partbounds.c

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/*-------------------------------------------------------------------------
 *
 * partbounds.c
 *      Support routines for manipulating partition bounds
 *
 * Portions Copyright (c) 1996-2026, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * IDENTIFICATION
 *        src/backend/partitioning/partbounds.c
 *
 *-------------------------------------------------------------------------
 */
 
#include "postgres.h"
 
#include "access/relation.h"
#include "access/table.h"
#include "access/tableam.h"
#include "catalog/namespace.h"
#include "catalog/partition.h"
#include "catalog/pg_inherits.h"
#include "catalog/pg_type.h"
#include "commands/tablecmds.h"
#include "common/hashfn.h"
#include "executor/executor.h"
#include "miscadmin.h"
#include "nodes/makefuncs.h"
#include "nodes/nodeFuncs.h"
#include "nodes/pathnodes.h"
#include "parser/parse_coerce.h"
#include "partitioning/partbounds.h"
#include "partitioning/partdesc.h"
#include "utils/array.h"
#include "utils/builtins.h"
#include "utils/datum.h"
#include "utils/fmgroids.h"
#include "utils/lsyscache.h"
#include "utils/partcache.h"
#include "utils/ruleutils.h"
#include "utils/snapmgr.h"
#include "utils/syscache.h"
 
/*
 * When qsort'ing partition bounds after reading from the catalog, each bound
 * is represented with one of the following structs.
 */
 
/* One bound of a hash partition */
typedef struct PartitionHashBound
{
    int         modulus;
    int         remainder;
    int         index;
} PartitionHashBound;
 
/* One value coming from some (index'th) list partition */
typedef struct PartitionListValue
{
    int         index;
    Datum       value;
} PartitionListValue;
 
/* One bound of a range partition */
typedef struct PartitionRangeBound
{
    int         index;
    Datum      *datums;         /* range bound datums */
    PartitionRangeDatumKind *kind;  /* the kind of each datum */
    bool        lower;          /* this is the lower (vs upper) bound */
} PartitionRangeBound;
 
/*
 * Mapping from partitions of a joining relation to partitions of a join
 * relation being computed (a.k.a merged partitions)
 */
typedef struct PartitionMap
{
    int         nparts;         /* number of partitions */
    int        *merged_indexes; /* indexes of merged partitions */
    bool       *merged;         /* flags to indicate whether partitions are
                                 * merged with non-dummy partitions */
    bool        did_remapping;  /* did we re-map partitions? */
    int        *old_indexes;    /* old indexes of merged partitions if
                                 * did_remapping */
} PartitionMap;
 
/* Macro for comparing two range bounds */
#define compare_range_bounds(partnatts, partsupfunc, partcollations, \
                             bound1, bound2) \
    (partition_rbound_cmp(partnatts, partsupfunc, partcollations, \
                          (bound1)->datums, (bound1)->kind, (bound1)->lower, \
                          bound2))
 
static int32 qsort_partition_hbound_cmp(const void *a, const void *b);
static int32 qsort_partition_list_value_cmp(const void *a, const void *b,
                                            void *arg);
static int32 qsort_partition_rbound_cmp(const void *a, const void *b,
                                        void *arg);
static PartitionBoundInfo create_hash_bounds(PartitionBoundSpec **boundspecs,
                                             int nparts, PartitionKey key, int **mapping);
static PartitionBoundInfo create_list_bounds(PartitionBoundSpec **boundspecs,
                                             int nparts, PartitionKey key, int **mapping);
static PartitionBoundInfo create_range_bounds(PartitionBoundSpec **boundspecs,
                                              int nparts, PartitionKey key, int **mapping);
static PartitionBoundInfo merge_list_bounds(FmgrInfo *partsupfunc,
                                            Oid *partcollation,
                                            RelOptInfo *outer_rel,
                                            RelOptInfo *inner_rel,
                                            JoinType jointype,
                                            List **outer_parts,
                                            List **inner_parts);
static PartitionBoundInfo merge_range_bounds(int partnatts,
                                             FmgrInfo *partsupfuncs,
                                             Oid *partcollations,
                                             RelOptInfo *outer_rel,
                                             RelOptInfo *inner_rel,
                                             JoinType jointype,
                                             List **outer_parts,
                                             List **inner_parts);
static void init_partition_map(RelOptInfo *rel, PartitionMap *map);
static void free_partition_map(PartitionMap *map);
static bool is_dummy_partition(RelOptInfo *rel, int part_index);
static int  merge_matching_partitions(PartitionMap *outer_map,
                                      PartitionMap *inner_map,
                                      int outer_index,
                                      int inner_index,
                                      int *next_index);
static int  process_outer_partition(PartitionMap *outer_map,
                                    PartitionMap *inner_map,
                                    bool outer_has_default,
                                    bool inner_has_default,
                                    int outer_index,
                                    int inner_default,
                                    JoinType jointype,
                                    int *next_index,
                                    int *default_index);
static int  process_inner_partition(PartitionMap *outer_map,
                                    PartitionMap *inner_map,
                                    bool outer_has_default,
                                    bool inner_has_default,
                                    int inner_index,
                                    int outer_default,
                                    JoinType jointype,
                                    int *next_index,
                                    int *default_index);
static void merge_null_partitions(PartitionMap *outer_map,
                                  PartitionMap *inner_map,
                                  bool outer_has_null,
                                  bool inner_has_null,
                                  int outer_null,
                                  int inner_null,
                                  JoinType jointype,
                                  int *next_index,
                                  int *null_index);
static void merge_default_partitions(PartitionMap *outer_map,
                                     PartitionMap *inner_map,
                                     bool outer_has_default,
                                     bool inner_has_default,
                                     int outer_default,
                                     int inner_default,
                                     JoinType jointype,
                                     int *next_index,
                                     int *default_index);
static int  merge_partition_with_dummy(PartitionMap *map, int index,
                                       int *next_index);
static void fix_merged_indexes(PartitionMap *outer_map,
                               PartitionMap *inner_map,
                               int nmerged, List *merged_indexes);
static void generate_matching_part_pairs(RelOptInfo *outer_rel,
                                         RelOptInfo *inner_rel,
                                         PartitionMap *outer_map,
                                         PartitionMap *inner_map,
                                         int nmerged,
                                         List **outer_parts,
                                         List **inner_parts);
static PartitionBoundInfo build_merged_partition_bounds(char strategy,
                                                        List *merged_datums,
                                                        List *merged_kinds,
                                                        List *merged_indexes,
                                                        int null_index,
                                                        int default_index);
static int  get_range_partition(RelOptInfo *rel,
                                PartitionBoundInfo bi,
                                int *lb_pos,
                                PartitionRangeBound *lb,
                                PartitionRangeBound *ub);
static int  get_range_partition_internal(PartitionBoundInfo bi,
                                         int *lb_pos,
                                         PartitionRangeBound *lb,
                                         PartitionRangeBound *ub);
static bool compare_range_partitions(int partnatts, FmgrInfo *partsupfuncs,
                                     Oid *partcollations,
                                     PartitionRangeBound *outer_lb,
                                     PartitionRangeBound *outer_ub,
                                     PartitionRangeBound *inner_lb,
                                     PartitionRangeBound *inner_ub,
                                     int *lb_cmpval, int *ub_cmpval);
static void get_merged_range_bounds(int partnatts, FmgrInfo *partsupfuncs,
                                    Oid *partcollations, JoinType jointype,
                                    PartitionRangeBound *outer_lb,
                                    PartitionRangeBound *outer_ub,
                                    PartitionRangeBound *inner_lb,
                                    PartitionRangeBound *inner_ub,
                                    int lb_cmpval, int ub_cmpval,
                                    PartitionRangeBound *merged_lb,
                                    PartitionRangeBound *merged_ub);
static void add_merged_range_bounds(int partnatts, FmgrInfo *partsupfuncs,
                                    Oid *partcollations,
                                    PartitionRangeBound *merged_lb,
                                    PartitionRangeBound *merged_ub,
                                    int merged_index,
                                    List **merged_datums,
                                    List **merged_kinds,
                                    List **merged_indexes);
static PartitionRangeBound *make_one_partition_rbound(PartitionKey key, int index,
                                                      List *datums, bool lower);
static int32 partition_hbound_cmp(int modulus1, int remainder1, int modulus2,
                                  int remainder2);
static int32 partition_rbound_cmp(int partnatts, FmgrInfo *partsupfunc,
                                  Oid *partcollation, Datum *datums1,
                                  PartitionRangeDatumKind *kind1, bool lower1,
                                  PartitionRangeBound *b2);
static int  partition_range_bsearch(int partnatts, FmgrInfo *partsupfunc,
                                    Oid *partcollation,
                                    PartitionBoundInfo boundinfo,
                                    PartitionRangeBound *probe, int32 *cmpval);
static Expr *make_partition_op_expr(PartitionKey key, int keynum,
                                    uint16 strategy, Expr *arg1, Expr *arg2);
static Oid  get_partition_operator(PartitionKey key, int col,
                                   StrategyNumber strategy, bool *need_relabel);
static List *get_qual_for_hash(Relation parent, PartitionBoundSpec *spec);
static List *get_qual_for_list(Relation parent, PartitionBoundSpec *spec);
static List *get_qual_for_range(Relation parent, PartitionBoundSpec *spec,
                                bool for_default);
static void get_range_key_properties(PartitionKey key, int keynum,
                                     PartitionRangeDatum *ldatum,
                                     PartitionRangeDatum *udatum,
                                     ListCell **partexprs_item,
                                     Expr **keyCol,
                                     Const **lower_val, Const **upper_val);
static List *get_range_nulltest(PartitionKey key);
 
/*
 * get_qual_from_partbound
 *      Given a parser node for partition bound, return the list of executable
 *      expressions as partition constraint
 */
List *
get_qual_from_partbound(Relation parent, PartitionBoundSpec *spec)
{
    PartitionKey key = RelationGetPartitionKey(parent);
    List       *my_qual = NIL;
 
    Assert(key != NULL);
 
    switch (key->strategy)
    {
        case PARTITION_STRATEGY_HASH:
            Assert(spec->strategy == PARTITION_STRATEGY_HASH);
            my_qual = get_qual_for_hash(parent, spec);
            break;
 
        case PARTITION_STRATEGY_LIST:
            Assert(spec->strategy == PARTITION_STRATEGY_LIST);
            my_qual = get_qual_for_list(parent, spec);
            break;
 
        case PARTITION_STRATEGY_RANGE:
            Assert(spec->strategy == PARTITION_STRATEGY_RANGE);
            my_qual = get_qual_for_range(parent, spec, false);
            break;
    }
 
    return my_qual;
}
 
/*
 *  partition_bounds_create
 *      Build a PartitionBoundInfo struct from a list of PartitionBoundSpec
 *      nodes
 *
 * This function creates a PartitionBoundInfo and fills the values of its
 * various members based on the input list.  Importantly, 'datums' array will
 * contain Datum representation of individual bounds (possibly after
 * de-duplication as in case of range bounds), sorted in a canonical order
 * defined by qsort_partition_* functions of respective partitioning methods.
 * 'indexes' array will contain as many elements as there are bounds (specific
 * exceptions to this rule are listed in the function body), which represent
 * the 0-based canonical positions of partitions.
 *
 * Upon return from this function, *mapping is set to an array of
 * list_length(boundspecs) elements, each of which maps the original index of
 * a partition to its canonical index.
 *
 * Note: The objects returned by this function are wholly allocated in the
 * current memory context.
 */
PartitionBoundInfo
partition_bounds_create(PartitionBoundSpec **boundspecs, int nparts,
                        PartitionKey key, int **mapping)
{
    int         i;
 
    Assert(nparts > 0);
 
    /*
     * For each partitioning method, we first convert the partition bounds
     * from their parser node representation to the internal representation,
     * along with any additional preprocessing (such as de-duplicating range
     * bounds).  Resulting bound datums are then added to the 'datums' array
     * in PartitionBoundInfo.  For each datum added, an integer indicating the
     * canonical partition index is added to the 'indexes' array.
     *
     * For each bound, we remember its partition's position (0-based) in the
     * original list to later map it to the canonical index.
     */
 
    /*
     * Initialize mapping array with invalid values, this is filled within
     * each sub-routine below depending on the bound type.
     */
    *mapping = palloc_array(int, nparts);
    for (i = 0; i < nparts; i++)
        (*mapping)[i] = -1;
 
    switch (key->strategy)
    {
        case PARTITION_STRATEGY_HASH:
            return create_hash_bounds(boundspecs, nparts, key, mapping);
 
        case PARTITION_STRATEGY_LIST:
            return create_list_bounds(boundspecs, nparts, key, mapping);
 
        case PARTITION_STRATEGY_RANGE:
            return create_range_bounds(boundspecs, nparts, key, mapping);
    }
 
    Assert(false);
    return NULL;                /* keep compiler quiet */
}
 
/*
 * create_hash_bounds
 *      Create a PartitionBoundInfo for a hash partitioned table
 */
static PartitionBoundInfo
create_hash_bounds(PartitionBoundSpec **boundspecs, int nparts,
                   PartitionKey key, int **mapping)
{
    PartitionBoundInfo boundinfo;
    PartitionHashBound *hbounds;
    int         i;
    int         greatest_modulus;
    Datum      *boundDatums;
 
    boundinfo = palloc0_object(PartitionBoundInfoData);
    boundinfo->strategy = key->strategy;
    /* No special hash partitions. */
    boundinfo->null_index = -1;
    boundinfo->default_index = -1;
 
    hbounds = palloc_array(PartitionHashBound, nparts);
 
    /* Convert from node to the internal representation */
    for (i = 0; i < nparts; i++)
    {
        PartitionBoundSpec *spec = boundspecs[i];
 
        if (spec->strategy != PARTITION_STRATEGY_HASH)
            elog(ERROR, "invalid strategy in partition bound spec");
 
        hbounds[i].modulus = spec->modulus;
        hbounds[i].remainder = spec->remainder;
        hbounds[i].index = i;
    }
 
    /* Sort all the bounds in ascending order */
    qsort(hbounds, nparts, sizeof(PartitionHashBound),
          qsort_partition_hbound_cmp);
 
    /* After sorting, moduli are now stored in ascending order. */
    greatest_modulus = hbounds[nparts - 1].modulus;
 
    boundinfo->ndatums = nparts;
    boundinfo->datums = palloc0_array(Datum *, nparts);
    boundinfo->kind = NULL;
    boundinfo->interleaved_parts = NULL;
    boundinfo->nindexes = greatest_modulus;
    boundinfo->indexes = (int *) palloc(greatest_modulus * sizeof(int));
    for (i = 0; i < greatest_modulus; i++)
        boundinfo->indexes[i] = -1;
 
    /*
     * In the loop below, to save from allocating a series of small datum
     * arrays, here we just allocate a single array and below we'll just
     * assign a portion of this array per partition.
     */
    boundDatums = (Datum *) palloc(nparts * 2 * sizeof(Datum));
 
    /*
     * For hash partitioning, there are as many datums (modulus and remainder
     * pairs) as there are partitions.  Indexes are simply values ranging from
     * 0 to (nparts - 1).
     */
    for (i = 0; i < nparts; i++)
    {
        int         modulus = hbounds[i].modulus;
        int         remainder = hbounds[i].remainder;
 
        boundinfo->datums[i] = &boundDatums[i * 2];
        boundinfo->datums[i][0] = Int32GetDatum(modulus);
        boundinfo->datums[i][1] = Int32GetDatum(remainder);
 
        while (remainder < greatest_modulus)
        {
            /* overlap? */
            Assert(boundinfo->indexes[remainder] == -1);
            boundinfo->indexes[remainder] = i;
            remainder += modulus;
        }
 
        (*mapping)[hbounds[i].index] = i;
    }
    pfree(hbounds);
 
    return boundinfo;
}
 
/*
 * get_non_null_list_datum_count
 *      Counts the number of non-null Datums in each partition.
 */
static int
get_non_null_list_datum_count(PartitionBoundSpec **boundspecs, int nparts)
{
    int         i;
    int         count = 0;
 
    for (i = 0; i < nparts; i++)
    {
        ListCell   *lc;
 
        foreach(lc, boundspecs[i]->listdatums)
        {
            Const      *val = lfirst_node(Const, lc);
 
            if (!val->constisnull)
                count++;
        }
    }
 
    return count;
}
 
/*
 * create_list_bounds
 *      Create a PartitionBoundInfo for a list partitioned table
 */
static PartitionBoundInfo
create_list_bounds(PartitionBoundSpec **boundspecs, int nparts,
                   PartitionKey key, int **mapping)
{
    PartitionBoundInfo boundinfo;
    PartitionListValue *all_values;
    int         i;
    int         j;
    int         ndatums;
    int         next_index = 0;
    int         default_index = -1;
    int         null_index = -1;
    Datum      *boundDatums;
 
    boundinfo = palloc0_object(PartitionBoundInfoData);
    boundinfo->strategy = key->strategy;
    /* Will be set correctly below. */
    boundinfo->null_index = -1;
    boundinfo->default_index = -1;
 
    ndatums = get_non_null_list_datum_count(boundspecs, nparts);
    all_values = (PartitionListValue *)
        palloc(ndatums * sizeof(PartitionListValue));
 
    /* Create a unified list of non-null values across all partitions. */
    for (j = 0, i = 0; i < nparts; i++)
    {
        PartitionBoundSpec *spec = boundspecs[i];
        ListCell   *c;
 
        if (spec->strategy != PARTITION_STRATEGY_LIST)
            elog(ERROR, "invalid strategy in partition bound spec");
 
        /*
         * Note the index of the partition bound spec for the default
         * partition.  There's no datum to add to the list on non-null datums
         * for this partition.
         */
        if (spec->is_default)
        {
            default_index = i;
            continue;
        }
 
        foreach(c, spec->listdatums)
        {
            Const      *val = lfirst_node(Const, c);
 
            if (!val->constisnull)
            {
                all_values[j].index = i;
                all_values[j].value = val->constvalue;
                j++;
            }
            else
            {
                /*
                 * Never put a null into the values array; save the index of
                 * the partition that stores nulls, instead.
                 */
                if (null_index != -1)
                    elog(ERROR, "found null more than once");
                null_index = i;
            }
        }
    }
 
    /* ensure we found a Datum for every slot in the all_values array */
    Assert(j == ndatums);
 
    qsort_arg(all_values, ndatums, sizeof(PartitionListValue),
              qsort_partition_list_value_cmp, key);
 
    boundinfo->ndatums = ndatums;
    boundinfo->datums = palloc0_array(Datum *, ndatums);
    boundinfo->kind = NULL;
    boundinfo->interleaved_parts = NULL;
    boundinfo->nindexes = ndatums;
    boundinfo->indexes = (int *) palloc(ndatums * sizeof(int));
 
    /*
     * In the loop below, to save from allocating a series of small datum
     * arrays, here we just allocate a single array and below we'll just
     * assign a portion of this array per datum.
     */
    boundDatums = (Datum *) palloc(ndatums * sizeof(Datum));
 
    /*
     * Copy values.  Canonical indexes are values ranging from 0 to (nparts -
     * 1) assigned to each partition such that all datums of a given partition
     * receive the same value. The value for a given partition is the index of
     * that partition's smallest datum in the all_values[] array.
     */
    for (i = 0; i < ndatums; i++)
    {
        int         orig_index = all_values[i].index;
 
        boundinfo->datums[i] = &boundDatums[i];
        boundinfo->datums[i][0] = datumCopy(all_values[i].value,
                                            key->parttypbyval[0],
                                            key->parttyplen[0]);
 
        /* If the old index has no mapping, assign one */
        if ((*mapping)[orig_index] == -1)
            (*mapping)[orig_index] = next_index++;
 
        boundinfo->indexes[i] = (*mapping)[orig_index];
    }
 
    pfree(all_values);
 
    /*
     * Set the canonical value for null_index, if any.
     *
     * It is possible that the null-accepting partition has not been assigned
     * an index yet, which could happen if such partition accepts only null
     * and hence not handled in the above loop which only looked at non-null
     * values.
     */
    if (null_index != -1)
    {
        Assert(null_index >= 0);
        if ((*mapping)[null_index] == -1)
            (*mapping)[null_index] = next_index++;
        boundinfo->null_index = (*mapping)[null_index];
    }
 
    /* Set the canonical value for default_index, if any. */
    if (default_index != -1)
    {
        /*
         * The default partition accepts any value not specified in the lists
         * of other partitions, hence it should not get mapped index while
         * assigning those for non-null datums.
         */
        Assert(default_index >= 0);
        Assert((*mapping)[default_index] == -1);
        (*mapping)[default_index] = next_index++;
        boundinfo->default_index = (*mapping)[default_index];
    }
 
    /*
     * Calculate interleaved partitions.  Here we look for partitions which
     * might be interleaved with other partitions and set a bit in
     * interleaved_parts for any partitions which may be interleaved with
     * another partition.
     */
 
    /*
     * There must be multiple partitions to have any interleaved partitions,
     * otherwise there's nothing to interleave with.
     */
    if (nparts > 1)
    {
        /*
         * Short-circuit check to see if only 1 Datum is allowed per
         * partition.  When this is true there's no need to do the more
         * expensive checks to look for interleaved values.
         */
        if (boundinfo->ndatums +
            partition_bound_accepts_nulls(boundinfo) +
            partition_bound_has_default(boundinfo) != nparts)
        {
            int         last_index = -1;
 
            /*
             * Since the indexes array is sorted in Datum order, if any
             * partitions are interleaved then it will show up by the
             * partition indexes not being in ascending order.  Here we check
             * for that and record all partitions that are out of order.
             */
            for (i = 0; i < boundinfo->nindexes; i++)
            {
                int         index = boundinfo->indexes[i];
 
                if (index < last_index)
                    boundinfo->interleaved_parts = bms_add_member(boundinfo->interleaved_parts,
                                                                  index);
 
                /*
                 * Otherwise, if the null_index exists in the indexes array,
                 * then the NULL partition must also allow some other Datum,
                 * therefore it's "interleaved".
                 */
                else if (partition_bound_accepts_nulls(boundinfo) &&
                         index == boundinfo->null_index)
                    boundinfo->interleaved_parts = bms_add_member(boundinfo->interleaved_parts,
                                                                  index);
 
                last_index = index;
            }
        }
 
        /*
         * The DEFAULT partition is the "catch-all" partition that can contain
         * anything that does not belong to any other partition.  If there are
         * any other partitions then the DEFAULT partition must be marked as
         * interleaved.
         */
        if (partition_bound_has_default(boundinfo))
            boundinfo->interleaved_parts = bms_add_member(boundinfo->interleaved_parts,
                                                          boundinfo->default_index);
    }
 
 
    /* All partitions must now have been assigned canonical indexes. */
    Assert(next_index == nparts);
    return boundinfo;
}
 
