparison semantics.  strat should be BTLessStrategyNumber to get the
 * least element, or BTGreaterStrategyNumber to get the greatest.
 */
static Datum
_bt_find_extreme_element(IndexScanDesc scan, ScanKey skey, Oid elemtype,
                         StrategyNumber strat,
                         const Datum *elems, int nelems)
{
    Relation    rel = scan->indexRelation;
    Oid         cmp_op;
    RegProcedure cmp_proc;
    FmgrInfo    flinfo;
    Datum       result;
    int         i;
 
    /*
     * Look up the appropriate comparison operator in the opfamily.
     *
     * Note: it's possible that this would fail, if the opfamily is
     * incomplete, but it seems quite unlikely that an opfamily would omit
     * non-cross-type comparison operators for any datatype that it supports
     * at all.
     */
    Assert(skey->sk_strategy != BTEqualStrategyNumber);
    Assert(OidIsValid(elemtype));
    cmp_op = get_opfamily_member(rel->rd_opfamily[skey->sk_attno - 1],
                                 elemtype,
                                 elemtype,
                                 strat);
    if (!OidIsValid(cmp_op))
        elog(ERROR, "missing operator %d(%u,%u) in opfamily %u",
             strat, elemtype, elemtype,
             rel->rd_opfamily[skey->sk_attno - 1]);
    cmp_proc = get_opcode(cmp_op);
    if (!RegProcedureIsValid(cmp_proc))
        elog(ERROR, "missing oprcode for operator %u", cmp_op);
 
    fmgr_info(cmp_proc, &flinfo);
 
    Assert(nelems > 0);
    result = elems[0];
    for (i = 1; i < nelems; i++)
    {
        if (DatumGetBool(FunctionCall2Coll(&flinfo,
                                           skey->sk_collation,
                                           elems[i],
                                           result)))
            result = elems[i];
    }
 
    return result;
}
 
/*
 * _bt_setup_array_cmp() -- Set up array comparison functions
 *
 * Sets ORDER proc in caller's orderproc argument, which is used during binary
 * searches of arrays during the index scan.  Also sets a same-type ORDER proc
 * in caller's *sortprocp argument, which is used when sorting the array.
 *
 * Preprocessing calls here with all equality strategy scan keys (when scan
 * uses equality array keys), including those not associated with any array.
 * See _bt_advance_array_keys for an explanation of why it'll need to treat
 * simple scalar equality scan keys as degenerate single element arrays.
 *
 * Caller should pass an orderproc pointing to space that'll store the ORDER
 * proc for the scan, and a *sortprocp pointing to its own separate space.
 * When calling here for a non-array scan key, sortprocp arg should be NULL.
 *
 * In the common case where we don't need to deal with cross-type operators,
 * only one ORDER proc is actually required by caller.  We'll set *sortprocp
 * to point to the same memory that caller's orderproc continues to point to.
 * Otherwise, *sortprocp will continue to point to caller's own space.  Either
 * way, *sortprocp will point to a same-type ORDER proc (since that's the only
 * safe way to sort/deduplicate the array associated with caller's scan key).
 */
static void
_bt_setup_array_cmp(IndexScanDesc scan, ScanKey skey, Oid elemtype,
                    FmgrInfo *orderproc, FmgrInfo **sortprocp)
{
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    Relation    rel = scan->indexRelation;
    RegProcedure cmp_proc;
    Oid         opcintype = rel->rd_opcintype[skey->sk_attno - 1];
 
    Assert(skey->sk_strategy == BTEqualStrategyNumber);
    Assert(OidIsValid(elemtype));
 
    /*
     * If scankey operator is not a cross-type comparison, we can use the
     * cached comparison function; otherwise gotta look it up in the catalogs
     */
    if (elemtype == opcintype)
    {
        /* Set same-type ORDER procs for caller */
        *orderproc = *index_getprocinfo(rel, skey->sk_attno, BTORDER_PROC);
        if (sortprocp)
            *sortprocp = orderproc;
 
        return;
    }
 
    /*
     * Look up the appropriate cross-type comparison function in the opfamily.
     *
     * Use the opclass input type as the left hand arg type, and the array
     * element type as the right hand arg type (since binary searches use an
     * index tuple's attribute value to search for a matching array element).
     *
     * Note: it's possible that this would fail, if the opfamily is
     * incomplete, but only in cases where it's quite likely that _bt_first
     * would fail in just the same way (had we not failed before it could).
     */
    cmp_proc = get_opfamily_proc(rel->rd_opfamily[skey->sk_attno - 1],
                                 opcintype, elemtype, BTORDER_PROC);
    if (!RegProcedureIsValid(cmp_proc))
        elog(ERROR, "missing support function %d(%u,%u) for attribute %d of index \"%s\"",
             BTORDER_PROC, opcintype, elemtype, skey->sk_attno,
             RelationGetRelationName(rel));
 
    /* Set cross-type ORDER proc for caller */
    fmgr_info_cxt(cmp_proc, orderproc, so->arrayContext);
 
    /* Done if caller doesn't actually have an array they'll need to sort */
    if (!sortprocp)
        return;
 
    /*
     * Look up the appropriate same-type comparison function in the opfamily.
     *
     * Note: it's possible that this would fail, if the opfamily is
     * incomplete, but it seems quite unlikely that an opfamily would omit
     * non-cross-type comparison procs for any datatype that it supports at
     * all.
     */
    cmp_proc = get_opfamily_proc(rel->rd_opfamily[skey->sk_attno - 1],
                                 elemtype, elemtype, BTORDER_PROC);
    if (!RegProcedureIsValid(cmp_proc))
        elog(ERROR, "missing support function %d(%u,%u) for attribute %d of index \"%s\"",
             BTORDER_PROC, elemtype, elemtype,
             skey->sk_attno, RelationGetRelationName(rel));
 