/*
 * create_range_bounds
 *      Create a PartitionBoundInfo for a range partitioned table
 */
static PartitionBoundInfo
create_range_bounds(PartitionBoundSpec **boundspecs, int nparts,
                    PartitionKey key, int **mapping)
{
    PartitionBoundInfo boundinfo;
    PartitionRangeBound **rbounds = NULL;
    PartitionRangeBound **all_bounds,
               *prev;
    int         i,
                k,
                partnatts;
    int         ndatums = 0;
    int         default_index = -1;
    int         next_index = 0;
    Datum      *boundDatums;
    PartitionRangeDatumKind *boundKinds;
 
    boundinfo = palloc0_object(PartitionBoundInfoData);
    boundinfo->strategy = key->strategy;
    /* There is no special null-accepting range partition. */
    boundinfo->null_index = -1;
    /* Will be set correctly below. */
    boundinfo->default_index = -1;
 
    all_bounds = palloc0_array(PartitionRangeBound *, 2 * nparts);
 
    /* Create a unified list of range bounds across all the partitions. */
    ndatums = 0;
    for (i = 0; i < nparts; i++)
    {
        PartitionBoundSpec *spec = boundspecs[i];
        PartitionRangeBound *lower,
                   *upper;
 
        if (spec->strategy != PARTITION_STRATEGY_RANGE)
            elog(ERROR, "invalid strategy in partition bound spec");
 
        /*
         * Note the index of the partition bound spec for the default
         * partition.  There's no datum to add to the all_bounds array for
         * this partition.
         */
        if (spec->is_default)
        {
            default_index = i;
            continue;
        }
 
        lower = make_one_partition_rbound(key, i, spec->lowerdatums, true);
        upper = make_one_partition_rbound(key, i, spec->upperdatums, false);
        all_bounds[ndatums++] = lower;
        all_bounds[ndatums++] = upper;
    }
 
    Assert(ndatums == nparts * 2 ||
           (default_index != -1 && ndatums == (nparts - 1) * 2));
 
    /* Sort all the bounds in ascending order */
    qsort_arg(all_bounds, ndatums,
              sizeof(PartitionRangeBound *),
              qsort_partition_rbound_cmp,
              key);
 
    /* Save distinct bounds from all_bounds into rbounds. */
    rbounds = (PartitionRangeBound **)
        palloc(ndatums * sizeof(PartitionRangeBound *));
    k = 0;
    prev = NULL;
    for (i = 0; i < ndatums; i++)
    {
        PartitionRangeBound *cur = all_bounds[i];
        bool        is_distinct = false;
        int         j;
 
        /* Is the current bound distinct from the previous one? */
        for (j = 0; j < key->partnatts; j++)
        {
            Datum       cmpval;
 
            if (prev == NULL || cur->kind[j] != prev->kind[j])
            {
                is_distinct = true;
                break;
            }
 
            /*
             * If the bounds are both MINVALUE or MAXVALUE, stop now and treat
             * them as equal, since any values after this point must be
             * ignored.
             */
            if (cur->kind[j] != PARTITION_RANGE_DATUM_VALUE)
                break;
 
            cmpval = FunctionCall2Coll(&key->partsupfunc[j],
                                       key->partcollation[j],
                                       cur->datums[j],
                                       prev->datums[j]);
            if (DatumGetInt32(cmpval) != 0)
            {
                is_distinct = true;
                break;
            }
        }
 
        /*
         * Only if the bound is distinct save it into a temporary array, i.e,
         * rbounds which is later copied into boundinfo datums array.
         */
        if (is_distinct)
            rbounds[k++] = all_bounds[i];
 
        prev = cur;
    }
 
    pfree(all_bounds);
 
    /* Update ndatums to hold the count of distinct datums. */
    ndatums = k;
 
    /*
     * Add datums to boundinfo.  Canonical indexes are values ranging from 0
     * to nparts - 1, assigned in that order to each partition's upper bound.
     * For 'datums' elements that are lower bounds, there is -1 in the
     * 'indexes' array to signify that no partition exists for the values less
     * than such a bound and greater than or equal to the previous upper
     * bound.
     */
    boundinfo->ndatums = ndatums;
    boundinfo->datums = palloc0_array(Datum *, ndatums);
    boundinfo->kind = palloc0_array(PartitionRangeDatumKind *, ndatums);
    boundinfo->interleaved_parts = NULL;
 
    /*
     * For range partitioning, an additional value of -1 is stored as the last
     * element of the indexes[] array.
     */
    boundinfo->nindexes = ndatums + 1;
    boundinfo->indexes = palloc_array(int, (ndatums + 1));
 
    /*
     * In the loop below, to save from allocating a series of small arrays,
     * here we just allocate a single array for Datums and another for
     * PartitionRangeDatumKinds, below we'll just assign a portion of these
     * arrays in each loop.
     */
    partnatts = key->partnatts;
    boundDatums = (Datum *) palloc(ndatums * partnatts * sizeof(Datum));
    boundKinds = palloc_array(PartitionRangeDatumKind, ndatums * partnatts);
 
    for (i = 0; i < ndatums; i++)
    {
        int         j;
 
        boundinfo->datums[i] = &boundDatums[i * partnatts];
        boundinfo->kind[i] = &boundKinds[i * partnatts];
        for (j = 0; j < partnatts; j++)
        {
            if (rbounds[i]->kind[j] == PARTITION_RANGE_DATUM_VALUE)
                boundinfo->datums[i][j] =
                    datumCopy(rbounds[i]->datums[j],
                              key->parttypbyval[j],
                              key->parttyplen[j]);
            boundinfo->kind[i][j] = rbounds[i]->kind[j];
        }
 
        /*
         * There is no mapping for invalid indexes.
         *
         * Any lower bounds in the rbounds array have invalid indexes
         * assigned, because the values between the previous bound (if there
         * is one) and this (lower) bound are not part of the range of any
         * existing partition.
         */
        if (rbounds[i]->lower)
            boundinfo->indexes[i] = -1;
        else
        {
            int         orig_index = rbounds[i]->index;
 
            /* If the old index has no mapping, assign one */
            if ((*mapping)[orig_index] == -1)
                (*mapping)[orig_index] = next_index++;
 
            boundinfo->indexes[i] = (*mapping)[orig_index];
        }
    }
 
    pfree(rbounds);
 
    /* Set the canonical value for default_index, if any. */
    if (default_index != -1)
    {
        Assert(default_index >= 0 && (*mapping)[default_index] == -1);
        (*mapping)[default_index] = next_index++;
        boundinfo->default_index = (*mapping)[default_index];
    }
 
    /* The extra -1 element. */
    Assert(i == ndatums);
    boundinfo->indexes[i] = -1;
 
    /* All partitions must now have been assigned canonical indexes. */
    Assert(next_index == nparts);
    return boundinfo;
}
 
/*
 * Are two partition bound collections logically equal?
 *
 * Used in the keep logic of relcache.c (ie, in RelationClearRelation()).
 * This is also useful when b1 and b2 are bound collections of two separate
 * relations, respectively, because PartitionBoundInfo is a canonical
 * representation of partition bounds.
 */
bool
partition_bounds_equal(int partnatts, int16 *parttyplen, bool *parttypbyval,
                       PartitionBoundInfo b1, PartitionBoundInfo b2)
{
    int         i;
 
    if (b1->strategy != b2->strategy)
        return false;
 
    if (b1->ndatums != b2->ndatums)
        return false;
 
    if (b1->nindexes != b2->nindexes)
        return false;
 
    if (b1->null_index != b2->null_index)
        return false;
 
    if (b1->default_index != b2->default_index)
        return false;
 
    /* For all partition strategies, the indexes[] arrays have to match */
    for (i = 0; i < b1->nindexes; i++)
    {
        if (b1->indexes[i] != b2->indexes[i])
            return false;
    }
 
    /* Finally, compare the datums[] arrays */
    if (b1->strategy == PARTITION_STRATEGY_HASH)
    {
        /*
         * We arrange the partitions in the ascending order of their moduli
         * and remainders.  Also every modulus is factor of next larger
         * modulus.  Therefore we can safely store index of a given partition
         * in indexes array at remainder of that partition.  Also entries at
         * (remainder + N * modulus) positions in indexes array are all same
         * for (modulus, remainder) specification for any partition.  Thus the
         * datums arrays from the given bounds are the same, if and only if
         * their indexes arrays are the same.  So, it suffices to compare the
         * indexes arrays.
         *
         * Nonetheless make sure that the bounds are indeed the same when the
         * indexes match.  Hash partition bound stores modulus and remainder
         * at b1->datums[i][0] and b1->datums[i][1] position respectively.
         */
#ifdef USE_ASSERT_CHECKING
        for (i = 0; i < b1->ndatums; i++)
            Assert((b1->datums[i][0] == b2->datums[i][0] &&
                    b1->datums[i][1] == b2->datums[i][1]));
#endif
    }
    else
    {
        for (i = 0; i < b1->ndatums; i++)
        {
            int         j;
 
            for (j = 0; j < partnatts; j++)
            {
                /* For range partitions, the bounds might not be finite. */
                if (b1->kind != NULL)
                {
                    /* The different kinds of bound all differ from each other */
                    if (b1->kind[i][j] != b2->kind[i][j])
                        return false;
 
                    /*
                     * Non-finite bounds are equal without further
                     * examination.
                     */
                    if (b1->kind[i][j] != PARTITION_RANGE_DATUM_VALUE)
                        continue;
                }
 
                /*
                 * Compare the actual values. Note that it would be both
                 * incorrect and unsafe to invoke the comparison operator
                 * derived from the partitioning specification here.  It would
                 * be incorrect because we want the relcache entry to be
                 * updated for ANY change to the partition bounds, not just
                 * those that the partitioning operator thinks are
                 * significant.  It would be unsafe because we might reach
                 * this code in the context of an aborted transaction, and an
                 * arbitrary partitioning operator might not be safe in that
                 * context.  datumIsEqual() should be simple enough to be
                 * safe.
                 */
                if (!datumIsEqual(b1->datums[i][j], b2->datums[i][j],
                                  parttypbyval[j], parttyplen[j]))
                    return false;
            }
        }
    }
    return true;
}
 
/*
 * Return a copy of given PartitionBoundInfo structure. The data types of bounds
 * are described by given partition key specification.
 *
 * Note: it's important that this function and its callees not do any catalog
 * access, nor anything else that would result in allocating memory other than
 * the returned data structure.  Since this is called in a long-lived context,
 * that would result in unwanted memory leaks.
 */
PartitionBoundInfo
partition_bounds_copy(PartitionBoundInfo src,
                      PartitionKey key)
{
    PartitionBoundInfo dest;
    int         i;
    int         ndatums;
    int         nindexes;
    int         partnatts;
 
    dest = (PartitionBoundInfo) palloc_object(PartitionBoundInfoData);
 
    dest->strategy = src->strategy;
    ndatums = dest->ndatums = src->ndatums;
    nindexes = dest->nindexes = src->nindexes;
    partnatts = key->partnatts;
 
    /* List partitioned tables have only a single partition key. */
    Assert(key->strategy != PARTITION_STRATEGY_LIST || partnatts == 1);
 
    dest->datums = palloc_array(Datum *, ndatums);
 
    if (src->kind != NULL && ndatums > 0)
    {
        PartitionRangeDatumKind *boundKinds;
 
        /* only RANGE partition should have a non-NULL kind */
        Assert(key->strategy == PARTITION_STRATEGY_RANGE);
 
        dest->kind = (PartitionRangeDatumKind **) palloc(ndatums *
                                                         sizeof(PartitionRangeDatumKind *));
 
        /*
         * In the loop below, to save from allocating a series of small arrays
         * for storing the PartitionRangeDatumKind, we allocate a single chunk
         * here and use a smaller portion of it for each datum.
         */
        boundKinds = (PartitionRangeDatumKind *) palloc(ndatums * partnatts *
                                                        sizeof(PartitionRangeDatumKind));
 
        for (i = 0; i < ndatums; i++)
        {
            dest->kind[i] = &boundKinds[i * partnatts];
            memcpy(dest->kind[i], src->kind[i],
                   sizeof(PartitionRangeDatumKind) * partnatts);
        }
    }
    else
        dest->kind = NULL;
 
    /* copy interleaved partitions for LIST partitioned tables */
    dest->interleaved_parts = bms_copy(src->interleaved_parts);
 
    /*
     * For hash partitioning, datums array will have two elements - modulus
     * and remainder.
     */
    if (ndatums > 0)
    {
        bool        hash_part = (key->strategy == PARTITION_STRATEGY_HASH);
        int         natts = hash_part ? 2 : partnatts;
        Datum      *boundDatums = palloc(ndatums * natts * sizeof(Datum));
 
        for (i = 0; i < ndatums; i++)
        {
            int         j;
 
            dest->datums[i] = &boundDatums[i * natts];
 
            for (j = 0; j < natts; j++)
            {
                if (dest->kind == NULL ||
                    dest->kind[i][j] == PARTITION_RANGE_DATUM_VALUE)
                {
                    bool        byval;
                    int         typlen;
 
                    if (hash_part)
                    {
                        typlen = sizeof(int32); /* Always int4 */
                        byval = true;   /* int4 is pass-by-value */
                    }
                    else
                    {
                        byval = key->parttypbyval[j];
                        typlen = key->parttyplen[j];
                    }
                    dest->datums[i][j] = datumCopy(src->datums[i][j],
                                                   byval, typlen);
                }
            }
        }
    }
 
    dest->indexes = palloc_array(int, nindexes);
    memcpy(dest->indexes, src->indexes, sizeof(int) * nindexes);
 
    dest->null_index = src->null_index;
    dest->default_index = src->default_index;
 
    return dest;
}
 
/*
 * partition_bounds_merge
 *      Check to see whether every partition of 'outer_rel' matches/overlaps
 *      one partition of 'inner_rel' at most, and vice versa; and if so, build
 *      and return the partition bounds for a join relation between the rels,
 *      generating two lists of the matching/overlapping partitions, which are
 *      returned to *outer_parts and *inner_parts respectively.
 *
 * The lists contain the same number of partitions, and the partitions at the
 * same positions in the lists indicate join pairs used for partitioned join.
 * If a partition on one side matches/overlaps multiple partitions on the other
 * side, this function returns NULL, setting *outer_parts and *inner_parts to
 * NIL.
 */
PartitionBoundInfo
partition_bounds_merge(int partnatts,
                       FmgrInfo *partsupfunc, Oid *partcollation,
                       RelOptInfo *outer_rel, RelOptInfo *inner_rel,
                       JoinType jointype,
                       List **outer_parts, List **inner_parts)
{
    /*
     * Currently, this function is called only from try_partitionwise_join(),
     * so the join type should be INNER, LEFT, FULL, SEMI, or ANTI.
     */
    Assert(jointype == JOIN_INNER || jointype == JOIN_LEFT ||
           jointype == JOIN_FULL || jointype == JOIN_SEMI ||
           jointype == JOIN_ANTI);
 
    /* The partitioning strategies should be the same. */
    Assert(outer_rel->boundinfo->strategy == inner_rel->boundinfo->strategy);
 
    *outer_parts = *inner_parts = NIL;
    switch (outer_rel->boundinfo->strategy)
    {
        case PARTITION_STRATEGY_HASH:
 
            /*
             * For hash partitioned tables, we currently support partitioned
             * join only when they have exactly the same partition bounds.
             *
             * XXX: it might be possible to relax the restriction to support
             * cases where hash partitioned tables have missing partitions
             * and/or different moduli, but it's not clear if it would be
             * useful to support the former case since it's unusual to have
             * missing partitions.  On the other hand, it would be useful to
             * support the latter case, but in that case, there is a high
             * probability that a partition on one side will match multiple
             * partitions on the other side, which is the scenario the current
             * implementation of partitioned join can't handle.
             */
            return NULL;
 
        case PARTITION_STRATEGY_LIST:
            return merge_list_bounds(partsupfunc,
                                     partcollation,
                                     outer_rel,
                                     inner_rel,
                                     jointype,
                                     outer_parts,
                                     inner_parts);
 
        case PARTITION_STRATEGY_RANGE:
            return merge_range_bounds(partnatts,
                                      partsupfunc,
                                      partcollation,
                                      outer_rel,
                                      inner_rel,
                                      jointype,
                                      outer_parts,
                                      inner_parts);
    }
 
    return NULL;
}
 
/*
 * merge_list_bounds
 *      Create the partition bounds for a join relation between list
 *      partitioned tables, if possible
 *
 * In this function we try to find sets of matching partitions from both sides
 * by comparing list values stored in their partition bounds.  Since the list
 * values appear in the ascending order, an algorithm similar to merge join is
 * used for that.  If a partition on one side doesn't have a matching
 * partition on the other side, the algorithm tries to match it with the
 * default partition on the other side if any; if not, the algorithm tries to
 * match it with a dummy partition on the other side if it's on the
 * non-nullable side of an outer join.  Also, if both sides have the default
 * partitions, the algorithm tries to match them with each other.  We give up
 * if the algorithm finds a partition matching multiple partitions on the
 * other side, which is the scenario the current implementation of partitioned
 * join can't handle.
 */
static PartitionBoundInfo
merge_list_bounds(FmgrInfo *partsupfunc, Oid *partcollation,
                  RelOptInfo *outer_rel, RelOptInfo *inner_rel,
                  JoinType jointype,
                  List **outer_parts, List **inner_parts)
{
    PartitionBoundInfo merged_bounds = NULL;
    PartitionBoundInfo outer_bi = outer_rel->boundinfo;
    PartitionBoundInfo inner_bi = inner_rel->boundinfo;
    bool        outer_has_default = partition_bound_has_default(outer_bi);
    bool        inner_has_default = partition_bound_has_default(inner_bi);
    int         outer_default = outer_bi->default_index;
    int         inner_default = inner_bi->default_index;
    bool        outer_has_null = partition_bound_accepts_nulls(outer_bi);
    bool        inner_has_null = partition_bound_accepts_nulls(inner_bi);
    PartitionMap outer_map;
    PartitionMap inner_map;
    int         outer_pos;
    int         inner_pos;
    int         next_index = 0;
    int         null_index = -1;
    int         default_index = -1;
    List       *merged_datums = NIL;
    List       *merged_indexes = NIL;
 
    Assert(*outer_parts == NIL);
    Assert(*inner_parts == NIL);
    Assert(outer_bi->strategy == inner_bi->strategy &&
           outer_bi->strategy == PARTITION_STRATEGY_LIST);
    /* List partitioning doesn't require kinds. */
    Assert(!outer_bi->kind && !inner_bi->kind);
 
    init_partition_map(outer_rel, &outer_map);
    init_partition_map(inner_rel, &inner_map);
 
    /*
     * If the default partitions (if any) have been proven empty, deem them
     * non-existent.
     */
    if (outer_has_default && is_dummy_partition(outer_rel, outer_default))
        outer_has_default = false;
    if (inner_has_default && is_dummy_partition(inner_rel, inner_default))
        inner_has_default = false;
 
    /*
     * Merge partitions from both sides.  In each iteration we compare a pair
     * of list values, one from each side, and decide whether the
     * corresponding partitions match or not.  If the two values match
     * exactly, move to the next pair of list values, otherwise move to the
     * next list value on the side with a smaller list value.
     */
    outer_pos = inner_pos = 0;
    while (outer_pos < outer_bi->ndatums || inner_pos < inner_bi->ndatums)
    {
        int         outer_index = -1;
        int         inner_index = -1;
        Datum      *outer_datums;
        Datum      *inner_datums;
        int         cmpval;
        Datum      *merged_datum = NULL;
        int         merged_index = -1;
 
        if (outer_pos < outer_bi->ndatums)
        {
            /*
             * If the partition on the outer side has been proven empty,
             * ignore it and move to the next datum on the outer side.
             */
            outer_index = outer_bi->indexes[outer_pos];
            if (is_dummy_partition(outer_rel, outer_index))
            {
                outer_pos++;
                continue;
            }
        }
        if (inner_pos < inner_bi->ndatums)
        {
            /*
             * If the partition on the inner side has been proven empty,
             * ignore it and move to the next datum on the inner side.
             */
            inner_index = inner_bi->indexes[inner_pos];
            if (is_dummy_partition(inner_rel, inner_index))
            {
                inner_pos++;
                continue;
            }
        }
 
        /* Get the list values. */
        outer_datums = outer_pos < outer_bi->ndatums ?
            outer_bi->datums[outer_pos] : NULL;
        inner_datums = inner_pos < inner_bi->ndatums ?
            inner_bi->datums[inner_pos] : NULL;
 
        /*
         * We run this loop till both sides finish.  This allows us to avoid
         * duplicating code to handle the remaining values on the side which
         * finishes later.  For that we set the comparison parameter cmpval in
         * such a way that it appears as if the side which finishes earlier
         * has an extra value higher than any other value on the unfinished
         * side. That way we advance the values on the unfinished side till
         * all of its values are exhausted.
         */
        if (outer_pos >= outer_bi->ndatums)
            cmpval = 1;
        else if (inner_pos >= inner_bi->ndatums)
            cmpval = -1;
        else
        {
            Assert(outer_datums != NULL && inner_datums != NULL);
            cmpval = DatumGetInt32(FunctionCall2Coll(&partsupfunc[0],
                                                     partcollation[0],
                                                     outer_datums[0],
                                                     inner_datums[0]));
        }
 
        if (cmpval == 0)
        {
            /* Two list values match exactly. */
            Assert(outer_pos < outer_bi->ndatums);
            Assert(inner_pos < inner_bi->ndatums);
            Assert(outer_index >= 0);
            Assert(inner_index >= 0);
 
            /*
             * Try merging both partitions.  If successful, add the list value
             * and index of the merged partition below.
             */
            merged_index = merge_matching_partitions(&outer_map, &inner_map,
                                                     outer_index, inner_index,
                                                     &next_index);
            if (merged_index == -1)
                goto cleanup;
 
            merged_datum = outer_datums;
 
            /* Move to the next pair of list values. */
            outer_pos++;
            inner_pos++;
        }
        else if (cmpval < 0)
        {
            /* A list value missing from the inner side. */
            Assert(outer_pos < outer_bi->ndatums);
 
            /*
             * If the inner side has the default partition, or this is an
             * outer join, try to assign a merged partition to the outer
             * partition (see process_outer_partition()).  Otherwise, the
             * outer partition will not contribute to the result.
             */
            if (inner_has_default || IS_OUTER_JOIN(jointype))
            {
                /* Get the outer partition. */
                outer_index = outer_bi->indexes[outer_pos];
                Assert(outer_index >= 0);
                merged_index = process_outer_partition(&outer_map,
                                                       &inner_map,
                                                       outer_has_default,
                                                       inner_has_default,
                                                       outer_index,
                                                       inner_default,
                                                       jointype,
                                                       &next_index,
                                                       &default_index);
                if (merged_index == -1)
                    goto cleanup;
                merged_datum = outer_datums;
            }
 
            /* Move to the next list value on the outer side. */
            outer_pos++;
        }
        else
        {
            /* A list value missing from the outer side. */
            Assert(cmpval > 0);
            Assert(inner_pos < inner_bi->ndatums);
 
            /*
             * If the outer side has the default partition, or this is a FULL
             * join, try to assign a merged partition to the inner partition
             * (see process_inner_partition()).  Otherwise, the inner
             * partition will not contribute to the result.
             */
            if (outer_has_default || jointype == JOIN_FULL)
            {
                /* Get the inner partition. */
                inner_index = inner_bi->indexes[inner_pos];
                Assert(inner_index >= 0);
                merged_index = process_inner_partition(&outer_map,
                                                       &inner_map,
                                                       outer_has_default,
                                                       inner_has_default,
                                                       inner_index,
                                                       outer_default,
                                                       jointype,
                                                       &next_index,
                                                       &default_index);
                if (merged_index == -1)
                    goto cleanup;
                merged_datum = inner_datums;
            }
 
            /* Move to the next list value on the inner side. */
            inner_pos++;
        }
 
        /*
         * If we assigned a merged partition, add the list value and index of
         * the merged partition if appropriate.
         */
        if (merged_index >= 0 && merged_index != default_index)
        {
            merged_datums = lappend(merged_datums, merged_datum);
            merged_indexes = lappend_int(merged_indexes, merged_index);
        }
    }
 
    /*
     * If the NULL partitions (if any) have been proven empty, deem them
     * non-existent.
     */
    if (outer_has_null &&
        is_dummy_partition(outer_rel, outer_bi->null_index))
        outer_has_null = false;
    if (inner_has_null &&
        is_dummy_partition(inner_rel, inner_bi->null_index))
        inner_has_null = false;
 
    /* Merge the NULL partitions if any. */
    if (outer_has_null || inner_has_null)
        merge_null_partitions(&outer_map, &inner_map,
                              outer_has_null, inner_has_null,
                              outer_bi->null_index, inner_bi->null_index,
                              jointype, &next_index, &null_index);
    else
        Assert(null_index == -1);
 
    /* Merge the default partitions if any. */
    if (outer_has_default || inner_has_default)
        merge_default_partitions(&outer_map, &inner_map,
                                 outer_has_default, inner_has_default,
                                 outer_default, inner_default,
                                 jointype, &next_index, &default_index);
    else
        Assert(default_index == -1);
 
    /* If we have merged partitions, create the partition bounds. */
    if (next_index > 0)
    {
        /* Fix the merged_indexes list if necessary. */
        if (outer_map.did_remapping || inner_map.did_remapping)
        {
            Assert(jointype == JOIN_FULL);
            fix_merged_indexes(&outer_map, &inner_map,
                               next_index, merged_indexes);
        }
 
        /* Use maps to match partitions from inputs. */
        generate_matching_part_pairs(outer_rel, inner_rel,
                                     &outer_map, &inner_map,
                                     next_index,
                                     outer_parts, inner_parts);
        Assert(*outer_parts != NIL);
        Assert(*inner_parts != NIL);
        Assert(list_length(*outer_parts) == list_length(*inner_parts));
        Assert(list_length(*outer_parts) <= next_index);
 
        /* Make a PartitionBoundInfo struct to return. */
        merged_bounds = build_merged_partition_bounds(outer_bi->strategy,
                                                      merged_datums,
                                                      NIL,
                                                      merged_indexes,
                                                      null_index,
                                                      default_index);
        Assert(merged_bounds);
    }
 
cleanup:
    /* Free local memory before returning. */
    list_free(merged_datums);
    list_free(merged_indexes);
    free_partition_map(&outer_map);
    free_partition_map(&inner_map);
 
    return merged_bounds;
}
 
/*
 * merge_range_bounds
 *      Create the partition bounds for a join relation between range
 *      partitioned tables, if possible
 *
 * In this function we try to find sets of overlapping partitions from both
 * sides by comparing ranges stored in their partition bounds.  Since the
 * ranges appear in the ascending order, an algorithm similar to merge join is
 * used for that.  If a partition on one side doesn't have an overlapping
 * partition on the other side, the algorithm tries to match it with the
 * default partition on the other side if any; if not, the algorithm tries to
 * match it with a dummy partition on the other side if it's on the
 * non-nullable side of an outer join.  Also, if both sides have the default
 * partitions, the algorithm tries to match them with each other.  We give up
 * if the algorithm finds a partition overlapping multiple partitions on the
 * other side, which is the scenario the current implementation of partitioned
 * join can't handle.
 */
static PartitionBoundInfo
merge_range_bounds(int partnatts, FmgrInfo *partsupfuncs,
                   Oid *partcollations,
                   RelOptInfo *outer_rel, RelOptInfo *inner_rel,
                   JoinType jointype,
                   List **outer_parts, List **inner_parts)
{
    PartitionBoundInfo merged_bounds = NULL;
    PartitionBoundInfo outer_bi = outer_rel->boundinfo;
    PartitionBoundInfo inner_bi = inner_rel->boundinfo;
    bool        outer_has_default = partition_bound_has_default(outer_bi);
    bool        inner_has_default = partition_bound_has_default(inner_bi);
    int         outer_default = outer_bi->default_index;
    int         inner_default = inner_bi->default_index;
    PartitionMap outer_map;
    PartitionMap inner_map;
    int         outer_index;
    int         inner_index;
    int         outer_lb_pos;
    int         inner_lb_pos;
    PartitionRangeBound outer_lb;
    PartitionRangeBound outer_ub;
    PartitionRangeBound inner_lb;
    PartitionRangeBound inner_ub;
    int         next_index = 0;
    int         default_index = -1;
    List       *merged_datums = NIL;
    List       *merged_kinds = NIL;
    List       *merged_indexes = NIL;
 
    Assert(*outer_parts == NIL);
    Assert(*inner_parts == NIL);
    Assert(outer_bi->strategy == inner_bi->strategy &&
           outer_bi->strategy == PARTITION_STRATEGY_RANGE);
 
    init_partition_map(outer_rel, &outer_map);
    init_partition_map(inner_rel, &inner_map);
 
    /*
     * If the default partitions (if any) have been proven empty, deem them
     * non-existent.
     */
    if (outer_has_default && is_dummy_partition(outer_rel, outer_default))
        outer_has_default = false;
    if (inner_has_default && is_dummy_partition(inner_rel, inner_default))
        inner_has_default = false;
 
    /*
     * Merge partitions from both sides.  In each iteration we compare a pair
     * of ranges, one from each side, and decide whether the corresponding
     * partitions match or not.  If the two ranges overlap, move to the next
     * pair of ranges, otherwise move to the next range on the side with a
     * lower range.  outer_lb_pos/inner_lb_pos keep track of the positions of
     * lower bounds in the datums arrays in the outer/inner
     * PartitionBoundInfos respectively.
     */
    outer_lb_pos = inner_lb_pos = 0;
    outer_index = get_range_partition(outer_rel, outer_bi, &outer_lb_pos,
                                      &outer_lb, &outer_ub);
    inner_index = get_range_partition(inner_rel, inner_bi, &inner_lb_pos,
                                      &inner_lb, &inner_ub);
    while (outer_index >= 0 || inner_index >= 0)
    {
        bool        overlap;
        int         ub_cmpval;
        int         lb_cmpval;
        PartitionRangeBound merged_lb = {-1, NULL, NULL, true};
        PartitionRangeBound merged_ub = {-1, NULL, NULL, false};
        int         merged_index = -1;
 
        /*
         * We run this loop till both sides finish.  This allows us to avoid
         * duplicating code to handle the remaining ranges on the side which
         * finishes later.  For that we set the comparison parameter cmpval in
         * such a way that it appears as if the side which finishes earlier
         * has an extra range higher than any other range on the unfinished
         * side. That way we advance the ranges on the unfinished side till
         * all of its ranges are exhausted.
         */
        if (outer_index == -1)
        {
            overlap = false;
            lb_cmpval = 1;
            ub_cmpval = 1;
        }
        else if (inner_index == -1)
        {
            overlap = false;
            lb_cmpval = -1;
            ub_cmpval = -1;
        }
        else
            overlap = compare_range_partitions(partnatts, partsupfuncs,
                                               partcollations,
                                               &outer_lb, &outer_ub,
                                               &inner_lb, &inner_ub,
                                               &lb_cmpval, &ub_cmpval);
 
        if (overlap)
        {
            /* Two ranges overlap; form a join pair. */
 
            PartitionRangeBound save_outer_ub;
            PartitionRangeBound save_inner_ub;
 
            /* Both partitions should not have been merged yet. */
            Assert(outer_index >= 0);
            Assert(outer_map.merged_indexes[outer_index] == -1 &&
                   outer_map.merged[outer_index] == false);
            Assert(inner_index >= 0);
            Assert(inner_map.merged_indexes[inner_index] == -1 &&
                   inner_map.merged[inner_index] == false);
 
            /*
             * Get the index of the merged partition.  Both partitions aren't
             * merged yet, so the partitions should be merged successfully.
             */
            merged_index = merge_matching_partitions(&outer_map, &inner_map,
                                                     outer_index, inner_index,
                                                     &next_index);
            Assert(merged_index >= 0);
 
            /* Get the range bounds of the merged partition. */
            get_merged_range_bounds(partnatts, partsupfuncs,
                                    partcollations, jointype,
                                    &outer_lb, &outer_ub,
                                    &inner_lb, &inner_ub,
                                    lb_cmpval, ub_cmpval,
                                    &merged_lb, &merged_ub);
 
            /* Save the upper bounds of both partitions for use below. */
            save_outer_ub = outer_ub;
            save_inner_ub = inner_ub;
 
            /* Move to the next pair of ranges. */
            outer_index = get_range_partition(outer_rel, outer_bi, &outer_lb_pos,
                                              &outer_lb, &outer_ub);
            inner_index = get_range_partition(inner_rel, inner_bi, &inner_lb_pos,
                                              &inner_lb, &inner_ub);
 
            /*
             * If the range of a partition on one side overlaps the range of
             * the next partition on the other side, that will cause the
             * partition on one side to match at least two partitions on the
             * other side, which is the case that we currently don't support
             * partitioned join for; give up.
             */
            if (ub_cmpval > 0 && inner_index >= 0 &&
                compare_range_bounds(partnatts, partsupfuncs, partcollations,
                                     &save_outer_ub, &inner_lb) > 0)
                goto cleanup;
            if (ub_cmpval < 0 && outer_index >= 0 &&
                compare_range_bounds(partnatts, partsupfuncs, partcollations,
                                     &outer_lb, &save_inner_ub) < 0)
                goto cleanup;
 
            /*
             * A row from a non-overlapping portion (if any) of a partition on
             * one side might find its join partner in the default partition
             * (if any) on the other side, causing the same situation as
             * above; give up in that case.
             */
            if ((outer_has_default && (lb_cmpval > 0 || ub_cmpval < 0)) ||
                (inner_has_default && (lb_cmpval < 0 || ub_cmpval > 0)))
                goto cleanup;
        }
        else if (ub_cmpval < 0)
        {
            /* A non-overlapping outer range. */
 
            /* The outer partition should not have been merged yet. */
            Assert(outer_index >= 0);
            Assert(outer_map.merged_indexes[outer_index] == -1 &&
                   outer_map.merged[outer_index] == false);
 
            /*
             * If the inner side has the default partition, or this is an
             * outer join, try to assign a merged partition to the outer
             * partition (see process_outer_partition()).  Otherwise, the
             * outer partition will not contribute to the result.
             */
            if (inner_has_default || IS_OUTER_JOIN(jointype))
            {
                merged_index = process_outer_partition(&outer_map,
                                                       &inner_map,
                                                       outer_has_default,
                                                       inner_has_default,
                                                       outer_index,
                                                       inner_default,
                                                       jointype,
                                                       &next_index,
                                                       &default_index);
                if (merged_index == -1)
                    goto cleanup;
                merged_lb = outer_lb;
                merged_ub = outer_ub;
            }
 
            /* Move to the next range on the outer side. */
            outer_index = get_range_partition(outer_rel, outer_bi, &outer_lb_pos,
                                              &outer_lb, &outer_ub);
        }
        else
        {
            /* A non-overlapping inner range. */
            Assert(ub_cmpval > 0);
 
            /* The inner partition should not have been merged yet. */
            Assert(inner_index >= 0);
            Assert(inner_map.merged_indexes[inner_index] == -1 &&
                   inner_map.merged[inner_index] == false);
 
            /*
             * If the outer side has the default partition, or this is a FULL
             * join, try to assign a merged partition to the inner partition
             * (see process_inner_partition()).  Otherwise, the inner
             * partition will not contribute to the result.
             */
            if (outer_has_default || jointype == JOIN_FULL)
            {
                merged_index = process_inner_partition(&outer_map,
                                                       &inner_map,
                                                       outer_has_default,
                                                       inner_has_default,
                                                       inner_index,
                                                       outer_default,
                                                       jointype,
                                                       &next_index,
                                                       &default_index);
                if (merged_index == -1)
                    goto cleanup;
                merged_lb = inner_lb;
                merged_ub = inner_ub;
            }
 
            /* Move to the next range on the inner side. */
            inner_index = get_range_partition(inner_rel, inner_bi, &inner_lb_pos,
                                              &inner_lb, &inner_ub);
        }
 
        /*
         * If we assigned a merged partition, add the range bounds and index
         * of the merged partition if appropriate.
         */
        if (merged_index >= 0 && merged_index != default_index)
            add_merged_range_bounds(partnatts, partsupfuncs, partcollations,
                                    &merged_lb, &merged_ub, merged_index,
                                    &merged_datums, &merged_kinds,
                                    &merged_indexes);
    }
 
    /* Merge the default partitions if any. */
    if (outer_has_default || inner_has_default)
        merge_default_partitions(&outer_map, &inner_map,
                                 outer_has_default, inner_has_default,
                                 outer_default, inner_default,
                                 jointype, &next_index, &default_index);
    else
        Assert(default_index == -1);
 
    /* If we have merged partitions, create the partition bounds. */
    if (next_index > 0)
    {
        /*
         * Unlike the case of list partitioning, we wouldn't have re-merged
         * partitions, so did_remapping should be left alone.
         */
        Assert(!outer_map.did_remapping);
        Assert(!inner_map.did_remapping);
 
        /* Use maps to match partitions from inputs. */
        generate_matching_part_pairs(outer_rel, inner_rel,
                                     &outer_map, &inner_map,
                                     next_index,
                                     outer_parts, inner_parts);
        Assert(*outer_parts != NIL);
        Assert(*inner_parts != NIL);
        Assert(list_length(*outer_parts) == list_length(*inner_parts));
        Assert(list_length(*outer_parts) == next_index);
 
        /* Make a PartitionBoundInfo struct to return. */
        merged_bounds = build_merged_partition_bounds(outer_bi->strategy,
                                                      merged_datums,
                                                      merged_kinds,
                                                      merged_indexes,
                                                      -1,
                                                      default_index);
        Assert(merged_bounds);
    }
 
cleanup:
    /* Free local memory before returning. */
    list_free(merged_datums);
    list_free(merged_kinds);
    list_free(merged_indexes);
    free_partition_map(&outer_map);
    free_partition_map(&inner_map);
 
    return merged_bounds;
}
 
/*
 * init_partition_map
 *      Initialize a PartitionMap struct for given relation
 */
static void
init_partition_map(RelOptInfo *rel, PartitionMap *map)
{
    int         nparts = rel->nparts;
    int         i;
 
    map->nparts = nparts;
    map->merged_indexes = palloc_array(int, nparts);
    map->merged = palloc_array(bool, nparts);
    map->did_remapping = false;
    map->old_indexes = palloc_array(int, nparts);
    for (i = 0; i < nparts; i++)
    {
        map->merged_indexes[i] = map->old_indexes[i] = -1;
        map->merged[i] = false;
    }
}
 
/*
 * free_partition_map
 */
static void
free_partition_map(PartitionMap *map)
{
    pfree(map->merged_indexes);
    pfree(map->merged);
    pfree(map->old_indexes);
}
 
/*
 * is_dummy_partition --- has partition been proven empty?
 */
static bool
is_dummy_partition(RelOptInfo *rel, int part_index)
{
    RelOptInfo *part_rel;
 
    Assert(part_index >= 0);
    part_rel = rel->part_rels[part_index];
    if (part_rel == NULL || IS_DUMMY_REL(part_rel))
        return true;
    return false;
}
 
/*
 * merge_matching_partitions
 *      Try to merge given outer/inner partitions, and return the index of a
 *      merged partition produced from them if successful, -1 otherwise
 *
 * If the merged partition is newly created, *next_index is incremented.
 */
static int
merge_matching_partitions(PartitionMap *outer_map, PartitionMap *inner_map,
                          int outer_index, int inner_index, int *next_index)
{
    int         outer_merged_index;
    int         inner_merged_index;
    bool        outer_merged;
    bool        inner_merged;
 
    Assert(outer_index >= 0 && outer_index < outer_map->nparts);
    outer_merged_index = outer_map->merged_indexes[outer_index];
    outer_merged = outer_map->merged[outer_index];
    Assert(inner_index >= 0 && inner_index < inner_map->nparts);
    inner_merged_index = inner_map->merged_indexes[inner_index];
    inner_merged = inner_map->merged[inner_index];
 
    /*
     * Handle cases where we have already assigned a merged partition to each
     * of the given partitions.
     */
    if (outer_merged_index >= 0 && inner_merged_index >= 0)
    {
        /*
         * If the merged partitions are the same, no need to do anything;
         * return the index of the merged partitions.  Otherwise, if each of
         * the given partitions has been merged with a dummy partition on the
         * other side, re-map them to either of the two merged partitions.
         * Otherwise, they can't be merged, so return -1.
         */
        if (outer_merged_index == inner_merged_index)
        {
            Assert(outer_merged);
            Assert(inner_merged);
            return outer_merged_index;
        }
        if (!outer_merged && !inner_merged)
        {
            /*
             * This can only happen for a list-partitioning case.  We re-map
             * them to the merged partition with the smaller of the two merged
             * indexes to preserve the property that the canonical order of
             * list partitions is determined by the indexes assigned to the
             * smallest list value of each partition.
             */
            if (outer_merged_index < inner_merged_index)
            {
                outer_map->merged[outer_index] = true;
                inner_map->merged_indexes[inner_index] = outer_merged_index;
                inner_map->merged[inner_index] = true;
                inner_map->did_remapping = true;
                inner_map->old_indexes[inner_index] = inner_merged_index;
                return outer_merged_index;
            }
            else
            {
                inner_map->merged[inner_index] = true;
                outer_map->merged_indexes[outer_index] = inner_merged_index;
                outer_map->merged[outer_index] = true;
                outer_map->did_remapping = true;
                outer_map->old_indexes[outer_index] = outer_merged_index;
                return inner_merged_index;
            }
        }
        return -1;
    }
 
    /* At least one of the given partitions should not have yet been merged. */
    Assert(outer_merged_index == -1 || inner_merged_index == -1);
 
    /*
     * If neither of them has been merged, merge them.  Otherwise, if one has
     * been merged with a dummy partition on the other side (and the other
     * hasn't yet been merged with anything), re-merge them.  Otherwise, they
     * can't be merged, so return -1.
     */
    if (outer_merged_index == -1 && inner_merged_index == -1)
    {
        int         merged_index = *next_index;
 
        Assert(!outer_merged);
        Assert(!inner_merged);
        outer_map->merged_indexes[outer_index] = merged_index;
        outer_map->merged[outer_index] = true;
        inner_map->merged_indexes[inner_index] = merged_index;
        inner_map->merged[inner_index] = true;
        *next_index = *next_index + 1;
        return merged_index;
    }
    if (outer_merged_index >= 0 && !outer_map->merged[outer_index])
    {
        Assert(inner_merged_index == -1);
        Assert(!inner_merged);
        inner_map->merged_indexes[inner_index] = outer_merged_index;
        inner_map->merged[inner_index] = true;
        outer_map->merged[outer_index] = true;
        return outer_merged_index;
    }
    if (inner_merged_index >= 0 && !inner_map->merged[inner_index])
    {
        Assert(outer_merged_index == -1);
        Assert(!outer_merged);
        outer_map->merged_indexes[outer_index] = inner_merged_index;
        outer_map->merged[outer_index] = true;
        inner_map->merged[inner_index] = true;
        return inner_merged_index;
    }
    return -1;
}
 
/*
 * process_outer_partition
 *      Try to assign given outer partition a merged partition, and return the
 *      index of the merged partition if successful, -1 otherwise
 *
 * If the partition is newly created, *next_index is incremented.  Also, if it
 * is the default partition of the join relation, *default_index is set to the
 * index if not already done.
 */
static int
process_outer_partition(PartitionMap *outer_map,
                        PartitionMap *inner_map,
                        bool outer_has_default,
                        bool inner_has_default,
                        int outer_index,
                        int inner_default,
                        JoinType jointype,
                        int *next_index,
                        int *default_index)
{
    int         merged_index = -1;
 
    Assert(outer_index >= 0);
 
    /*
     * If the inner side has the default partition, a row from the outer
     * partition might find its join partner in the default partition; try
     * merging the outer partition with the default partition.  Otherwise,
     * this should be an outer join, in which case the outer partition has to
     * be scanned all the way anyway; merge the outer partition with a dummy
     * partition on the other side.
     */
    if (inner_has_default)
    {
        Assert(inner_default >= 0);
 
        /*
         * If the outer side has the default partition as well, the default
         * partition on the inner side will have two matching partitions on
         * the other side: the outer partition and the default partition on
         * the outer side.  Partitionwise join doesn't handle this scenario
         * yet.
         */
        if (outer_has_default)
            return -1;
 
        merged_index = merge_matching_partitions(outer_map, inner_map,
                                                 outer_index, inner_default,
                                                 next_index);
        if (merged_index == -1)
            return -1;
 
        /*
         * If this is a FULL join, the default partition on the inner side has
         * to be scanned all the way anyway, so the resulting partition will
         * contain all key values from the default partition, which any other
         * partition of the join relation will not contain.  Thus the
         * resulting partition will act as the default partition of the join
         * relation; record the index in *default_index if not already done.
         */
        if (jointype == JOIN_FULL)
        {
            if (*default_index == -1)
                *default_index = merged_index;
            else
                Assert(*default_index == merged_index);
        }
    }
    else
    {
        Assert(IS_OUTER_JOIN(jointype));
        Assert(jointype != JOIN_RIGHT);
 
        /* If we have already assigned a partition, no need to do anything. */
        merged_index = outer_map->merged_indexes[outer_index];
        if (merged_index == -1)
            merged_index = merge_partition_with_dummy(outer_map, outer_index,
                                                      next_index);
    }
    return merged_index;
}
 
/*
 * process_inner_partition
 *      Try to assign given inner partition a merged partition, and return the
 *      index of the merged partition if successful, -1 otherwise
 *
 * If the partition is newly created, *next_index is incremented.  Also, if it
 * is the default partition of the join relation, *default_index is set to the
 * index if not already done.
 */
static int
process_inner_partition(PartitionMap *outer_map,
                        PartitionMap *inner_map,
                        bool outer_has_default,
                        bool inner_has_default,
                        int inner_index,
                        int outer_default,
                        JoinType jointype,
                        int *next_index,
                        int *default_index)
{
    int         merged_index = -1;
 
    Assert(inner_index >= 0);
 
    /*
     * If the outer side has the default partition, a row from the inner
     * partition might find its join partner in the default partition; try
     * merging the inner partition with the default partition.  Otherwise,
     * this should be a FULL join, in which case the inner partition has to be
     * scanned all the way anyway; merge the inner partition with a dummy
     * partition on the other side.
     */
    if (outer_has_default)
    {
        Assert(outer_default >= 0);
 