    /* Set same-type ORDER proc for caller */
    fmgr_info_cxt(cmp_proc, *sortprocp, so->arrayContext);
}
 
/*
 * _bt_sort_array_elements() -- sort and de-dup array elements
 *
 * The array elements are sorted in-place, and the new number of elements
 * after duplicate removal is returned.
 *
 * skey identifies the index column whose opfamily determines the comparison
 * semantics, and sortproc is a corresponding ORDER proc.  If reverse is true,
 * we sort in descending order.
 */
static int
_bt_sort_array_elements(ScanKey skey, FmgrInfo *sortproc, bool reverse,
                        Datum *elems, int nelems)
{
    BTSortArrayContext cxt;
 
    if (nelems <= 1)
        return nelems;          /* no work to do */
 
    /* Sort the array elements */
    cxt.sortproc = sortproc;
    cxt.collation = skey->sk_collation;
    cxt.reverse = reverse;
    qsort_arg(elems, nelems, sizeof(Datum),
              _bt_compare_array_elements, &cxt);
 
    /* Now scan the sorted elements and remove duplicates */
    return qunique_arg(elems, nelems, sizeof(Datum),
                       _bt_compare_array_elements, &cxt);
}
 
/*
 * _bt_merge_arrays() -- merge next array's elements into an original array
 *
 * Called when preprocessing encounters a pair of array equality scan keys,
 * both against the same index attribute (during initial array preprocessing).
 * Merging reorganizes caller's original array (the left hand arg) in-place,
 * without ever copying elements from one array into the other. (Mixing the
 * elements together like this would be wrong, since they don't necessarily
 * use the same underlying element type, despite all the other similarities.)
 *
 * Both arrays must have already been sorted and deduplicated by calling
 * _bt_sort_array_elements.  sortproc is the same-type ORDER proc that was
 * just used to sort and deduplicate caller's "next" array.  We'll usually be
 * able to reuse that order PROC to merge the arrays together now.  If not,
 * then we'll perform a separate ORDER proc lookup.
 *
 * If the opfamily doesn't supply a complete set of cross-type ORDER procs we
 * may not be able to determine which elements are contradictory.  If we have
 * the required ORDER proc then we return true (and validly set *nelems_orig),
 * guaranteeing that at least the next array can be considered redundant.  We
 * return false if the required comparisons cannot be made (caller must keep
 * both arrays when this happens).
 */
static bool
_bt_merge_arrays(IndexScanDesc scan, ScanKey skey, FmgrInfo *sortproc,
                 bool reverse, Oid origelemtype, Oid nextelemtype,
                 Datum *elems_orig, int *nelems_orig,
                 Datum *elems_next, int nelems_next)
{
    Relation    rel = scan->indexRelation;
    BTScanOpaque so = (BTScanOpaque) scan->opaque;
    BTSortArrayContext cxt;
    int         nelems_orig_start = *nelems_orig,
                nelems_orig_merged = 0;
    FmgrInfo   *mergeproc = sortproc;
    FmgrInfo    crosstypeproc;
 
    Assert(skey->sk_strategy == BTEqualStrategyNumber);
    Assert(OidIsValid(origelemtype) && OidIsValid(nextelemtype));
 
    if (origelemtype != nextelemtype)
    {
        RegProcedure cmp_proc;
 
        /*
         * Cross-array-element-type merging is required, so can't just reuse
         * sortproc when merging
         */
        cmp_proc = get_opfamily_proc(rel->rd_opfamily[skey->sk_attno - 1],
                                     origelemtype, nextelemtype, BTORDER_PROC);
        if (!RegProcedureIsValid(cmp_proc))
        {
            /* Can't make the required comparisons */
            return false;
        }
 
        /* We have all we need to determine redundancy/contradictoriness */
        mergeproc = &crosstypeproc;
        fmgr_info_cxt(cmp_proc, mergeproc, so->arrayContext);
    }
 
    cxt.sortproc = mergeproc;
    cxt.collation = skey->sk_collation;
    cxt.reverse = reverse;
 
    for (int i = 0, j = 0; i < nelems_orig_start && j < nelems_next;)
    {
        Datum      *oelem = elems_orig + i,
                   *nelem = elems_next + j;
        int         res = _bt_compare_array_elements(oelem, nelem, &cxt);
 
        if (res == 0)
        {
            elems_orig[nelems_orig_merged++] = *oelem;
            i++;
            j++;
        }
        else if (res < 0)
            i++;
        else                    /* res > 0 */
            j++;
    }
 
    *nelems_orig = nelems_orig_merged;
 
    return true;
}
 
/*
 * qsort_arg comparator for sorting array elements
 */
static int
_bt_compare_array_elements(const void *a, const void *b, void *arg)
{
    Datum       da = *((const Datum *) a);
    Datum       db = *((const Datum *) b);
    BTSortArrayContext *cxt = (BTSortArrayContext *) arg;
    int32       compare;
 
    compare = DatumGetInt32(FunctionCall2Coll(cxt->sortproc,
                                              cxt->collation,
                                              da, db));
    if (cxt->reverse)
        INVERT_COMPARE_RESULT(compare);
    return compare;
}