        /*
         * If the inner side has the default partition as well, the default
         * partition on the outer side will have two matching partitions on
         * the other side: the inner partition and the default partition on
         * the inner side.  Partitionwise join doesn't handle this scenario
         * yet.
         */
        if (inner_has_default)
            return -1;
 
        merged_index = merge_matching_partitions(outer_map, inner_map,
                                                 outer_default, inner_index,
                                                 next_index);
        if (merged_index == -1)
            return -1;
 
        /*
         * If this is an outer join, the default partition on the outer side
         * has to be scanned all the way anyway, so the resulting partition
         * will contain all key values from the default partition, which any
         * other partition of the join relation will not contain.  Thus the
         * resulting partition will act as the default partition of the join
         * relation; record the index in *default_index if not already done.
         */
        if (IS_OUTER_JOIN(jointype))
        {
            Assert(jointype != JOIN_RIGHT);
            if (*default_index == -1)
                *default_index = merged_index;
            else
                Assert(*default_index == merged_index);
        }
    }
    else
    {
        Assert(jointype == JOIN_FULL);
 
        /* If we have already assigned a partition, no need to do anything. */
        merged_index = inner_map->merged_indexes[inner_index];
        if (merged_index == -1)
            merged_index = merge_partition_with_dummy(inner_map, inner_index,
                                                      next_index);
    }
    return merged_index;
}
 
/*
 * merge_null_partitions
 *      Merge the NULL partitions from a join's outer and inner sides.
 *
 * If the merged partition produced from them is the NULL partition of the join
 * relation, *null_index is set to the index of the merged partition.
 *
 * Note: We assume here that the join clause for a partitioned join is strict
 * because have_partkey_equi_join() requires that the corresponding operator
 * be mergejoinable, and we currently assume that mergejoinable operators are
 * strict (see MJEvalOuterValues()/MJEvalInnerValues()).
 */
static void
merge_null_partitions(PartitionMap *outer_map,
                      PartitionMap *inner_map,
                      bool outer_has_null,
                      bool inner_has_null,
                      int outer_null,
                      int inner_null,
                      JoinType jointype,
                      int *next_index,
                      int *null_index)
{
    bool        consider_outer_null = false;
    bool        consider_inner_null = false;
 
    Assert(outer_has_null || inner_has_null);
    Assert(*null_index == -1);
 
    /*
     * Check whether the NULL partitions have already been merged and if so,
     * set the consider_outer_null/consider_inner_null flags.
     */
    if (outer_has_null)
    {
        Assert(outer_null >= 0 && outer_null < outer_map->nparts);
        if (outer_map->merged_indexes[outer_null] == -1)
            consider_outer_null = true;
    }
    if (inner_has_null)
    {
        Assert(inner_null >= 0 && inner_null < inner_map->nparts);
        if (inner_map->merged_indexes[inner_null] == -1)
            consider_inner_null = true;
    }
 
    /* If both flags are set false, we don't need to do anything. */
    if (!consider_outer_null && !consider_inner_null)
        return;
 
    if (consider_outer_null && !consider_inner_null)
    {
        Assert(outer_has_null);
 
        /*
         * If this is an outer join, the NULL partition on the outer side has
         * to be scanned all the way anyway; merge the NULL partition with a
         * dummy partition on the other side.  In that case
         * consider_outer_null means that the NULL partition only contains
         * NULL values as the key values, so the merged partition will do so;
         * treat it as the NULL partition of the join relation.
         */
        if (IS_OUTER_JOIN(jointype))
        {
            Assert(jointype != JOIN_RIGHT);
            *null_index = merge_partition_with_dummy(outer_map, outer_null,
                                                     next_index);
        }
    }
    else if (!consider_outer_null && consider_inner_null)
    {
        Assert(inner_has_null);
 
        /*
         * If this is a FULL join, the NULL partition on the inner side has to
         * be scanned all the way anyway; merge the NULL partition with a
         * dummy partition on the other side.  In that case
         * consider_inner_null means that the NULL partition only contains
         * NULL values as the key values, so the merged partition will do so;
         * treat it as the NULL partition of the join relation.
         */
        if (jointype == JOIN_FULL)
            *null_index = merge_partition_with_dummy(inner_map, inner_null,
                                                     next_index);
    }
    else
    {
        Assert(consider_outer_null && consider_inner_null);
        Assert(outer_has_null);
        Assert(inner_has_null);
 
        /*
         * If this is an outer join, the NULL partition on the outer side (and
         * that on the inner side if this is a FULL join) have to be scanned
         * all the way anyway, so merge them.  Note that each of the NULL
         * partitions isn't merged yet, so they should be merged successfully.
         * Like the above, each of the NULL partitions only contains NULL
         * values as the key values, so the merged partition will do so; treat
         * it as the NULL partition of the join relation.
         *
         * Note: if this an INNER/SEMI join, the join clause will never be
         * satisfied by two NULL values (see comments above), so both the NULL
         * partitions can be eliminated.
         */
        if (IS_OUTER_JOIN(jointype))
        {
            Assert(jointype != JOIN_RIGHT);
            *null_index = merge_matching_partitions(outer_map, inner_map,
                                                    outer_null, inner_null,
                                                    next_index);
            Assert(*null_index >= 0);
        }
    }
}
 
/*
 * merge_default_partitions
 *      Merge the default partitions from a join's outer and inner sides.
 *
 * If the merged partition produced from them is the default partition of the
 * join relation, *default_index is set to the index of the merged partition.
 */
static void
merge_default_partitions(PartitionMap *outer_map,
                         PartitionMap *inner_map,
                         bool outer_has_default,
                         bool inner_has_default,
                         int outer_default,
                         int inner_default,
                         JoinType jointype,
                         int *next_index,
                         int *default_index)
{
    int         outer_merged_index = -1;
    int         inner_merged_index = -1;
 
    Assert(outer_has_default || inner_has_default);
 
    /* Get the merged partition indexes for the default partitions. */
    if (outer_has_default)
    {
        Assert(outer_default >= 0 && outer_default < outer_map->nparts);
        outer_merged_index = outer_map->merged_indexes[outer_default];
    }
    if (inner_has_default)
    {
        Assert(inner_default >= 0 && inner_default < inner_map->nparts);
        inner_merged_index = inner_map->merged_indexes[inner_default];
    }
 
    if (outer_has_default && !inner_has_default)
    {
        /*
         * If this is an outer join, the default partition on the outer side
         * has to be scanned all the way anyway; if we have not yet assigned a
         * partition, merge the default partition with a dummy partition on
         * the other side.  The merged partition will act as the default
         * partition of the join relation (see comments in
         * process_inner_partition()).
         */
        if (IS_OUTER_JOIN(jointype))
        {
            Assert(jointype != JOIN_RIGHT);
            if (outer_merged_index == -1)
            {
                Assert(*default_index == -1);
                *default_index = merge_partition_with_dummy(outer_map,
                                                            outer_default,
                                                            next_index);
            }
            else
                Assert(*default_index == outer_merged_index);
        }
        else
            Assert(*default_index == -1);
    }
    else if (!outer_has_default && inner_has_default)
    {
        /*
         * If this is a FULL join, the default partition on the inner side has
         * to be scanned all the way anyway; if we have not yet assigned a
         * partition, merge the default partition with a dummy partition on
         * the other side.  The merged partition will act as the default
         * partition of the join relation (see comments in
         * process_outer_partition()).
         */
        if (jointype == JOIN_FULL)
        {
            if (inner_merged_index == -1)
            {
                Assert(*default_index == -1);
                *default_index = merge_partition_with_dummy(inner_map,
                                                            inner_default,
                                                            next_index);
            }
            else
                Assert(*default_index == inner_merged_index);
        }
        else
            Assert(*default_index == -1);
    }
    else
    {
        Assert(outer_has_default && inner_has_default);
 
        /*
         * The default partitions have to be joined with each other, so merge
         * them.  Note that each of the default partitions isn't merged yet
         * (see, process_outer_partition()/process_inner_partition()), so they
         * should be merged successfully.  The merged partition will act as
         * the default partition of the join relation.
         */
        Assert(outer_merged_index == -1);
        Assert(inner_merged_index == -1);
        Assert(*default_index == -1);
        *default_index = merge_matching_partitions(outer_map,
                                                   inner_map,
                                                   outer_default,
                                                   inner_default,
                                                   next_index);
        Assert(*default_index >= 0);
    }
}
 
/*
 * merge_partition_with_dummy
 *      Assign given partition a new partition of a join relation
 *
 * Note: The caller assumes that the given partition doesn't have a non-dummy
 * matching partition on the other side, but if the given partition finds the
 * matching partition later, we will adjust the assignment.
 */
static int
merge_partition_with_dummy(PartitionMap *map, int index, int *next_index)
{
    int         merged_index = *next_index;
 
    Assert(index >= 0 && index < map->nparts);
    Assert(map->merged_indexes[index] == -1);
    Assert(!map->merged[index]);
    map->merged_indexes[index] = merged_index;
    /* Leave the merged flag alone! */
    *next_index = *next_index + 1;
    return merged_index;
}
 
/*
 * fix_merged_indexes
 *      Adjust merged indexes of re-merged partitions
 */
static void
fix_merged_indexes(PartitionMap *outer_map, PartitionMap *inner_map,
                   int nmerged, List *merged_indexes)
{
    int        *new_indexes;
    int         merged_index;
    int         i;
    ListCell   *lc;
 
    Assert(nmerged > 0);
 
    new_indexes = palloc_array(int, nmerged);
    for (i = 0; i < nmerged; i++)
        new_indexes[i] = -1;
 
    /* Build the mapping of old merged indexes to new merged indexes. */
    if (outer_map->did_remapping)
    {
        for (i = 0; i < outer_map->nparts; i++)
        {
            merged_index = outer_map->old_indexes[i];
            if (merged_index >= 0)
                new_indexes[merged_index] = outer_map->merged_indexes[i];
        }
    }
    if (inner_map->did_remapping)
    {
        for (i = 0; i < inner_map->nparts; i++)
        {
            merged_index = inner_map->old_indexes[i];
            if (merged_index >= 0)
                new_indexes[merged_index] = inner_map->merged_indexes[i];
        }
    }
 
    /* Fix the merged_indexes list using the mapping. */
    foreach(lc, merged_indexes)
    {
        merged_index = lfirst_int(lc);
        Assert(merged_index >= 0);
        if (new_indexes[merged_index] >= 0)
            lfirst_int(lc) = new_indexes[merged_index];
    }
 
    pfree(new_indexes);
}
 
/*
 * generate_matching_part_pairs
 *      Generate a pair of lists of partitions that produce merged partitions
 *
 * The lists of partitions are built in the order of merged partition indexes,
 * and returned in *outer_parts and *inner_parts.
 */
static void
generate_matching_part_pairs(RelOptInfo *outer_rel, RelOptInfo *inner_rel,
                             PartitionMap *outer_map, PartitionMap *inner_map,
                             int nmerged,
                             List **outer_parts, List **inner_parts)
{
    int         outer_nparts = outer_map->nparts;
    int         inner_nparts = inner_map->nparts;
    int        *outer_indexes;
    int        *inner_indexes;
    int         max_nparts;
    int         i;
 
    Assert(nmerged > 0);
    Assert(*outer_parts == NIL);
    Assert(*inner_parts == NIL);
 
    outer_indexes = palloc_array(int, nmerged);
    inner_indexes = palloc_array(int, nmerged);
    for (i = 0; i < nmerged; i++)
        outer_indexes[i] = inner_indexes[i] = -1;
 
    /* Set pairs of matching partitions. */
    Assert(outer_nparts == outer_rel->nparts);
    Assert(inner_nparts == inner_rel->nparts);
    max_nparts = Max(outer_nparts, inner_nparts);
    for (i = 0; i < max_nparts; i++)
    {
        if (i < outer_nparts)
        {
            int         merged_index = outer_map->merged_indexes[i];
 
            if (merged_index >= 0)
            {
                Assert(merged_index < nmerged);
                outer_indexes[merged_index] = i;
            }
        }
        if (i < inner_nparts)
        {
            int         merged_index = inner_map->merged_indexes[i];
 
            if (merged_index >= 0)
            {
                Assert(merged_index < nmerged);
                inner_indexes[merged_index] = i;
            }
        }
    }
 
    /* Build the list pairs. */
    for (i = 0; i < nmerged; i++)
    {
        int         outer_index = outer_indexes[i];
        int         inner_index = inner_indexes[i];
 
        /*
         * If both partitions are dummy, it means the merged partition that
         * had been assigned to the outer/inner partition was removed when
         * re-merging the outer/inner partition in
         * merge_matching_partitions(); ignore the merged partition.
         */
        if (outer_index == -1 && inner_index == -1)
            continue;
 
        *outer_parts = lappend(*outer_parts, outer_index >= 0 ?
                               outer_rel->part_rels[outer_index] : NULL);
        *inner_parts = lappend(*inner_parts, inner_index >= 0 ?
                               inner_rel->part_rels[inner_index] : NULL);
    }
 
    pfree(outer_indexes);
    pfree(inner_indexes);
}
 
/*
 * build_merged_partition_bounds
 *      Create a PartitionBoundInfo struct from merged partition bounds
 */
static PartitionBoundInfo
build_merged_partition_bounds(char strategy, List *merged_datums,
                              List *merged_kinds, List *merged_indexes,
                              int null_index, int default_index)
{
    PartitionBoundInfo merged_bounds;
    int         ndatums = list_length(merged_datums);
    int         pos;
    ListCell   *lc;
 
    merged_bounds = palloc_object(PartitionBoundInfoData);
    merged_bounds->strategy = strategy;
    merged_bounds->ndatums = ndatums;
 
    merged_bounds->datums = palloc_array(Datum *, ndatums);
    pos = 0;
    foreach(lc, merged_datums)
        merged_bounds->datums[pos++] = (Datum *) lfirst(lc);
 
    if (strategy == PARTITION_STRATEGY_RANGE)
    {
        Assert(list_length(merged_kinds) == ndatums);
        merged_bounds->kind = palloc_array(PartitionRangeDatumKind *, ndatums);
        pos = 0;
        foreach(lc, merged_kinds)
            merged_bounds->kind[pos++] = (PartitionRangeDatumKind *) lfirst(lc);
 
        /* There are ndatums+1 indexes in the case of range partitioning. */
        merged_indexes = lappend_int(merged_indexes, -1);
        ndatums++;
    }
    else
    {
        Assert(strategy == PARTITION_STRATEGY_LIST);
        Assert(merged_kinds == NIL);
        merged_bounds->kind = NULL;
    }
 
    /* interleaved_parts is always NULL for join relations. */
    merged_bounds->interleaved_parts = NULL;
 
    Assert(list_length(merged_indexes) == ndatums);
    merged_bounds->nindexes = ndatums;
    merged_bounds->indexes = palloc_array(int, ndatums);
    pos = 0;
    foreach(lc, merged_indexes)
        merged_bounds->indexes[pos++] = lfirst_int(lc);
 
    merged_bounds->null_index = null_index;
    merged_bounds->default_index = default_index;
 
    return merged_bounds;
}
 
/*
 * get_range_partition
 *      Get the next non-dummy partition of a range-partitioned relation,
 *      returning the index of that partition
 *
 * *lb and *ub are set to the lower and upper bounds of that partition
 * respectively, and *lb_pos is advanced to the next lower bound, if any.
 */
static int
get_range_partition(RelOptInfo *rel,
                    PartitionBoundInfo bi,
                    int *lb_pos,
                    PartitionRangeBound *lb,
                    PartitionRangeBound *ub)
{
    int         part_index;
 
    Assert(bi->strategy == PARTITION_STRATEGY_RANGE);
 
    do
    {
        part_index = get_range_partition_internal(bi, lb_pos, lb, ub);
        if (part_index == -1)
            return -1;
    } while (is_dummy_partition(rel, part_index));
 
    return part_index;
}
 
static int
get_range_partition_internal(PartitionBoundInfo bi,
                             int *lb_pos,
                             PartitionRangeBound *lb,
                             PartitionRangeBound *ub)
{
    /* Return the index as -1 if we've exhausted all lower bounds. */
    if (*lb_pos >= bi->ndatums)
        return -1;
 
    /* A lower bound should have at least one more bound after it. */
    Assert(*lb_pos + 1 < bi->ndatums);
 
    /* Set the lower bound. */
    lb->index = bi->indexes[*lb_pos];
    lb->datums = bi->datums[*lb_pos];
    lb->kind = bi->kind[*lb_pos];
    lb->lower = true;
    /* Set the upper bound. */
    ub->index = bi->indexes[*lb_pos + 1];
    ub->datums = bi->datums[*lb_pos + 1];
    ub->kind = bi->kind[*lb_pos + 1];
    ub->lower = false;
 
    /* The index assigned to an upper bound should be valid. */
    Assert(ub->index >= 0);
 
    /*
     * Advance the position to the next lower bound.  If there are no bounds
     * left beyond the upper bound, we have reached the last lower bound.
     */
    if (*lb_pos + 2 >= bi->ndatums)
        *lb_pos = bi->ndatums;
    else
    {
        /*
         * If the index assigned to the bound next to the upper bound isn't
         * valid, that is the next lower bound; else, the upper bound is also
         * the lower bound of the next range partition.
         */
        if (bi->indexes[*lb_pos + 2] < 0)
            *lb_pos = *lb_pos + 2;
        else
            *lb_pos = *lb_pos + 1;
    }
 
    return ub->index;
}
 
/*
 * compare_range_partitions
 *      Compare the bounds of two range partitions, and return true if the
 *      two partitions overlap, false otherwise
 *
 * *lb_cmpval is set to -1, 0, or 1 if the outer partition's lower bound is
 * lower than, equal to, or higher than the inner partition's lower bound
 * respectively.  Likewise, *ub_cmpval is set to -1, 0, or 1 if the outer
 * partition's upper bound is lower than, equal to, or higher than the inner
 * partition's upper bound respectively.
 */
static bool
compare_range_partitions(int partnatts, FmgrInfo *partsupfuncs,
                         Oid *partcollations,
                         PartitionRangeBound *outer_lb,
                         PartitionRangeBound *outer_ub,
                         PartitionRangeBound *inner_lb,
                         PartitionRangeBound *inner_ub,
                         int *lb_cmpval, int *ub_cmpval)
{
    /*
     * Check if the outer partition's upper bound is lower than the inner
     * partition's lower bound; if so the partitions aren't overlapping.
     */
    if (compare_range_bounds(partnatts, partsupfuncs, partcollations,
                             outer_ub, inner_lb) < 0)
    {
        *lb_cmpval = -1;
        *ub_cmpval = -1;
        return false;
    }
 
    /*
     * Check if the outer partition's lower bound is higher than the inner
     * partition's upper bound; if so the partitions aren't overlapping.
     */
    if (compare_range_bounds(partnatts, partsupfuncs, partcollations,
                             outer_lb, inner_ub) > 0)
    {
        *lb_cmpval = 1;
        *ub_cmpval = 1;
        return false;
    }
 
    /* All other cases indicate overlapping partitions. */
    *lb_cmpval = compare_range_bounds(partnatts, partsupfuncs, partcollations,
                                      outer_lb, inner_lb);
    *ub_cmpval = compare_range_bounds(partnatts, partsupfuncs, partcollations,
                                      outer_ub, inner_ub);
    return true;
}
 
/*
 * get_merged_range_bounds
 *      Given the bounds of range partitions to be joined, determine the bounds
 *      of a merged partition produced from the range partitions
 *
 * *merged_lb and *merged_ub are set to the lower and upper bounds of the
 * merged partition.
 */
static void
get_merged_range_bounds(int partnatts, FmgrInfo *partsupfuncs,
                        Oid *partcollations, JoinType jointype,
                        PartitionRangeBound *outer_lb,
                        PartitionRangeBound *outer_ub,
                        PartitionRangeBound *inner_lb,
                        PartitionRangeBound *inner_ub,
                        int lb_cmpval, int ub_cmpval,
                        PartitionRangeBound *merged_lb,
                        PartitionRangeBound *merged_ub)
{
    Assert(compare_range_bounds(partnatts, partsupfuncs, partcollations,
                                outer_lb, inner_lb) == lb_cmpval);
    Assert(compare_range_bounds(partnatts, partsupfuncs, partcollations,
                                outer_ub, inner_ub) == ub_cmpval);
 
    switch (jointype)
    {
        case JOIN_INNER:
        case JOIN_SEMI:
 
            /*
             * An INNER/SEMI join will have the rows that fit both sides, so
             * the lower bound of the merged partition will be the higher of
             * the two lower bounds, and the upper bound of the merged
             * partition will be the lower of the two upper bounds.
             */
            *merged_lb = (lb_cmpval > 0) ? *outer_lb : *inner_lb;
            *merged_ub = (ub_cmpval < 0) ? *outer_ub : *inner_ub;
            break;
 
        case JOIN_LEFT:
        case JOIN_ANTI:
 
            /*
             * A LEFT/ANTI join will have all the rows from the outer side, so
             * the bounds of the merged partition will be the same as the
             * outer bounds.
             */
            *merged_lb = *outer_lb;
            *merged_ub = *outer_ub;
            break;
 
        case JOIN_FULL:
 
            /*
             * A FULL join will have all the rows from both sides, so the
             * lower bound of the merged partition will be the lower of the
             * two lower bounds, and the upper bound of the merged partition
             * will be the higher of the two upper bounds.
             */
            *merged_lb = (lb_cmpval < 0) ? *outer_lb : *inner_lb;
            *merged_ub = (ub_cmpval > 0) ? *outer_ub : *inner_ub;
            break;
 
        default:
            elog(ERROR, "unrecognized join type: %d", (int) jointype);
    }
}
 
/*
 * add_merged_range_bounds
 *      Add the bounds of a merged partition to the lists of range bounds
 */
static void
add_merged_range_bounds(int partnatts, FmgrInfo *partsupfuncs,
                        Oid *partcollations,
                        PartitionRangeBound *merged_lb,
                        PartitionRangeBound *merged_ub,
                        int merged_index,
                        List **merged_datums,
                        List **merged_kinds,
                        List **merged_indexes)
{
    int         cmpval;
 
    if (!*merged_datums)
    {
        /* First merged partition */
        Assert(!*merged_kinds);
        Assert(!*merged_indexes);
        cmpval = 1;
    }
    else
    {
        PartitionRangeBound prev_ub;
 
        Assert(*merged_datums);
        Assert(*merged_kinds);
        Assert(*merged_indexes);
 
        /* Get the last upper bound. */
        prev_ub.index = llast_int(*merged_indexes);
        prev_ub.datums = (Datum *) llast(*merged_datums);
        prev_ub.kind = (PartitionRangeDatumKind *) llast(*merged_kinds);
        prev_ub.lower = false;
 
        /*
         * We pass lower1 = false to partition_rbound_cmp() to prevent it from
         * considering the last upper bound to be smaller than the lower bound
         * of the merged partition when the values of the two range bounds
         * compare equal.
         */
        cmpval = partition_rbound_cmp(partnatts, partsupfuncs, partcollations,
                                      merged_lb->datums, merged_lb->kind,
                                      false, &prev_ub);
        Assert(cmpval >= 0);
    }
 
    /*
     * If the lower bound is higher than the last upper bound, add the lower
     * bound with the index as -1 indicating that that is a lower bound; else,
     * the last upper bound will be reused as the lower bound of the merged
     * partition, so skip this.
     */
    if (cmpval > 0)
    {
        *merged_datums = lappend(*merged_datums, merged_lb->datums);
        *merged_kinds = lappend(*merged_kinds, merged_lb->kind);
        *merged_indexes = lappend_int(*merged_indexes, -1);
    }
 
    /* Add the upper bound and index of the merged partition. */
    *merged_datums = lappend(*merged_datums, merged_ub->datums);
    *merged_kinds = lappend(*merged_kinds, merged_ub->kind);
    *merged_indexes = lappend_int(*merged_indexes, merged_index);
}
 
/*
 * partitions_are_ordered
 *      Determine whether the partitions described by 'boundinfo' are ordered,
 *      that is partitions appearing earlier in the PartitionDesc sequence
 *      contain partition keys strictly less than those appearing later.
 *      Also, if NULL values are possible, they must come in the last
 *      partition defined in the PartitionDesc.  'live_parts' marks which
 *      partitions we should include when checking the ordering.  Partitions
 *      that do not appear in 'live_parts' are ignored.
 *
 * If out of order, or there is insufficient info to know the order,
 * then we return false.
 */
bool
partitions_are_ordered(PartitionBoundInfo boundinfo, Bitmapset *live_parts)
{
    Assert(boundinfo != NULL);
 
    switch (boundinfo->strategy)
    {
        case PARTITION_STRATEGY_RANGE:
 
            /*
             * RANGE-type partitioning guarantees that the partitions can be
             * scanned in the order that they're defined in the PartitionDesc
             * to provide sequential, non-overlapping ranges of tuples.
             * However, if a DEFAULT partition exists and it's contained
             * within live_parts, then the partitions are not ordered.
             */
            if (!partition_bound_has_default(boundinfo) ||
                !bms_is_member(boundinfo->default_index, live_parts))
                return true;
            break;
 
        case PARTITION_STRATEGY_LIST:
 
            /*
             * LIST partitioned are ordered providing none of live_parts
             * overlap with the partitioned table's interleaved partitions.
             */
            if (!bms_overlap(live_parts, boundinfo->interleaved_parts))
                return true;
 
            break;
        case PARTITION_STRATEGY_HASH:
            break;
    }
 
    return false;
}
 
/*
 * check_new_partition_bound
 *
 * Checks if the new partition's bound overlaps any of the existing partitions
 * of parent.  Also performs additional checks as necessary per strategy.
 */
void
check_new_partition_bound(char *relname, Relation parent,
                          PartitionBoundSpec *spec, ParseState *pstate)
{
    PartitionKey key = RelationGetPartitionKey(parent);
    PartitionDesc partdesc = RelationGetPartitionDesc(parent, false);
    PartitionBoundInfo boundinfo = partdesc->boundinfo;
    int         with = -1;
    bool        overlap = false;
    int         overlap_location = -1;
 
    if (spec->is_default)
    {
        /*
         * The default partition bound never conflicts with any other
         * partition's; if that's what we're attaching, the only possible
         * problem is that one already exists, so check for that and we're
         * done.
         */
        if (boundinfo == NULL || !partition_bound_has_default(boundinfo))
            return;
 
        /* Default partition already exists, error out. */
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                 errmsg("partition \"%s\" conflicts with existing default partition \"%s\"",
                        relname, get_rel_name(partdesc->oids[boundinfo->default_index])),
                 parser_errposition(pstate, spec->location)));
    }
 
    switch (key->strategy)
    {
        case PARTITION_STRATEGY_HASH:
            {
                Assert(spec->strategy == PARTITION_STRATEGY_HASH);
                Assert(spec->remainder >= 0 && spec->remainder < spec->modulus);
 
                if (partdesc->nparts > 0)
                {
                    int         greatest_modulus;
                    int         remainder;
                    int         offset;
 
                    /*
                     * Check rule that every modulus must be a factor of the
                     * next larger modulus.  (For example, if you have a bunch
                     * of partitions that all have modulus 5, you can add a
                     * new partition with modulus 10 or a new partition with
                     * modulus 15, but you cannot add both a partition with
                     * modulus 10 and a partition with modulus 15, because 10
                     * is not a factor of 15.)  We need only check the next
                     * smaller and next larger existing moduli, relying on
                     * previous enforcement of this rule to be sure that the
                     * rest are in line.
                     */
 
                    /*
                     * Get the greatest (modulus, remainder) pair contained in
                     * boundinfo->datums that is less than or equal to the
                     * (spec->modulus, spec->remainder) pair.
                     */
                    offset = partition_hash_bsearch(boundinfo,
                                                    spec->modulus,
                                                    spec->remainder);
                    if (offset < 0)
                    {
                        int         next_modulus;
 
                        /*
                         * All existing moduli are greater or equal, so the
                         * new one must be a factor of the smallest one, which
                         * is first in the boundinfo.
                         */
                        next_modulus = DatumGetInt32(boundinfo->datums[0][0]);
                        if (next_modulus % spec->modulus != 0)
                            ereport(ERROR,
                                    (errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                                     errmsg("every hash partition modulus must be a factor of the next larger modulus"),
                                     errdetail("The new modulus %d is not a factor of %d, the modulus of existing partition \"%s\".",
                                               spec->modulus, next_modulus,
                                               get_rel_name(partdesc->oids[0]))));
                    }
                    else
                    {
                        int         prev_modulus;
 
                        /*
                         * We found the largest (modulus, remainder) pair less
                         * than or equal to the new one.  That modulus must be
                         * a divisor of, or equal to, the new modulus.
                         */
                        prev_modulus = DatumGetInt32(boundinfo->datums[offset][0]);
 
                        if (spec->modulus % prev_modulus != 0)
                            ereport(ERROR,
                                    (errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                                     errmsg("every hash partition modulus must be a factor of the next larger modulus"),
                                     errdetail("The new modulus %d is not divisible by %d, the modulus of existing partition \"%s\".",
                                               spec->modulus,
                                               prev_modulus,
                                               get_rel_name(partdesc->oids[offset]))));
 
                        if (offset + 1 < boundinfo->ndatums)
                        {
                            int         next_modulus;
 
                            /*
                             * Look at the next higher (modulus, remainder)
                             * pair.  That could have the same modulus and a
                             * larger remainder than the new pair, in which
                             * case we're good.  If it has a larger modulus,
                             * the new modulus must divide that one.
                             */
                            next_modulus = DatumGetInt32(boundinfo->datums[offset + 1][0]);
 
                            if (next_modulus % spec->modulus != 0)
                                ereport(ERROR,
                                        (errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                                         errmsg("every hash partition modulus must be a factor of the next larger modulus"),
                                         errdetail("The new modulus %d is not a factor of %d, the modulus of existing partition \"%s\".",
                                                   spec->modulus, next_modulus,
                                                   get_rel_name(partdesc->oids[offset + 1]))));
                        }
                    }
 
                    greatest_modulus = boundinfo->nindexes;
                    remainder = spec->remainder;
 
                    /*
                     * Normally, the lowest remainder that could conflict with
                     * the new partition is equal to the remainder specified
                     * for the new partition, but when the new partition has a
                     * modulus higher than any used so far, we need to adjust.
                     */
                    if (remainder >= greatest_modulus)
                        remainder = remainder % greatest_modulus;
 
                    /* Check every potentially-conflicting remainder. */
                    do
                    {
                        if (boundinfo->indexes[remainder] != -1)
                        {
                            overlap = true;
                            overlap_location = spec->location;
                            with = boundinfo->indexes[remainder];
                            break;
                        }
                        remainder += spec->modulus;
                    } while (remainder < greatest_modulus);
                }
 
                break;
            }
 
        case PARTITION_STRATEGY_LIST:
            {
                Assert(spec->strategy == PARTITION_STRATEGY_LIST);
 
                if (partdesc->nparts > 0)
                {
                    ListCell   *cell;
 
                    Assert(boundinfo &&
                           boundinfo->strategy == PARTITION_STRATEGY_LIST &&
                           (boundinfo->ndatums > 0 ||
                            partition_bound_accepts_nulls(boundinfo) ||
                            partition_bound_has_default(boundinfo)));
 
                    foreach(cell, spec->listdatums)
                    {
                        Const      *val = lfirst_node(Const, cell);
 
                        overlap_location = val->location;
                        if (!val->constisnull)
                        {
                            int         offset;
                            bool        equal;
 
                            offset = partition_list_bsearch(&key->partsupfunc[0],
                                                            key->partcollation,
                                                            boundinfo,
                                                            val->constvalue,
                                                            &equal);
                            if (offset >= 0 && equal)
                            {
                                overlap = true;
                                with = boundinfo->indexes[offset];
                                break;
                            }
                        }
                        else if (partition_bound_accepts_nulls(boundinfo))
                        {
                            overlap = true;
                            with = boundinfo->null_index;
                            break;
                        }
                    }
                }
 
                break;
            }
 
        case PARTITION_STRATEGY_RANGE:
            {
                PartitionRangeBound *lower,
                           *upper;
                int         cmpval;
 
                Assert(spec->strategy == PARTITION_STRATEGY_RANGE);
                lower = make_one_partition_rbound(key, -1, spec->lowerdatums, true);
                upper = make_one_partition_rbound(key, -1, spec->upperdatums, false);
 
                /*
                 * First check if the resulting range would be empty with
                 * specified lower and upper bounds.  partition_rbound_cmp
                 * cannot return zero here, since the lower-bound flags are
                 * different.
                 */
                cmpval = partition_rbound_cmp(key->partnatts,
                                              key->partsupfunc,
                                              key->partcollation,
                                              lower->datums, lower->kind,
                                              true, upper);
                Assert(cmpval != 0);
                if (cmpval > 0)
                {
                    /* Point to problematic key in the lower datums list. */
                    PartitionRangeDatum *datum = list_nth(spec->lowerdatums,
                                                          cmpval - 1);
 
                    ereport(ERROR,
                            (errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                             errmsg("empty range bound specified for partition \"%s\"",
                                    relname),
                             errdetail("Specified lower bound %s is greater than or equal to upper bound %s.",
                                       get_range_partbound_string(spec->lowerdatums),
                                       get_range_partbound_string(spec->upperdatums)),
                             parser_errposition(pstate, datum->location)));
                }
 
                if (partdesc->nparts > 0)
                {
                    int         offset;
 
                    Assert(boundinfo &&
                           boundinfo->strategy == PARTITION_STRATEGY_RANGE &&
                           (boundinfo->ndatums > 0 ||
                            partition_bound_has_default(boundinfo)));
 
                    /*
                     * Test whether the new lower bound (which is treated
                     * inclusively as part of the new partition) lies inside
                     * an existing partition, or in a gap.
                     *
                     * If it's inside an existing partition, the bound at
                     * offset + 1 will be the upper bound of that partition,
                     * and its index will be >= 0.
                     *
                     * If it's in a gap, the bound at offset + 1 will be the
                     * lower bound of the next partition, and its index will
                     * be -1. This is also true if there is no next partition,
                     * since the index array is initialised with an extra -1
                     * at the end.
                     */
                    offset = partition_range_bsearch(key->partnatts,
                                                     key->partsupfunc,
                                                     key->partcollation,
                                                     boundinfo, lower,
                                                     &cmpval);
 
                    if (boundinfo->indexes[offset + 1] < 0)
                    {
                        /*
                         * Check that the new partition will fit in the gap.
                         * For it to fit, the new upper bound must be less
                         * than or equal to the lower bound of the next
                         * partition, if there is one.
                         */
                        if (offset + 1 < boundinfo->ndatums)
                        {
                            Datum      *datums;
                            PartitionRangeDatumKind *kind;
                            bool        is_lower;
 
                            datums = boundinfo->datums[offset + 1];
                            kind = boundinfo->kind[offset + 1];
                            is_lower = (boundinfo->indexes[offset + 1] == -1);
 
                            cmpval = partition_rbound_cmp(key->partnatts,
                                                          key->partsupfunc,
                                                          key->partcollation,
                                                          datums, kind,
                                                          is_lower, upper);
                            if (cmpval < 0)
                            {
                                /*
                                 * Point to problematic key in the upper
                                 * datums list.
                                 */
                                PartitionRangeDatum *datum =
                                    list_nth(spec->upperdatums, abs(cmpval) - 1);
 
                                /*
                                 * The new partition overlaps with the
                                 * existing partition between offset + 1 and
                                 * offset + 2.
                                 */
                                overlap = true;
                                overlap_location = datum->location;
                                with = boundinfo->indexes[offset + 2];
                            }
                        }
                    }
                    else
                    {
                        /*
                         * The new partition overlaps with the existing
                         * partition between offset and offset + 1.
                         */
                        PartitionRangeDatum *datum;
 
                        /*
                         * Point to problematic key in the lower datums list;
                         * if we have equality, point to the first one.
                         */
                        datum = cmpval == 0 ? linitial(spec->lowerdatums) :
                            list_nth(spec->lowerdatums, abs(cmpval) - 1);
                        overlap = true;
                        overlap_location = datum->location;
                        with = boundinfo->indexes[offset + 1];
                    }
                }
 
                break;
            }
    }
 
    if (overlap)
    {
        Assert(with >= 0);
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                 errmsg("partition \"%s\" would overlap partition \"%s\"",
                        relname, get_rel_name(partdesc->oids[with])),
                 parser_errposition(pstate, overlap_location)));
    }
}
 
/*
 * check_default_partition_contents
 *
 * This function checks if there exists a row in the default partition that
 * would properly belong to the new partition being added.  If it finds one,
 * it throws an error.
 */
void
check_default_partition_contents(Relation parent, Relation default_rel,
                                 PartitionBoundSpec *new_spec)
{
    List       *new_part_constraints;
    List       *def_part_constraints;
    List       *all_parts;
    ListCell   *lc;
 
    new_part_constraints = (new_spec->strategy == PARTITION_STRATEGY_LIST)
        ? get_qual_for_list(parent, new_spec)
        : get_qual_for_range(parent, new_spec, false);
    def_part_constraints =
        get_proposed_default_constraint(new_part_constraints);
 
    /*
     * Map the Vars in the constraint expression from parent's attnos to
     * default_rel's.
     */
    def_part_constraints =
        map_partition_varattnos(def_part_constraints, 1, default_rel,
                                parent);
 
    /*
     * If the existing constraints on the default partition imply that it will
     * not contain any row that would belong to the new partition, we can
     * avoid scanning the default partition.
     */
    if (PartConstraintImpliedByRelConstraint(default_rel, def_part_constraints))
    {
        ereport(DEBUG1,
                (errmsg_internal("updated partition constraint for default partition \"%s\" is implied by existing constraints",
                                 RelationGetRelationName(default_rel))));
        return;
    }
 
    /*
     * Scan the default partition and its subpartitions, and check for rows
     * that do not satisfy the revised partition constraints.
     */
    if (default_rel->rd_rel->relkind == RELKIND_PARTITIONED_TABLE)
        all_parts = find_all_inheritors(RelationGetRelid(default_rel),
                                        AccessExclusiveLock, NULL);
    else
        all_parts = list_make1_oid(RelationGetRelid(default_rel));
 
    foreach(lc, all_parts)
    {
        Oid         part_relid = lfirst_oid(lc);
        Relation    part_rel;
        Expr       *partition_constraint;
        EState     *estate;
        ExprState  *partqualstate = NULL;
        Snapshot    snapshot;
        ExprContext *econtext;
        TableScanDesc scan;
        MemoryContext oldCxt;
        TupleTableSlot *tupslot;
 
        /* Lock already taken above. */
        if (part_relid != RelationGetRelid(default_rel))
        {
            part_rel = table_open(part_relid, NoLock);
 
            /*
             * Map the Vars in the constraint expression from default_rel's
             * the sub-partition's.
             */
            partition_constraint = make_ands_explicit(def_part_constraints);
            partition_constraint = (Expr *)
                map_partition_varattnos((List *) partition_constraint, 1,
                                        part_rel, default_rel);
 
            /*
             * If the partition constraints on default partition child imply
             * that it will not contain any row that would belong to the new
             * partition, we can avoid scanning the child table.
             */
            if (PartConstraintImpliedByRelConstraint(part_rel,
                                                     def_part_constraints))
            {
                ereport(DEBUG1,
                        (errmsg_internal("updated partition constraint for default partition \"%s\" is implied by existing constraints",
                                         RelationGetRelationName(part_rel))));
 
                table_close(part_rel, NoLock);
                continue;
            }
        }
        else
        {
            part_rel = default_rel;
            partition_constraint = make_ands_explicit(def_part_constraints);
        }
 
        /*
         * Only RELKIND_RELATION relations (i.e. leaf partitions) need to be
         * scanned.
         */
        if (part_rel->rd_rel->relkind != RELKIND_RELATION)
        {
            if (part_rel->rd_rel->relkind == RELKIND_FOREIGN_TABLE)
                ereport(WARNING,
                        (errcode(ERRCODE_CHECK_VIOLATION),
                         errmsg("skipped scanning foreign table \"%s\" which is a partition of default partition \"%s\"",
                                RelationGetRelationName(part_rel),
                                RelationGetRelationName(default_rel))));
 
            if (RelationGetRelid(default_rel) != RelationGetRelid(part_rel))
                table_close(part_rel, NoLock);
 
            continue;
        }
 
        estate = CreateExecutorState();
 
        /* Build expression execution states for partition check quals */
        partqualstate = ExecPrepareExpr(partition_constraint, estate);
 
        econtext = GetPerTupleExprContext(estate);
        snapshot = RegisterSnapshot(GetLatestSnapshot());
        tupslot = table_slot_create(part_rel, &estate->es_tupleTable);
        scan = table_beginscan(part_rel, snapshot, 0, NULL);
 
        /*
         * Switch to per-tuple memory context and reset it for each tuple
         * produced, so we don't leak memory.
         */
        oldCxt = MemoryContextSwitchTo(GetPerTupleMemoryContext(estate));
 
        while (table_scan_getnextslot(scan, ForwardScanDirection, tupslot))
        {
            econtext->ecxt_scantuple = tupslot;
 
            if (!ExecCheck(partqualstate, econtext))
                ereport(ERROR,
                        (errcode(ERRCODE_CHECK_VIOLATION),
                         errmsg("updated partition constraint for default partition \"%s\" would be violated by some row",
                                RelationGetRelationName(default_rel)),
                         errtable(default_rel)));
 
            ResetExprContext(econtext);
            CHECK_FOR_INTERRUPTS();
        }
 
        MemoryContextSwitchTo(oldCxt);
        table_endscan(scan);
        UnregisterSnapshot(snapshot);
        ExecDropSingleTupleTableSlot(tupslot);
        FreeExecutorState(estate);
 
        if (RelationGetRelid(default_rel) != RelationGetRelid(part_rel))
            table_close(part_rel, NoLock);  /* keep the lock until commit */
    }
}
 
/*
 * get_hash_partition_greatest_modulus
 *
 * Returns the greatest modulus of the hash partition bound.
 * This is no longer used in the core code, but we keep it around
 * in case external modules are using it.
 */
int
get_hash_partition_greatest_modulus(PartitionBoundInfo bound)
{
    Assert(bound && bound->strategy == PARTITION_STRATEGY_HASH);
    return bound->nindexes;
}
 
/*
 * make_one_partition_rbound
 *
 * Return a PartitionRangeBound given a list of PartitionRangeDatum elements
 * and a flag telling whether the bound is lower or not.  Made into a function
 * because there are multiple sites that want to use this facility.
 */
static PartitionRangeBound *
make_one_partition_rbound(PartitionKey key, int index, List *datums, bool lower)
{
    PartitionRangeBound *bound;
    ListCell   *lc;
    int         i;
 
    Assert(datums != NIL);
 
    bound = palloc0_object(PartitionRangeBound);
    bound->index = index;
    bound->datums = palloc0_array(Datum, key->partnatts);
    bound->kind = palloc0_array(PartitionRangeDatumKind, key->partnatts);
    bound->lower = lower;
 
    i = 0;
    foreach(lc, datums)
    {
        PartitionRangeDatum *datum = lfirst_node(PartitionRangeDatum, lc);
 
        /* What's contained in this range datum? */
        bound->kind[i] = datum->kind;
 
        if (datum->kind == PARTITION_RANGE_DATUM_VALUE)
        {
            Const      *val = castNode(Const, datum->value);
 
            if (val->constisnull)
                elog(ERROR, "invalid range bound datum");
            bound->datums[i] = val->constvalue;
        }
 
        i++;
    }
 
    return bound;
}
 
/*
 * partition_rbound_cmp
 *
 * For two range bounds this decides whether the 1st one (specified by
 * datums1, kind1, and lower1) is <, =, or > the bound specified in *b2.
 *
 * 0 is returned if they are equal, otherwise a non-zero integer whose sign
 * indicates the ordering, and whose absolute value gives the 1-based
 * partition key number of the first mismatching column.
 *
 * partnatts, partsupfunc and partcollation give the number of attributes in the
 * bounds to be compared, comparison function to be used and the collations of
 * attributes, respectively.
 *
 * Note that if the values of the two range bounds compare equal, then we take
 * into account whether they are upper or lower bounds, and an upper bound is
 * considered to be smaller than a lower bound. This is important to the way
 * that RelationBuildPartitionDesc() builds the PartitionBoundInfoData
 * structure, which only stores the upper bound of a common boundary between
 * two contiguous partitions.
 */
static int32
partition_rbound_cmp(int partnatts, FmgrInfo *partsupfunc,
                     Oid *partcollation,
                     Datum *datums1, PartitionRangeDatumKind *kind1,
                     bool lower1, PartitionRangeBound *b2)
{
    int32       colnum = 0;
    int32       cmpval = 0;     /* placate compiler */
    int         i;
    Datum      *datums2 = b2->datums;
    PartitionRangeDatumKind *kind2 = b2->kind;
    bool        lower2 = b2->lower;
 
    for (i = 0; i < partnatts; i++)
    {
        /* Track column number in case we need it for result */
        colnum++;
 
        /*
         * First, handle cases where the column is unbounded, which should not
         * invoke the comparison procedure, and should not consider any later
         * columns. Note that the PartitionRangeDatumKind enum elements
         * compare the same way as the values they represent.
         */
        if (kind1[i] < kind2[i])
            return -colnum;
        else if (kind1[i] > kind2[i])
            return colnum;
        else if (kind1[i] != PARTITION_RANGE_DATUM_VALUE)
        {
            /*
             * The column bounds are both MINVALUE or both MAXVALUE. No later
             * columns should be considered, but we still need to compare
             * whether they are upper or lower bounds.
             */
            break;
        }
 
        cmpval = DatumGetInt32(FunctionCall2Coll(&partsupfunc[i],
                                                 partcollation[i],
                                                 datums1[i],
                                                 datums2[i]));
        if (cmpval != 0)
            break;
    }
 
    /*
     * If the comparison is anything other than equal, we're done. If they
     * compare equal though, we still have to consider whether the boundaries
     * are inclusive or exclusive.  Exclusive one is considered smaller of the
     * two.
     */
    if (cmpval == 0 && lower1 != lower2)
        cmpval = lower1 ? 1 : -1;
 
    return cmpval == 0 ? 0 : (cmpval < 0 ? -colnum : colnum);
}
 
/*
 * partition_rbound_datum_cmp
 *
 * Return whether range bound (specified in rb_datums and rb_kind)
 * is <, =, or > partition key of tuple (tuple_datums)
 *
 * n_tuple_datums, partsupfunc and partcollation give number of attributes in
 * the bounds to be compared, comparison function to be used and the collations
 * of attributes resp.
 */
int32
partition_rbound_datum_cmp(FmgrInfo *partsupfunc, Oid *partcollation,
                           const Datum *rb_datums, PartitionRangeDatumKind *rb_kind,
                           const Datum *tuple_datums, int n_tuple_datums)
{
    int         i;
    int32       cmpval = -1;
 
    for (i = 0; i < n_tuple_datums; i++)
    {
        if (rb_kind[i] == PARTITION_RANGE_DATUM_MINVALUE)
            return -1;
        else if (rb_kind[i] == PARTITION_RANGE_DATUM_MAXVALUE)
            return 1;
 
        cmpval = DatumGetInt32(FunctionCall2Coll(&partsupfunc[i],
                                                 partcollation[i],
                                                 rb_datums[i],
                                                 tuple_datums[i]));
        if (cmpval != 0)
            break;
    }
 
    return cmpval;
}
 
/*
 * partition_hbound_cmp
 *
 * Compares modulus first, then remainder if modulus is equal.
 */
static int32
partition_hbound_cmp(int modulus1, int remainder1, int modulus2, int remainder2)
{
    if (modulus1 < modulus2)
        return -1;
    if (modulus1 > modulus2)
        return 1;
    if (modulus1 == modulus2 && remainder1 != remainder2)
        return (remainder1 > remainder2) ? 1 : -1;
    return 0;
}
 
/*
 * partition_list_bsearch
 *      Returns the index of the greatest bound datum that is less than equal
 *      to the given value or -1 if all of the bound datums are greater
 *
 * *is_equal is set to true if the bound datum at the returned index is equal
 * to the input value.
 */
int
partition_list_bsearch(FmgrInfo *partsupfunc, Oid *partcollation,
                       PartitionBoundInfo boundinfo,
                       Datum value, bool *is_equal)
{
    int         lo,
                hi,
                mid;
 
    lo = -1;
    hi = boundinfo->ndatums - 1;
    while (lo < hi)
    {
        int32       cmpval;
 
        mid = (lo + hi + 1) / 2;
        cmpval = DatumGetInt32(FunctionCall2Coll(&partsupfunc[0],
                                                 partcollation[0],
                                                 boundinfo->datums[mid][0],
                                                 value));
        if (cmpval <= 0)
        {
            lo = mid;
            *is_equal = (cmpval == 0);
            if (*is_equal)
                break;
        }
        else
            hi = mid - 1;
    }
 
    return lo;
}
 
/*
 * partition_range_bsearch
 *      Returns the index of the greatest range bound that is less than or
 *      equal to the given range bound or -1 if all of the range bounds are
 *      greater
 *
 * Upon return from this function, *cmpval is set to 0 if the bound at the
 * returned index matches the input range bound exactly, otherwise a
 * non-zero integer whose sign indicates the ordering, and whose absolute
 * value gives the 1-based partition key number of the first mismatching
 * column.
 */
static int
partition_range_bsearch(int partnatts, FmgrInfo *partsupfunc,
                        Oid *partcollation,
                        PartitionBoundInfo boundinfo,
                        PartitionRangeBound *probe, int32 *cmpval)
{
    int         lo,
                hi,
                mid;
 
    lo = -1;
    hi = boundinfo->ndatums - 1;
    while (lo < hi)
    {
        mid = (lo + hi + 1) / 2;
        *cmpval = partition_rbound_cmp(partnatts, partsupfunc,
                                       partcollation,
                                       boundinfo->datums[mid],
                                       boundinfo->kind[mid],
                                       (boundinfo->indexes[mid] == -1),
                                       probe);
        if (*cmpval <= 0)
        {
            lo = mid;
            if (*cmpval == 0)
                break;
        }
        else
            hi = mid - 1;
    }
 
    return lo;
}
 
/*
 * partition_range_datum_bsearch
 *      Returns the index of the greatest range bound that is less than or
 *      equal to the given tuple or -1 if all of the range bounds are greater
 *
 * *is_equal is set to true if the range bound at the returned index is equal
 * to the input tuple.
 */
int
partition_range_datum_bsearch(FmgrInfo *partsupfunc, Oid *partcollation,
                              PartitionBoundInfo boundinfo,
                              int nvalues, const Datum *values, bool *is_equal)
{
    int         lo,
                hi,
                mid;
 
    lo = -1;
    hi = boundinfo->ndatums - 1;
    while (lo < hi)
    {
        int32       cmpval;
 
        mid = (lo + hi + 1) / 2;
        cmpval = partition_rbound_datum_cmp(partsupfunc,
                                            partcollation,
                                            boundinfo->datums[mid],
                                            boundinfo->kind[mid],
                                            values,
                                            nvalues);
        if (cmpval <= 0)
        {
            lo = mid;
            *is_equal = (cmpval == 0);
 
            if (*is_equal)
                break;
        }
        else
            hi = mid - 1;
    }
 
    return lo;
}
 
/*
 * partition_hash_bsearch
 *      Returns the index of the greatest (modulus, remainder) pair that is
 *      less than or equal to the given (modulus, remainder) pair or -1 if
 *      all of them are greater
 */
int
partition_hash_bsearch(PartitionBoundInfo boundinfo,
                       int modulus, int remainder)
{
    int         lo,
                hi,
                mid;
 
    lo = -1;
    hi = boundinfo->ndatums - 1;
    while (lo < hi)
    {
        int32       cmpval,
                    bound_modulus,
                    bound_remainder;
 
        mid = (lo + hi + 1) / 2;
        bound_modulus = DatumGetInt32(boundinfo->datums[mid][0]);
        bound_remainder = DatumGetInt32(boundinfo->datums[mid][1]);
        cmpval = partition_hbound_cmp(bound_modulus, bound_remainder,
                                      modulus, remainder);
        if (cmpval <= 0)
        {
            lo = mid;
 
            if (cmpval == 0)
                break;
        }
        else
            hi = mid - 1;
    }
 
    return lo;
}
 
/*
 * qsort_partition_hbound_cmp
 *
 * Hash bounds are sorted by modulus, then by remainder.
 */
static int32
qsort_partition_hbound_cmp(const void *a, const void *b)
{
    const PartitionHashBound *h1 = (const PartitionHashBound *) a;
    const PartitionHashBound *h2 = (const PartitionHashBound *) b;
 
    return partition_hbound_cmp(h1->modulus, h1->remainder,
                                h2->modulus, h2->remainder);
}
 
/*
 * qsort_partition_list_value_cmp
 *
 * Compare two list partition bound datums.
 */
static int32
qsort_partition_list_value_cmp(const void *a, const void *b, void *arg)
{
    Datum       val1 = ((const PartitionListValue *) a)->value,
                val2 = ((const PartitionListValue *) b)->value;
    PartitionKey key = (PartitionKey) arg;
 
    return DatumGetInt32(FunctionCall2Coll(&key->partsupfunc[0],
                                           key->partcollation[0],
                                           val1, val2));
}
 
/*
 * qsort_partition_rbound_cmp
 *
 * Used when sorting range bounds across all range partitions.
 */
static int32
qsort_partition_rbound_cmp(const void *a, const void *b, void *arg)
{
    PartitionRangeBound *b1 = (*(PartitionRangeBound *const *) a);
    PartitionRangeBound *b2 = (*(PartitionRangeBound *const *) b);
    PartitionKey key = (PartitionKey) arg;
 
    return compare_range_bounds(key->partnatts, key->partsupfunc,
                                key->partcollation,
                                b1, b2);
}
 
/*
 * get_partition_operator
 *
 * Return oid of the operator of the given strategy for the given partition
 * key column.  It is assumed that the partitioning key is of the same type as
 * the chosen partitioning opclass, or at least binary-compatible.  In the
 * latter case, *need_relabel is set to true if the opclass is not of a
 * polymorphic type (indicating a RelabelType node needed on top), otherwise
 * false.
 */
static Oid
get_partition_operator(PartitionKey key, int col, StrategyNumber strategy,
                       bool *need_relabel)
{
    Oid         operoid;
 
    /*
     * Get the operator in the partitioning opfamily using the opclass'
     * declared input type as both left- and righttype.
     */
    operoid = get_opfamily_member(key->partopfamily[col],
                                  key->partopcintype[col],
                                  key->partopcintype[col],
                                  strategy);
    if (!OidIsValid(operoid))
        elog(ERROR, "missing operator %d(%u,%u) in partition opfamily %u",
             strategy, key->partopcintype[col], key->partopcintype[col],
             key->partopfamily[col]);
 
    /*
     * If the partition key column is not of the same type as the operator
     * class and not polymorphic, tell caller to wrap the non-Const expression
     * in a RelabelType.  This matches what parse_coerce.c does.
     */
    *need_relabel = (key->parttypid[col] != key->partopcintype[col] &&
                     key->partopcintype[col] != RECORDOID &&
                     !IsPolymorphicType(key->partopcintype[col]));
 
    return operoid;
}
 
/*
 * make_partition_op_expr
 *      Returns an Expr for the given partition key column with arg1 and
 *      arg2 as its leftop and rightop, respectively
 */
static Expr *
make_partition_op_expr(PartitionKey key, int keynum,
                       uint16 strategy, Expr *arg1, Expr *arg2)
{
    Oid         operoid;
    bool        need_relabel = false;
    Expr       *result = NULL;
 
    /* Get the correct btree operator for this partitioning column */
    operoid = get_partition_operator(key, keynum, strategy, &need_relabel);
 
    /*
     * Chosen operator may be such that the non-Const operand needs to be
     * coerced, so apply the same; see the comment in
     * get_partition_operator().
     */
    if (!IsA(arg1, Const) &&
        (need_relabel ||
         key->partcollation[keynum] != key->parttypcoll[keynum]))
        arg1 = (Expr *) makeRelabelType(arg1,
                                        key->partopcintype[keynum],
                                        -1,
                                        key->partcollation[keynum],
                                        COERCE_EXPLICIT_CAST);
 
    /* Generate the actual expression */
    switch (key->strategy)
    {
        case PARTITION_STRATEGY_LIST:
            {
                List       *elems = (List *) arg2;
                int         nelems = list_length(elems);
 
                Assert(nelems >= 1);
                Assert(keynum == 0);
 
                if (nelems > 1 &&
                    !type_is_array(key->parttypid[keynum]))
                {
                    ArrayExpr  *arrexpr;
                    ScalarArrayOpExpr *saopexpr;
 
                    /* Construct an ArrayExpr for the right-hand inputs */
                    arrexpr = makeNode(ArrayExpr);
                    arrexpr->array_typeid =
                        get_array_type(key->parttypid[keynum]);
                    arrexpr->array_collid = key->parttypcoll[keynum];
                    arrexpr->element_typeid = key->parttypid[keynum];
                    arrexpr->elements = elems;
                    arrexpr->multidims = false;
                    arrexpr->location = -1;
 
                    /* Build leftop = ANY (rightop) */
                    saopexpr = makeNode(ScalarArrayOpExpr);
                    saopexpr->opno = operoid;
                    saopexpr->opfuncid = get_opcode(operoid);
                    saopexpr->hashfuncid = InvalidOid;
                    saopexpr->negfuncid = InvalidOid;
                    saopexpr->useOr = true;
                    saopexpr->inputcollid = key->partcollation[keynum];
                    saopexpr->args = list_make2(arg1, arrexpr);
                    saopexpr->location = -1;
 
                    result = (Expr *) saopexpr;
                }
                else
                {
                    List       *elemops = NIL;
                    ListCell   *lc;
 
                    foreach(lc, elems)
                    {
                        Expr       *elem = lfirst(lc),
                                   *elemop;
 
                        elemop = make_opclause(operoid,
                                               BOOLOID,
                                               false,
                                               arg1, elem,
                                               InvalidOid,
                                               key->partcollation[keynum]);
                        elemops = lappend(elemops, elemop);
                    }
 
                    result = nelems > 1 ? makeBoolExpr(OR_EXPR, elemops, -1) : linitial(elemops);
                }
                break;
            }
 
        case PARTITION_STRATEGY_RANGE:
            result = make_opclause(operoid,
                                   BOOLOID,
                                   false,
                                   arg1, arg2,
                                   InvalidOid,
                                   key->partcollation[keynum]);
            break;
 
        case PARTITION_STRATEGY_HASH:
            Assert(false);
            break;
    }
 
    return result;
}
 
/*
 * get_qual_for_hash
 *
 * Returns a CHECK constraint expression to use as a hash partition's
 * constraint, given the parent relation and partition bound structure.
 *
 * The partition constraint for a hash partition is always a call to the
 * built-in function satisfies_hash_partition().
 */
static List *
get_qual_for_hash(Relation parent, PartitionBoundSpec *spec)
{
    PartitionKey key = RelationGetPartitionKey(parent);
    FuncExpr   *fexpr;
    Node       *relidConst;
    Node       *modulusConst;
    Node       *remainderConst;
    List       *args;
    ListCell   *partexprs_item;
    int         i;
 
    /* Fixed arguments. */
    relidConst = (Node *) makeConst(OIDOID,
                                    -1,
                                    InvalidOid,
                                    sizeof(Oid),
                                    ObjectIdGetDatum(RelationGetRelid(parent)),
                                    false,
                                    true);
 
    modulusConst = (Node *) makeConst(INT4OID,
                                      -1,
                                      InvalidOid,
                                      sizeof(int32),
                                      Int32GetDatum(spec->modulus),
                                      false,
                                      true);
 
    remainderConst = (Node *) makeConst(INT4OID,
                                        -1,
                                        InvalidOid,
                                        sizeof(int32),
                                        Int32GetDatum(spec->remainder),
                                        false,
                                        true);
 
    args = list_make3(relidConst, modulusConst, remainderConst);
    partexprs_item = list_head(key->partexprs);
 
    /* Add an argument for each key column. */
    for (i = 0; i < key->partnatts; i++)
    {
        Node       *keyCol;
 
        /* Left operand */
        if (key->partattrs[i] != 0)
        {
            keyCol = (Node *) makeVar(1,
                                      key->partattrs[i],
                                      key->parttypid[i],
                                      key->parttypmod[i],
                                      key->parttypcoll[i],
                                      0);
        }
        else
        {
            keyCol = (Node *) copyObject(lfirst(partexprs_item));
            partexprs_item = lnext(key->partexprs, partexprs_item);
        }
 
        args = lappend(args, keyCol);
    }
 
    fexpr = makeFuncExpr(F_SATISFIES_HASH_PARTITION,
                         BOOLOID,
                         args,
                         InvalidOid,
                         InvalidOid,
                         COERCE_EXPLICIT_CALL);
 
    return list_make1(fexpr);
}
 
/*
 * get_qual_for_list
 *
 * Returns an implicit-AND list of expressions to use as a list partition's
 * constraint, given the parent relation and partition bound structure.
 *
 * The function returns NIL for a default partition when it's the only
 * partition since in that case there is no constraint.
 */
static List *
get_qual_for_list(Relation parent, PartitionBoundSpec *spec)
{
    PartitionKey key = RelationGetPartitionKey(parent);
    List       *result;
    Expr       *keyCol;
    Expr       *opexpr;
    NullTest   *nulltest;
    ListCell   *cell;
    List       *elems = NIL;
    bool        list_has_null = false;
 
    /*
     * Only single-column list partitioning is supported, so we are worried
     * only about the partition key with index 0.
     */
    Assert(key->partnatts == 1);
 
    /* Construct Var or expression representing the partition column */
    if (key->partattrs[0] != 0)
        keyCol = (Expr *) makeVar(1,
                                  key->partattrs[0],
                                  key->parttypid[0],
                                  key->parttypmod[0],
                                  key->parttypcoll[0],
                                  0);
    else
        keyCol = (Expr *) copyObject(linitial(key->partexprs));
 
    /*
     * For default list partition, collect datums for all the partitions. The
     * default partition constraint should check that the partition key is
     * equal to none of those.
     */
    if (spec->is_default)
    {
        int         i;
        int         ndatums = 0;
        PartitionDesc pdesc = RelationGetPartitionDesc(parent, false);
        PartitionBoundInfo boundinfo = pdesc->boundinfo;
 
        if (boundinfo)
        {
            ndatums = boundinfo->ndatums;
 
            if (partition_bound_accepts_nulls(boundinfo))
                list_has_null = true;
        }
 
        /*
         * If default is the only partition, there need not be any partition
         * constraint on it.
         */
        if (ndatums == 0 && !list_has_null)
            return NIL;
 
        for (i = 0; i < ndatums; i++)
        {
            Const      *val;
 
            /*
             * Construct Const from known-not-null datum.  We must be careful
             * to copy the value, because our result has to be able to outlive
             * the relcache entry we're copying from.
             */
            val = makeConst(key->parttypid[0],
                            key->parttypmod[0],
                            key->parttypcoll[0],
                            key->parttyplen[0],
                            datumCopy(*boundinfo->datums[i],
                                      key->parttypbyval[0],
                                      key->parttyplen[0]),
                            false,  /* isnull */
                            key->parttypbyval[0]);
 
            elems = lappend(elems, val);
        }
    }
    else
    {
        /*
         * Create list of Consts for the allowed values, excluding any nulls.
         */
        foreach(cell, spec->listdatums)
        {
            Const      *val = lfirst_node(Const, cell);
 
            if (val->constisnull)
                list_has_null = true;
            else
                elems = lappend(elems, copyObject(val));
        }
    }
 
    if (elems)
    {
        /*
         * Generate the operator expression from the non-null partition
         * values.
         */
        opexpr = make_partition_op_expr(key, 0, BTEqualStrategyNumber,
                                        keyCol, (Expr *) elems);
    }
    else
    {
        /*
         * If there are no partition values, we don't need an operator
         * expression.
         */
        opexpr = NULL;
    }
 
    if (!list_has_null)
    {
        /*
         * Gin up a "col IS NOT NULL" test that will be ANDed with the main
         * expression.  This might seem redundant, but the partition routing
         * machinery needs it.
         */
        nulltest = makeNode(NullTest);
        nulltest->arg = keyCol;
        nulltest->nulltesttype = IS_NOT_NULL;
        nulltest->argisrow = false;
        nulltest->location = -1;
 
        result = opexpr ? list_make2(nulltest, opexpr) : list_make1(nulltest);
    }
    else
    {
        /*
         * Gin up a "col IS NULL" test that will be OR'd with the main
         * expression.
         */
        nulltest = makeNode(NullTest);
        nulltest->arg = keyCol;
        nulltest->nulltesttype = IS_NULL;
        nulltest->argisrow = false;
        nulltest->location = -1;
 
        if (opexpr)
        {
            Expr       *or;
 
            or = makeBoolExpr(OR_EXPR, list_make2(nulltest, opexpr), -1);
            result = list_make1(or);
        }
        else
            result = list_make1(nulltest);
    }
 
    /*
     * Note that, in general, applying NOT to a constraint expression doesn't
     * necessarily invert the set of rows it accepts, because NOT (NULL) is
     * NULL.  However, the partition constraints we construct here never
     * evaluate to NULL, so applying NOT works as intended.
     */
    if (spec->is_default)
    {
        result = list_make1(make_ands_explicit(result));
        result = list_make1(makeBoolExpr(NOT_EXPR, result, -1));
    }
 
    return result;
}
 
/*
 * get_qual_for_range
 *
 * Returns an implicit-AND list of expressions to use as a range partition's
 * constraint, given the parent relation and partition bound structure.
 *
 * For a multi-column range partition key, say (a, b, c), with (al, bl, cl)
 * as the lower bound tuple and (au, bu, cu) as the upper bound tuple, we
 * generate an expression tree of the following form:
 *
 *  (a IS NOT NULL) and (b IS NOT NULL) and (c IS NOT NULL)
 *      AND
 *  (a > al OR (a = al AND b > bl) OR (a = al AND b = bl AND c >= cl))
 *      AND
 *  (a < au OR (a = au AND b < bu) OR (a = au AND b = bu AND c < cu))
 *
 * It is often the case that a prefix of lower and upper bound tuples contains
 * the same values, for example, (al = au), in which case, we will emit an
 * expression tree of the following form:
 *
 *  (a IS NOT NULL) and (b IS NOT NULL) and (c IS NOT NULL)
 *      AND
 *  (a = al)
 *      AND
 *  (b > bl OR (b = bl AND c >= cl))
 *      AND
 *  (b < bu OR (b = bu AND c < cu))
 *
 * If a bound datum is either MINVALUE or MAXVALUE, these expressions are
 * simplified using the fact that any value is greater than MINVALUE and less
 * than MAXVALUE. So, for example, if cu = MAXVALUE, c < cu is automatically
 * true, and we need not emit any expression for it, and the last line becomes
 *
 *  (b < bu) OR (b = bu), which is simplified to (b <= bu)
 *
 * In most common cases with only one partition column, say a, the following
 * expression tree will be generated: a IS NOT NULL AND a >= al AND a < au
 *
 * For default partition, it returns the negation of the constraints of all
 * the other partitions.
 *
 * External callers should pass for_default as false; we set it to true only
 * when recursing.
 */
static List *
get_qual_for_range(Relation parent, PartitionBoundSpec *spec,
                   bool for_default)
{
    List       *result = NIL;
    ListCell   *cell1,
               *cell2,
               *partexprs_item,
               *partexprs_item_saved;
    int         i,
                j;
    PartitionRangeDatum *ldatum,
               *udatum;
    PartitionKey key = RelationGetPartitionKey(parent);
    Expr       *keyCol;
    Const      *lower_val,
               *upper_val;
    List       *lower_or_arms,
               *upper_or_arms;
    int         num_or_arms,
                current_or_arm;
    ListCell   *lower_or_start_datum,
               *upper_or_start_datum;
    bool        need_next_lower_arm,
                need_next_upper_arm;
 
    if (spec->is_default)
    {
        List       *or_expr_args = NIL;
        PartitionDesc pdesc = RelationGetPartitionDesc(parent, false);
        Oid        *inhoids = pdesc->oids;
        int         nparts = pdesc->nparts,
                    k;
 
        for (k = 0; k < nparts; k++)
        {
            Oid         inhrelid = inhoids[k];
            HeapTuple   tuple;
            Datum       datum;
            PartitionBoundSpec *bspec;
 
            tuple = SearchSysCache1(RELOID, ObjectIdGetDatum(inhrelid));
            if (!HeapTupleIsValid(tuple))
                elog(ERROR, "cache lookup failed for relation %u", inhrelid);
 
            datum = SysCacheGetAttrNotNull(RELOID, tuple,
                                           Anum_pg_class_relpartbound);
            bspec = (PartitionBoundSpec *)
                stringToNode(TextDatumGetCString(datum));
            if (!IsA(bspec, PartitionBoundSpec))
                elog(ERROR, "expected PartitionBoundSpec");
 
            if (!bspec->is_default)
            {
                List       *part_qual;
 
                part_qual = get_qual_for_range(parent, bspec, true);
 
                /*
                 * AND the constraints of the partition and add to
                 * or_expr_args
                 */
                or_expr_args = lappend(or_expr_args, list_length(part_qual) > 1
                                       ? makeBoolExpr(AND_EXPR, part_qual, -1)
                                       : linitial(part_qual));
            }
            ReleaseSysCache(tuple);
        }
 
        if (or_expr_args != NIL)
        {
            Expr       *other_parts_constr;
 
            /*
             * Combine the constraints obtained for non-default partitions
             * using OR.  As requested, each of the OR's args doesn't include
             * the NOT NULL test for partition keys (which is to avoid its
             * useless repetition).  Add the same now.
             */
            other_parts_constr =
                makeBoolExpr(AND_EXPR,
                             lappend(get_range_nulltest(key),
                                     list_length(or_expr_args) > 1
                                     ? makeBoolExpr(OR_EXPR, or_expr_args,
                                                    -1)
                                     : linitial(or_expr_args)),
                             -1);
 
            /*
             * Finally, the default partition contains everything *NOT*
             * contained in the non-default partitions.
             */
            result = list_make1(makeBoolExpr(NOT_EXPR,
                                             list_make1(other_parts_constr), -1));
        }
 
        return result;
    }
 
    /*
     * If it is the recursive call for default, we skip the get_range_nulltest
     * to avoid accumulating the NullTest on the same keys for each partition.
     */
    if (!for_default)
        result = get_range_nulltest(key);
 
    /*
     * Iterate over the key columns and check if the corresponding lower and
     * upper datums are equal using the btree equality operator for the
     * column's type.  If equal, we emit single keyCol = common_value
     * expression.  Starting from the first column for which the corresponding
     * lower and upper bound datums are not equal, we generate OR expressions
     * as shown in the function's header comment.
     */
    i = 0;
    partexprs_item = list_head(key->partexprs);
    partexprs_item_saved = partexprs_item;  /* placate compiler */
    forboth(cell1, spec->lowerdatums, cell2, spec->upperdatums)
    {
        EState     *estate;
        MemoryContext oldcxt;
        Expr       *test_expr;
        ExprState  *test_exprstate;
        Datum       test_result;
        bool        isNull;
 
        ldatum = lfirst_node(PartitionRangeDatum, cell1);
        udatum = lfirst_node(PartitionRangeDatum, cell2);
 
        /*
         * Since get_range_key_properties() modifies partexprs_item, and we
         * might need to start over from the previous expression in the later
         * part of this function, save away the current value.
         */
        partexprs_item_saved = partexprs_item;
 
        get_range_key_properties(key, i, ldatum, udatum,
                                 &partexprs_item,
                                 &keyCol,
                                 &lower_val, &upper_val);
 
        /*
         * If either value is NULL, the corresponding partition bound is
         * either MINVALUE or MAXVALUE, and we treat them as unequal, because
         * even if they're the same, there is no common value to equate the
         * key column with.
         */
        if (!lower_val || !upper_val)
            break;
 
        /* Create the test expression */
        estate = CreateExecutorState();
        oldcxt = MemoryContextSwitchTo(estate->es_query_cxt);
        test_expr = make_partition_op_expr(key, i, BTEqualStrategyNumber,
                                           (Expr *) lower_val,
                                           (Expr *) upper_val);
        fix_opfuncids((Node *) test_expr);
        test_exprstate = ExecInitExpr(test_expr, NULL);
        test_result = ExecEvalExprSwitchContext(test_exprstate,
                                                GetPerTupleExprContext(estate),
                                                &isNull);
        MemoryContextSwitchTo(oldcxt);
        FreeExecutorState(estate);
 
        /* If not equal, go generate the OR expressions */
        if (!DatumGetBool(test_result))
            break;
 
        /*
         * The bounds for the last key column can't be equal, because such a
         * range partition would never be allowed to be defined (it would have
         * an empty range otherwise).
         */
        if (i == key->partnatts - 1)
            elog(ERROR, "invalid range bound specification");
 
        /* Equal, so generate keyCol = lower_val expression */
        result = lappend(result,
                         make_partition_op_expr(key, i, BTEqualStrategyNumber,
                                                keyCol, (Expr *) lower_val));
 
        i++;
    }
 
    /* First pair of lower_val and upper_val that are not equal. */
    lower_or_start_datum = cell1;
    upper_or_start_datum = cell2;
 
    /* OR will have as many arms as there are key columns left. */
    num_or_arms = key->partnatts - i;
    current_or_arm = 0;
    lower_or_arms = upper_or_arms = NIL;
    need_next_lower_arm = need_next_upper_arm = true;
    while (current_or_arm < num_or_arms)
    {
        List       *lower_or_arm_args = NIL,
                   *upper_or_arm_args = NIL;
 
        /* Restart scan of columns from the i'th one */
        j = i;
        partexprs_item = partexprs_item_saved;
 
        for_both_cell(cell1, spec->lowerdatums, lower_or_start_datum,
                      cell2, spec->upperdatums, upper_or_start_datum)
        {
            PartitionRangeDatum *ldatum_next = NULL,
                       *udatum_next = NULL;
 
            ldatum = lfirst_node(PartitionRangeDatum, cell1);
            if (lnext(spec->lowerdatums, cell1))
                ldatum_next = castNode(PartitionRangeDatum,
                                       lfirst(lnext(spec->lowerdatums, cell1)));
            udatum = lfirst_node(PartitionRangeDatum, cell2);
            if (lnext(spec->upperdatums, cell2))
                udatum_next = castNode(PartitionRangeDatum,
                                       lfirst(lnext(spec->upperdatums, cell2)));
            get_range_key_properties(key, j, ldatum, udatum,
                                     &partexprs_item,
                                     &keyCol,
                                     &lower_val, &upper_val);
 
            if (need_next_lower_arm && lower_val)
            {
                uint16      strategy;
 
                /*
                 * For the non-last columns of this arm, use the EQ operator.
                 * For the last column of this arm, use GT, unless this is the
                 * last column of the whole bound check, or the next bound
                 * datum is MINVALUE, in which case use GE.
                 */
                if (j - i < current_or_arm)
                    strategy = BTEqualStrategyNumber;
                else if (j == key->partnatts - 1 ||
                         (ldatum_next &&
                          ldatum_next->kind == PARTITION_RANGE_DATUM_MINVALUE))
                    strategy = BTGreaterEqualStrategyNumber;
                else
                    strategy = BTGreaterStrategyNumber;
 
                lower_or_arm_args = lappend(lower_or_arm_args,
                                            make_partition_op_expr(key, j,
                                                                   strategy,
                                                                   keyCol,
                                                                   (Expr *) lower_val));
            }
 
            if (need_next_upper_arm && upper_val)
            {
                uint16      strategy;
 
                /*
                 * For the non-last columns of this arm, use the EQ operator.
                 * For the last column of this arm, use LT, unless the next
                 * bound datum is MAXVALUE, in which case use LE.
                 */
                if (j - i < current_or_arm)
                    strategy = BTEqualStrategyNumber;
                else if (udatum_next &&
                         udatum_next->kind == PARTITION_RANGE_DATUM_MAXVALUE)
                    strategy = BTLessEqualStrategyNumber;
                else
                    strategy = BTLessStrategyNumber;
 
                upper_or_arm_args = lappend(upper_or_arm_args,
                                            make_partition_op_expr(key, j,
                                                                   strategy,
                                                                   keyCol,
                                                                   (Expr *) upper_val));
            }
 
            /*
             * Did we generate enough of OR's arguments?  First arm considers
             * the first of the remaining columns, second arm considers first
             * two of the remaining columns, and so on.
             */
            ++j;
            if (j - i > current_or_arm)
            {
                /*
                 * We must not emit any more arms if the new column that will
                 * be considered is unbounded, or this one was.
                 */
                if (!lower_val || !ldatum_next ||
                    ldatum_next->kind != PARTITION_RANGE_DATUM_VALUE)
                    need_next_lower_arm = false;
                if (!upper_val || !udatum_next ||
                    udatum_next->kind != PARTITION_RANGE_DATUM_VALUE)
                    need_next_upper_arm = false;
                break;
            }
        }
 
        if (lower_or_arm_args != NIL)
            lower_or_arms = lappend(lower_or_arms,
                                    list_length(lower_or_arm_args) > 1
                                    ? makeBoolExpr(AND_EXPR, lower_or_arm_args, -1)
                                    : linitial(lower_or_arm_args));
 
        if (upper_or_arm_args != NIL)
            upper_or_arms = lappend(upper_or_arms,
                                    list_length(upper_or_arm_args) > 1
                                    ? makeBoolExpr(AND_EXPR, upper_or_arm_args, -1)
                                    : linitial(upper_or_arm_args));
 
        /* If no work to do in the next iteration, break away. */
        if (!need_next_lower_arm && !need_next_upper_arm)
            break;
 
        ++current_or_arm;
    }
 
    /*
     * Generate the OR expressions for each of lower and upper bounds (if
     * required), and append to the list of implicitly ANDed list of
     * expressions.
     */
    if (lower_or_arms != NIL)
        result = lappend(result,
                         list_length(lower_or_arms) > 1
                         ? makeBoolExpr(OR_EXPR, lower_or_arms, -1)
                         : linitial(lower_or_arms));
    if (upper_or_arms != NIL)
        result = lappend(result,
                         list_length(upper_or_arms) > 1
                         ? makeBoolExpr(OR_EXPR, upper_or_arms, -1)
                         : linitial(upper_or_arms));
 
    /*
     * As noted above, for non-default, we return list with constant TRUE. If
     * the result is NIL during the recursive call for default, it implies
     * this is the only other partition which can hold every value of the key
     * except NULL. Hence we return the NullTest result skipped earlier.
     */
    if (result == NIL)
        result = for_default
            ? get_range_nulltest(key)
            : list_make1(makeBoolConst(true, false));
 
    return result;
}
 
/*
 * get_range_key_properties
 *      Returns range partition key information for a given column
 *
 * This is a subroutine for get_qual_for_range, and its API is pretty
 * specialized to that caller.
 *
 * Constructs an Expr for the key column (returned in *keyCol) and Consts
 * for the lower and upper range limits (returned in *lower_val and
 * *upper_val).  For MINVALUE/MAXVALUE limits, NULL is returned instead of
 * a Const.  All of these structures are freshly palloc'd.
 *
 * *partexprs_item points to the cell containing the next expression in
 * the key->partexprs list, or NULL.  It may be advanced upon return.
 */
static void
get_range_key_properties(PartitionKey key, int keynum,
                         PartitionRangeDatum *ldatum,
                         PartitionRangeDatum *udatum,
                         ListCell **partexprs_item,
                         Expr **keyCol,
                         Const **lower_val, Const **upper_val)
{
    /* Get partition key expression for this column */
    if (key->partattrs[keynum] != 0)
    {
        *keyCol = (Expr *) makeVar(1,
                                   key->partattrs[keynum],
                                   key->parttypid[keynum],
                                   key->parttypmod[keynum],
                                   key->parttypcoll[keynum],
                                   0);
    }
    else
    {
        if (*partexprs_item == NULL)
            elog(ERROR, "wrong number of partition key expressions");
        *keyCol = copyObject(lfirst(*partexprs_item));
        *partexprs_item = lnext(key->partexprs, *partexprs_item);
    }
 
    /* Get appropriate Const nodes for the bounds */
    if (ldatum->kind == PARTITION_RANGE_DATUM_VALUE)
        *lower_val = castNode(Const, copyObject(ldatum->value));
    else
        *lower_val = NULL;
 
    if (udatum->kind == PARTITION_RANGE_DATUM_VALUE)
        *upper_val = castNode(Const, copyObject(udatum->value));
    else
        *upper_val = NULL;
}
 
/*
 * get_range_nulltest
 *
 * A non-default range partition table does not currently allow partition
 * keys to be null, so emit an IS NOT NULL expression for each key column.
 */
static List *
get_range_nulltest(PartitionKey key)
{
    List       *result = NIL;
    NullTest   *nulltest;
    ListCell   *partexprs_item;
    int         i;
 
    partexprs_item = list_head(key->partexprs);
    for (i = 0; i < key->partnatts; i++)
    {
        Expr       *keyCol;
 
        if (key->partattrs[i] != 0)
        {
            keyCol = (Expr *) makeVar(1,
                                      key->partattrs[i],
                                      key->parttypid[i],
                                      key->parttypmod[i],
                                      key->parttypcoll[i],
                                      0);
        }
        else
        {
            if (partexprs_item == NULL)
                elog(ERROR, "wrong number of partition key expressions");
            keyCol = copyObject(lfirst(partexprs_item));
            partexprs_item = lnext(key->partexprs, partexprs_item);
        }
 
        nulltest = makeNode(NullTest);
        nulltest->arg = keyCol;
        nulltest->nulltesttype = IS_NOT_NULL;
        nulltest->argisrow = false;
        nulltest->location = -1;
        result = lappend(result, nulltest);
    }
 
    return result;
}
 
/*
 * compute_partition_hash_value
 *
 * Compute the hash value for given partition key values.
 */
uint64
compute_partition_hash_value(int partnatts, FmgrInfo *partsupfunc, const Oid *partcollation,
                             const Datum *values, const bool *isnull)
{
    int         i;
    uint64      rowHash = 0;
    Datum       seed = UInt64GetDatum(HASH_PARTITION_SEED);
 
    for (i = 0; i < partnatts; i++)
    {
        /* Nulls are just ignored */
        if (!isnull[i])
        {
            Datum       hash;
 
            Assert(OidIsValid(partsupfunc[i].fn_oid));
 
            /*
             * Compute hash for each datum value by calling respective
             * datatype-specific hash functions of each partition key
             * attribute.
             */
            hash = FunctionCall2Coll(&partsupfunc[i], partcollation[i],
                                     values[i], seed);
 
            /* Form a single 64-bit hash value */
            rowHash = hash_combine64(rowHash, DatumGetUInt64(hash));
        }
    }
 
    return rowHash;
}
 
/*
 * satisfies_hash_partition
 *
 * This is an SQL-callable function for use in hash partition constraints.
 * The first three arguments are the parent table OID, modulus, and remainder.
 * The remaining arguments are the value of the partitioning columns (or
 * expressions); these are hashed and the results are combined into a single
 * hash value by calling hash_combine64.
 *
 * Returns true if remainder produced when this computed single hash value is
 * divided by the given modulus is equal to given remainder, otherwise false.
 * NB: it's important that this never return null, as the constraint machinery
 * would consider that to be a "pass".
 *
 * See get_qual_for_hash() for usage.
 */
Datum
satisfies_hash_partition(PG_FUNCTION_ARGS)
{
    typedef struct ColumnsHashData
    {
        Oid         relid;
        int         nkeys;
        Oid         variadic_type;
        int16       variadic_typlen;
        bool        variadic_typbyval;
        char        variadic_typalign;
        Oid         partcollid[PARTITION_MAX_KEYS];
        FmgrInfo    partsupfunc[FLEXIBLE_ARRAY_MEMBER];
    } ColumnsHashData;
    Oid         parentId;
    int         modulus;
    int         remainder;
    Datum       seed = UInt64GetDatum(HASH_PARTITION_SEED);
    ColumnsHashData *my_extra;
    uint64      rowHash = 0;
 
    /* Return false if the parent OID, modulus, or remainder is NULL. */
    if (PG_ARGISNULL(0) || PG_ARGISNULL(1) || PG_ARGISNULL(2))
        PG_RETURN_BOOL(false);
    parentId = PG_GETARG_OID(0);
    modulus = PG_GETARG_INT32(1);
    remainder = PG_GETARG_INT32(2);
 
    /* Sanity check modulus and remainder. */
    if (modulus <= 0)
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                 errmsg("modulus for hash partition must be an integer value greater than zero")));
    if (remainder < 0)
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                 errmsg("remainder for hash partition must be an integer value greater than or equal to zero")));
    if (remainder >= modulus)
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                 errmsg("remainder for hash partition must be less than modulus")));
 
    /*
     * Cache hash function information.
     */
    my_extra = (ColumnsHashData *) fcinfo->flinfo->fn_extra;
    if (my_extra == NULL || my_extra->relid != parentId)
    {
        Relation    parent;
        PartitionKey key;
        int         j;
 
        /* Open parent relation and fetch partition key info */
        parent = relation_open(parentId, AccessShareLock);
        key = RelationGetPartitionKey(parent);
 
        /* Reject parent table that is not hash-partitioned. */
        if (key == NULL || key->strategy != PARTITION_STRATEGY_HASH)
            ereport(ERROR,
                    (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                     errmsg("\"%s\" is not a hash partitioned table",
                            get_rel_name(parentId))));
 
        if (!get_fn_expr_variadic(fcinfo->flinfo))
        {
            int         nargs = PG_NARGS() - 3;
 
            /* complain if wrong number of column values */
            if (key->partnatts != nargs)
                ereport(ERROR,
                        (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                         errmsg("number of partitioning columns (%d) does not match number of partition keys provided (%d)",
                                key->partnatts, nargs)));
 
            /* allocate space for our cache */
            fcinfo->flinfo->fn_extra =
                MemoryContextAllocZero(fcinfo->flinfo->fn_mcxt,
                                       offsetof(ColumnsHashData, partsupfunc) +
                                       sizeof(FmgrInfo) * nargs);
            my_extra = (ColumnsHashData *) fcinfo->flinfo->fn_extra;
            my_extra->relid = parentId;
            my_extra->nkeys = key->partnatts;
            memcpy(my_extra->partcollid, key->partcollation,
                   key->partnatts * sizeof(Oid));
 
            /* check argument types and save fmgr_infos */
            for (j = 0; j < key->partnatts; ++j)
            {
                Oid         argtype = get_fn_expr_argtype(fcinfo->flinfo, j + 3);
 
                if (argtype != key->parttypid[j] && !IsBinaryCoercible(argtype, key->parttypid[j]))
                    ereport(ERROR,
                            (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                             errmsg("column %d of the partition key has type %s, but supplied value is of type %s",
                                    j + 1, format_type_be(key->parttypid[j]), format_type_be(argtype))));
 
                fmgr_info_copy(&my_extra->partsupfunc[j],
                               &key->partsupfunc[j],
                               fcinfo->flinfo->fn_mcxt);
            }
        }
        else
        {
            ArrayType  *variadic_array = PG_GETARG_ARRAYTYPE_P(3);
 
            /* allocate space for our cache -- just one FmgrInfo in this case */
            fcinfo->flinfo->fn_extra =
                MemoryContextAllocZero(fcinfo->flinfo->fn_mcxt,
                                       offsetof(ColumnsHashData, partsupfunc) +
                                       sizeof(FmgrInfo));
            my_extra = (ColumnsHashData *) fcinfo->flinfo->fn_extra;
            my_extra->relid = parentId;
            my_extra->nkeys = key->partnatts;
            my_extra->variadic_type = ARR_ELEMTYPE(variadic_array);
            get_typlenbyvalalign(my_extra->variadic_type,
                                 &my_extra->variadic_typlen,
                                 &my_extra->variadic_typbyval,
                                 &my_extra->variadic_typalign);
            my_extra->partcollid[0] = key->partcollation[0];
 
            /* check argument types */
            for (j = 0; j < key->partnatts; ++j)
                if (key->parttypid[j] != my_extra->variadic_type)
                    ereport(ERROR,
                            (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                             errmsg("column %d of the partition key has type \"%s\", but supplied value is of type \"%s\"",
                                    j + 1,
                                    format_type_be(key->parttypid[j]),
                                    format_type_be(my_extra->variadic_type))));
 
            fmgr_info_copy(&my_extra->partsupfunc[0],
                           &key->partsupfunc[0],
                           fcinfo->flinfo->fn_mcxt);
        }
 
        /* Hold lock until commit */
        relation_close(parent, NoLock);
    }
 
    if (!OidIsValid(my_extra->variadic_type))
    {
        int         nkeys = my_extra->nkeys;
        int         i;
 
        /*
         * For a non-variadic call, neither the number of arguments nor their
         * types can change across calls, so avoid the expense of rechecking
         * here.
         */
 
        for (i = 0; i < nkeys; i++)
        {
            Datum       hash;
 
            /* keys start from fourth argument of function. */
            int         argno = i + 3;
 
            if (PG_ARGISNULL(argno))
                continue;
 
            hash = FunctionCall2Coll(&my_extra->partsupfunc[i],
                                     my_extra->partcollid[i],
                                     PG_GETARG_DATUM(argno),
                                     seed);
 
            /* Form a single 64-bit hash value */
            rowHash = hash_combine64(rowHash, DatumGetUInt64(hash));
        }
    }
    else
    {
        ArrayType  *variadic_array = PG_GETARG_ARRAYTYPE_P(3);
        int         i;
        int         nelems;
        Datum      *datum;
        bool       *isnull;
 
        deconstruct_array(variadic_array,
                          my_extra->variadic_type,
                          my_extra->variadic_typlen,
                          my_extra->variadic_typbyval,
                          my_extra->variadic_typalign,
                          &datum, &isnull, &nelems);
 
        /* complain if wrong number of column values */
        if (nelems != my_extra->nkeys)
            ereport(ERROR,
                    (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                     errmsg("number of partitioning columns (%d) does not match number of partition keys provided (%d)",
                            my_extra->nkeys, nelems)));
 
        for (i = 0; i < nelems; i++)
        {
            Datum       hash;
 
            if (isnull[i])
                continue;
 
            hash = FunctionCall2Coll(&my_extra->partsupfunc[0],
                                     my_extra->partcollid[0],
                                     datum[i],
                                     seed);
 
            /* Form a single 64-bit hash value */
            rowHash = hash_combine64(rowHash, DatumGetUInt64(hash));
        }
    }
 
    PG_RETURN_BOOL(rowHash % modulus == remainder);
}
 
/*
 * check_two_partitions_bounds_range
 *
 * (function for BY RANGE partitioning)
 *
 * This is a helper function for check_partitions_for_split() and
 * calculate_partition_bound_for_merge().  This function compares the upper
 * bound of first_bound and the lower bound of second_bound.  These bounds
 * should be equal except when "defaultPart == true" (this means that one of
 * the split partitions is DEFAULT).  In this case, the upper bound of
 * first_bound can be less than the lower bound of second_bound because
 * the space between these bounds will be included in the DEFAULT partition.
 *
 * parent:          partitioned table
 * first_name:      name of the first partition
 * first_bound:     bound of the first partition
 * second_name:     name of the second partition
 * second_bound:    bound of the second partition
 * defaultPart:     true if one of the new partitions is DEFAULT
 * is_merge:        true indicates the operation is MERGE PARTITIONS;
 *                  false indicates the operation is SPLIT PARTITION.
 * pstate:          pointer to ParseState struct for determining error position
 */
static void
check_two_partitions_bounds_range(Relation parent,
                                  RangeVar *first_name,
                                  PartitionBoundSpec *first_bound,
                                  RangeVar *second_name,
                                  PartitionBoundSpec *second_bound,
                                  bool defaultPart,
                                  bool is_merge,
                                  ParseState *pstate)
{
    PartitionKey key = RelationGetPartitionKey(parent);
    PartitionRangeBound *first_upper;
    PartitionRangeBound *second_lower;
    int         cmpval;
 
    Assert(key->strategy == PARTITION_STRATEGY_RANGE);
 
    first_upper = make_one_partition_rbound(key, -1, first_bound->upperdatums, false);
    second_lower = make_one_partition_rbound(key, -1, second_bound->lowerdatums, true);
 
    /*
     * lower1 argument of partition_rbound_cmp() is set to false for the
     * correct comparison result of the lower and upper bounds.
     */
    cmpval = partition_rbound_cmp(key->partnatts,
                                  key->partsupfunc,
                                  key->partcollation,
                                  second_lower->datums, second_lower->kind,
                                  false, first_upper);
    if ((!defaultPart && cmpval) || (defaultPart && cmpval < 0))
    {
        PartitionRangeDatum *datum = linitial(second_bound->lowerdatums);
 
        if (is_merge)
            ereport(ERROR,
                    errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                    errmsg("can not merge partition \"%s\" together with partition \"%s\"",
                           second_name->relname, first_name->relname),
                    errdetail("lower bound of partition \"%s\" is not equal to the upper bound of partition \"%s\"",
                              second_name->relname, first_name->relname),
                    errhint("ALTER TABLE ... MERGE PARTITIONS requires the partition bounds to be adjacent."),
                    parser_errposition(pstate, datum->location));
        else
            ereport(ERROR,
                    errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                    errmsg("can not split to partition \"%s\" together with partition \"%s\"",
                           second_name->relname, first_name->relname),
                    errdetail("lower bound of partition \"%s\" is not equal to the upper bound of partition \"%s\"",
                              second_name->relname, first_name->relname),
                    errhint("ALTER TABLE ... SPLIT PARTITION requires the partition bounds to be adjacent."),
                    parser_errposition(pstate, datum->location));
    }
}
 
/*
 * get_partition_bound_spec
 *
 * Returns the PartitionBoundSpec for the partition with the given OID partOid.
 */
static PartitionBoundSpec *
get_partition_bound_spec(Oid partOid)
{
    HeapTuple   tuple;
    Datum       datum;
    bool        isnull;
    PartitionBoundSpec *boundspec = NULL;
 
    /* Try fetching the tuple from the catcache, for speed. */
    tuple = SearchSysCache1(RELOID, partOid);
    if (!HeapTupleIsValid(tuple))
        elog(ERROR, "cache lookup failed for relation %u", partOid);
 
    datum = SysCacheGetAttr(RELOID, tuple,
                            Anum_pg_class_relpartbound,
                            &isnull);
    if (isnull)
        elog(ERROR, "partition bound for relation %u is null",
             partOid);
 
    boundspec = stringToNode(TextDatumGetCString(datum));
 
    if (!IsA(boundspec, PartitionBoundSpec))
        elog(ERROR, "expected PartitionBoundSpec for relation %u",
             partOid);
 
    ReleaseSysCache(tuple);
    return boundspec;
}
 
/*
 * calculate_partition_bound_for_merge
 *
 * Calculates the bound of the merged partition "spec" by using the bounds of
 * the partitions to be merged.
 *
 * parent:          partitioned table
 * partNames:       names of partitions to be merged
 * partOids:        Oids of partitions to be merged
 * spec (out):      bounds specification of the merged partition
 * pstate:          pointer to ParseState struct to determine error position
 */
void
calculate_partition_bound_for_merge(Relation parent,
                                    List *partNames,
                                    List *partOids,
                                    PartitionBoundSpec *spec,
                                    ParseState *pstate)
{
    PartitionKey key = RelationGetPartitionKey(parent);
    PartitionBoundSpec *bound;
 
    Assert(!spec->is_default);
 
    switch (key->strategy)
    {
        case PARTITION_STRATEGY_RANGE:
            {
                int         i;
                PartitionRangeBound **lower_bounds;
                int         nparts = list_length(partOids);
                List       *bounds = NIL;
 
                lower_bounds = palloc0_array(PartitionRangeBound *, nparts);
 
                /*
                 * Create an array of lower bounds and a list of
                 * PartitionBoundSpec.
                 */
                foreach_oid(partoid, partOids)
                {
                    bound = get_partition_bound_spec(partoid);
                    i = foreach_current_index(partoid);
 
                    lower_bounds[i] = make_one_partition_rbound(key, i, bound->lowerdatums, true);
                    bounds = lappend(bounds, bound);
                }
 
                /* Sort the array of lower bounds. */
                qsort_arg(lower_bounds, nparts, sizeof(PartitionRangeBound *),
                          qsort_partition_rbound_cmp, key);
 
                /* Ranges of partitions should be adjacent. */
                for (i = 1; i < nparts; i++)
                {
                    int         index = lower_bounds[i]->index;
                    int         prev_index = lower_bounds[i - 1]->index;
 
                    check_two_partitions_bounds_range(parent,
                                                      (RangeVar *) list_nth(partNames, prev_index),
                                                      (PartitionBoundSpec *) list_nth(bounds, prev_index),
                                                      (RangeVar *) list_nth(partNames, index),
                                                      (PartitionBoundSpec *) list_nth(bounds, index),
                                                      false,
                                                      true,
                                                      pstate);
                }
 
                /*
                 * The lower bound of the first partition is the lower bound
                 * of the merged partition.
                 */
                spec->lowerdatums =
                    ((PartitionBoundSpec *) list_nth(bounds, lower_bounds[0]->index))->lowerdatums;
 
                /*
                 * The upper bound of the last partition is the upper bound of
                 * the merged partition.
                 */
                spec->upperdatums =
                    ((PartitionBoundSpec *) list_nth(bounds, lower_bounds[nparts - 1]->index))->upperdatums;
 
                pfree(lower_bounds);
                list_free(bounds);
                break;
            }
 
        case PARTITION_STRATEGY_LIST:
            {
                /* Consolidate bounds for all partitions in the list. */
                foreach_oid(partoid, partOids)
                {
                    bound = get_partition_bound_spec(partoid);
                    spec->listdatums = list_concat(spec->listdatums, bound->listdatums);
                }
                break;
            }
 
        default:
            elog(ERROR, "unexpected partition strategy: %d",
                 (int) key->strategy);
    }
}
 
/*
 * partitions_listdatum_intersection
 *
 * (function for BY LIST partitioning)
 *
 * Function compares lists of values for different partitions.
 * Return a list that contains *one* cell that is present in both list1 and
 * list2.  The returned list is freshly allocated via palloc(), but the
 * cells themselves point to the same objects as the cells of the
 * input lists.
 *
 * Currently, there is no need to collect all common partition datums from the
 * two lists.
 */
static List *
partitions_listdatum_intersection(FmgrInfo *partsupfunc, Oid *partcollation,
                                  const List *list1, const List *list2)
{
    List       *result = NIL;
 
    if (list1 == NIL || list2 == NIL)
        return result;
 
    foreach_node(Const, val1, list1)
    {
        bool        isnull1 = val1->constisnull;
 
        foreach_node(Const, val2, list2)
        {
            if (val2->constisnull)
            {
                if (isnull1)
                {
                    result = lappend(result, val1);
                    return result;
                }
                continue;
            }
            else if (isnull1)
                continue;
 
            /* Compare two datum values. */
            if (DatumGetInt32(FunctionCall2Coll(&partsupfunc[0],
                                                partcollation[0],
                                                val1->constvalue,
                                                val2->constvalue)) == 0)
            {
                result = lappend(result, val1);
                return result;
            }
        }
    }
 
    return result;
}
 
/*
 * check_partitions_not_overlap_list
 *
 * (function for BY LIST partitioning)
 *
 * This is a helper function for check_partitions_for_split().
 * Checks that the values of the new partitions do not overlap.
 *
 * parent:  partitioned table
 * parts:   array of SinglePartitionSpec structs with info about split partitions
 * nparts:  size of array "parts"
 */
static void
check_partitions_not_overlap_list(Relation parent,
                                  SinglePartitionSpec **parts,
                                  int nparts,
                                  ParseState *pstate)
{
    PartitionKey key PG_USED_FOR_ASSERTS_ONLY = RelationGetPartitionKey(parent);
    int         i,
                j;
    SinglePartitionSpec *sps1,
               *sps2;
    List       *overlap;
 
    Assert(key->strategy == PARTITION_STRATEGY_LIST);
 
    for (i = 0; i < nparts; i++)
    {
        sps1 = parts[i];
 
        for (j = i + 1; j < nparts; j++)
        {
            sps2 = parts[j];
 
            overlap = partitions_listdatum_intersection(&key->partsupfunc[0],
                                                        key->partcollation,
                                                        sps1->bound->listdatums,
                                                        sps2->bound->listdatums);
            if (list_length(overlap) > 0)
            {
                Const      *val = (Const *) linitial_node(Const, overlap);
 
                ereport(ERROR,
                        errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                        errmsg("new partition \"%s\" would overlap with another new partition \"%s\"",
                               sps1->name->relname, sps2->name->relname),
                        parser_errposition(pstate, exprLocation((Node *) val)));
            }
        }
    }
}
 
/*
 * check_partition_bounds_for_split_range
 *
 * (function for BY RANGE partitioning)
 *
 * Checks that bounds of new partition "spec" are inside bounds of split
 * partition (with Oid splitPartOid). If first=true (this means that "spec" is
 * the first of the new partitions), then the lower bound of "spec" should be
 * equal (or greater than or equal in case defaultPart=true) to the lower
 * bound of the split partition. If last=true (this means that "spec" is the
 * last of the new partitions), then the upper bound of "spec" should be
 * equal (or less than or equal in case defaultPart=true) to the upper bound
 * of the split partition.
 *
 * parent:          partitioned table
 * relname:         name of the new partition
 * spec:            bounds specification of the new partition
 * splitPartOid:    split partition Oid
 * first:           true iff the new partition "spec" is the first of the
 *                  new partitions
 * last:            true iff the new partition "spec" is the last of the
 *                  new partitions
 * defaultPart:     true iff new partitions contain the DEFAULT partition
 * pstate:          pointer to ParseState struct to determine error position
 */
static void
check_partition_bounds_for_split_range(Relation parent,
                                       char *relname,
                                       PartitionBoundSpec *spec,
                                       Oid splitPartOid,
                                       bool first,
                                       bool last,
                                       bool defaultPart,
                                       ParseState *pstate)
{
    PartitionKey key = RelationGetPartitionKey(parent);
    PartitionRangeBound *lower,
               *upper;
    int         cmpval;
 
    Assert(key->strategy == PARTITION_STRATEGY_RANGE);
    Assert(spec->strategy == PARTITION_STRATEGY_RANGE);
 
    lower = make_one_partition_rbound(key, -1, spec->lowerdatums, true);
    upper = make_one_partition_rbound(key, -1, spec->upperdatums, false);
 
    /*
     * First, check if the resulting range would be empty with the specified
     * lower and upper bounds.  partition_rbound_cmp cannot return zero here,
     * since the lower-bound flags are different.
     */
    cmpval = partition_rbound_cmp(key->partnatts,
                                  key->partsupfunc,
                                  key->partcollation,
                                  lower->datums, lower->kind,
                                  true, upper);
    Assert(cmpval != 0);
    if (cmpval > 0)
    {
        /* Point to the problematic key in the lower datums list. */
        PartitionRangeDatum *datum = list_nth(spec->lowerdatums, cmpval - 1);
 
        ereport(ERROR,
                errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                errmsg("empty range bound specified for partition \"%s\"",
                       relname),
                errdetail("Specified lower bound %s is greater than or equal to upper bound %s.",
                          get_range_partbound_string(spec->lowerdatums),
                          get_range_partbound_string(spec->upperdatums)),
                parser_errposition(pstate, exprLocation((Node *) datum)));
    }
 
    /*
     * Need to check first and last partitions (from the set of new
     * partitions)
     */
    if (first || last)
    {
        PartitionBoundSpec *split_spec = get_partition_bound_spec(splitPartOid);
        PartitionRangeDatum *datum;
 
        if (first)
        {
            PartitionRangeBound *split_lower;
 
            split_lower = make_one_partition_rbound(key, -1, split_spec->lowerdatums, true);
 
            cmpval = partition_rbound_cmp(key->partnatts,
                                          key->partsupfunc,
                                          key->partcollation,
                                          lower->datums, lower->kind,
                                          true, split_lower);
            if (cmpval != 0)
                datum = list_nth(spec->lowerdatums, abs(cmpval) - 1);
 
            /*
             * The lower bound of "spec" must equal the lower bound of the
             * split partition.  However, if one of the new partitions is
             * DEFAULT, then it is ok for the new partition's lower bound to
             * be greater than that of the split partition.
             */
            if (!defaultPart)
            {
                if (cmpval != 0)
                    ereport(ERROR,
                            errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                            errmsg("lower bound of partition \"%s\" is not equal to lower bound of split partition \"%s\"",
                                   relname,
                                   get_rel_name(splitPartOid)),
                            errhint("%s require combined bounds of new partitions must exactly match the bound of the split partition",
                                    "ALTER TABLE ... SPLIT PARTITION"),
                            parser_errposition(pstate, exprLocation((Node *) datum)));
            }
            else if (cmpval < 0)
                ereport(ERROR,
                        errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                        errmsg("lower bound of partition \"%s\" is less than lower bound of split partition \"%s\"",
                               relname,
                               get_rel_name(splitPartOid)),
                        errhint("%s require combined bounds of new partitions must exactly match the bound of the split partition",
                                "ALTER TABLE ... SPLIT PARTITION"),
                        parser_errposition(pstate, exprLocation((Node *) datum)));
        }
        else
        {
            PartitionRangeBound *split_upper;
 
            split_upper = make_one_partition_rbound(key, -1, split_spec->upperdatums, false);
 
            cmpval = partition_rbound_cmp(key->partnatts,
                                          key->partsupfunc,
                                          key->partcollation,
                                          upper->datums, upper->kind,
                                          false, split_upper);
            if (cmpval != 0)
                datum = list_nth(spec->upperdatums, abs(cmpval) - 1);
 
            /*
             * The upper bound of "spec" must equal the upper bound of the
             * split partition.  However, if one of the new partitions is
             * DEFAULT, then it is ok for the new partition's upper bound to
             * be less than that of the split partition.
             */
            if (!defaultPart)
            {
                if (cmpval != 0)
                    ereport(ERROR,
                            errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                            errmsg("upper bound of partition \"%s\" is not equal to upper bound of split partition \"%s\"",
                                   relname,
                                   get_rel_name(splitPartOid)),
                            errhint("%s require combined bounds of new partitions must exactly match the bound of the split partition",
                                    "ALTER TABLE ... SPLIT PARTITION"),
                            parser_errposition(pstate, exprLocation((Node *) datum)));
            }
            else if (cmpval > 0)
                ereport(ERROR,
                        errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                        errmsg("upper bound of partition \"%s\" is greater than upper bound of split partition \"%s\"",
                               relname,
                               get_rel_name(splitPartOid)),
                        errhint("%s require combined bounds of new partitions must exactly match the bound of the split partition",
                                "ALTER TABLE ... SPLIT PARTITION"),
                        parser_errposition(pstate, exprLocation((Node *) datum)));
        }
    }
}
 
/*
 * check_partition_bounds_for_split_list
 *
 * (function for BY LIST partitioning)
 *
 * Checks that the bounds of the new partition are inside the bounds of the
 * split partition (with Oid splitPartOid).
 *
 * parent:          partitioned table
 * relname:         name of the new partition
 * spec:            bounds specification of the new partition
 * splitPartOid:    split partition Oid
 * pstate:          pointer to ParseState struct to determine error position
 */
static void
check_partition_bounds_for_split_list(Relation parent, char *relname,
                                      PartitionBoundSpec *spec,
                                      Oid splitPartOid,
                                      ParseState *pstate)
{
    PartitionKey key = RelationGetPartitionKey(parent);
    PartitionDesc partdesc = RelationGetPartitionDesc(parent, false);
    PartitionBoundInfo boundinfo = partdesc->boundinfo;
    int         with = -1;
    bool        overlap = false;
    int         overlap_location = -1;
 
    Assert(key->strategy == PARTITION_STRATEGY_LIST);
    Assert(spec->strategy == PARTITION_STRATEGY_LIST);
    Assert(boundinfo && boundinfo->strategy == PARTITION_STRATEGY_LIST);
 
    /*
     * Search each value of the new partition "spec" in the existing
     * partitions.  All of them should be in the split partition (with Oid
     * splitPartOid).
     */
    foreach_node(Const, val, spec->listdatums)
    {
        overlap_location = exprLocation((Node *) val);
        if (!val->constisnull)
        {
            int         offset;
            bool        equal;
 
            offset = partition_list_bsearch(&key->partsupfunc[0],
                                            key->partcollation,
                                            boundinfo,
                                            val->constvalue,
                                            &equal);
            if (offset >= 0 && equal)
            {
                with = boundinfo->indexes[offset];
                if (partdesc->oids[with] != splitPartOid)
                {
                    overlap = true;
                    break;
                }
            }
            else
                ereport(ERROR,
                        errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                        errmsg("new partition \"%s\" cannot have this value because split partition \"%s\" does not have",
                               relname,
                               get_rel_name(splitPartOid)),
                        parser_errposition(pstate, overlap_location));
        }
        else if (partition_bound_accepts_nulls(boundinfo))
        {
            with = boundinfo->null_index;
            if (partdesc->oids[with] != splitPartOid)
            {
                overlap = true;
                break;
            }
        }
        else
            ereport(ERROR,
                    errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                    errmsg("new partition \"%s\" cannot have NULL value because split partition \"%s\" does not have",
                           relname,
                           get_rel_name(splitPartOid)),
                    parser_errposition(pstate, overlap_location));
    }
 
    if (overlap)
    {
        Assert(with >= 0);
        ereport(ERROR,
                errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                errmsg("new partition \"%s\" would overlap with another (not split) partition \"%s\"",
                       relname, get_rel_name(partdesc->oids[with])),
                parser_errposition(pstate, overlap_location));
    }
}
 
/*
 * find_value_in_new_partitions_list
 *
 * (function for BY LIST partitioning)
 *
 * Function returns true iff any of the new partitions contains the value
 * "value".
 *
 * partsupfunc:     information about the comparison function associated with
 *                  the partition key
 * partcollation:   partitioning collation
 * parts:           pointer to an array with new partition descriptions
 * nparts:          number of new partitions
 * value:           the value that we are looking for
 * isnull:          true if the value that we are looking for is NULL
 */
static bool
find_value_in_new_partitions_list(FmgrInfo *partsupfunc,
                                  Oid *partcollation,
                                  SinglePartitionSpec **parts,
                                  int nparts,
                                  Datum value,
                                  bool isnull)
{
    for (int i = 0; i < nparts; i++)
    {
        SinglePartitionSpec *sps = parts[i];
 
        foreach_node(Const, val, sps->bound->listdatums)
        {
            if (isnull && val->constisnull)
                return true;
 
            if (!isnull && !val->constisnull)
            {
                if (DatumGetInt32(FunctionCall2Coll(&partsupfunc[0],
                                                    partcollation[0],
                                                    val->constvalue,
                                                    value)) == 0)
                    return true;
            }
        }
    }
    return false;
}
 
/*
 * check_parent_values_in_new_partitions
 *
 * (function for BY LIST partitioning)
 *
 * Checks that all values of split partition (with Oid partOid) are contained
 * in new partitions.
 *
 * parent:  partitioned table
 * partOid: split partition Oid
 * parts:   pointer to an array with new partition descriptions
 * nparts:  number of new partitions
 * pstate:  pointer to ParseState struct to determine error position
 */
static void
check_parent_values_in_new_partitions(Relation parent,
                                      Oid partOid,
                                      SinglePartitionSpec **parts,
                                      int nparts,
                                      ParseState *pstate)
{
    PartitionKey key = RelationGetPartitionKey(parent);
    PartitionDesc partdesc = RelationGetPartitionDesc(parent, false);
    PartitionBoundInfo boundinfo = partdesc->boundinfo;
    int         i;
    bool        found = true;
    Datum       datum = PointerGetDatum(NULL);
 
    Assert(key->strategy == PARTITION_STRATEGY_LIST);
 
    /*
     * Special processing for NULL value. Search for a NULL value if the split
     * partition (partOid) contains it.
     */
    if (partition_bound_accepts_nulls(boundinfo) &&
        partdesc->oids[boundinfo->null_index] == partOid)
    {
        if (!find_value_in_new_partitions_list(&key->partsupfunc[0],
                                               key->partcollation, parts, nparts, datum, true))
            found = false;
    }
 
    if (!found)
        ereport(ERROR,
                errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                errmsg("new partitions combined partition bounds do not contain value (%s) but split partition \"%s\" does",
                       "NULL",
                       get_rel_name(partOid)),
                errhint("%s require combined bounds of new partitions must exactly match the bound of the split partition",
                        "ALTER TABLE ... SPLIT PARTITION"));
 
    /*
     * Search all values of split partition with partOid in the PartitionDesc
     * of partitioned table.
     */
    for (i = 0; i < boundinfo->ndatums; i++)
    {
        if (partdesc->oids[boundinfo->indexes[i]] == partOid)
        {
            /* We found the value that the split partition contains. */
            datum = boundinfo->datums[i][0];
            if (!find_value_in_new_partitions_list(&key->partsupfunc[0],
                                                   key->partcollation, parts, nparts, datum, false))
            {
                found = false;
                break;
            }
        }
    }
 
    if (!found)
    {
        Const      *notFoundVal;
 
        /*
         * Make a Const for getting the string representation of the missing
         * value.
         */
        notFoundVal = makeConst(key->parttypid[0],
                                key->parttypmod[0],
                                key->parttypcoll[0],
                                key->parttyplen[0],
                                datum,
                                false,  /* isnull */
                                key->parttypbyval[0]);
 
        ereport(ERROR,
                errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                errmsg("new partitions combined partition bounds do not contain value (%s) but split partition \"%s\" does",
                       deparse_expression((Node *) notFoundVal, NIL, false, false),
                       get_rel_name(partOid)),
                errhint("%s require combined bounds of new partitions must exactly match the bound of the split partition",
                        "ALTER TABLE ... SPLIT PARTITION"));
    }
}
 
/*
 * check_partitions_for_split
 *
 * Checks new partitions for the SPLIT PARTITION command:
 * 1. Bounds of new partitions should not overlap with new and existing
 *    partitions.
 * 2. In the case when new or existing partitions contain the DEFAULT
 *    partition, new partitions can have any bounds inside the split partition
 *    bound (can be spaces between partition bounds).
 * 3. In case new partitions don't contain the DEFAULT partition and the
 *    partitioned table does not have the DEFAULT partition, the following
 *    should be true: the sum of the bounds of new partitions should be equal
 &    to the bound of the split partition.
 *
 * parent:          partitioned table
 * splitPartOid:    split partition Oid
 * partlist:        list of new partitions after partition split
 * pstate:          pointer to ParseState struct for determine error position
 */
void
check_partitions_for_split(Relation parent,
                           Oid splitPartOid,
                           List *partlist,
                           ParseState *pstate)
{
    PartitionKey key;
    char        strategy;
    Oid         defaultPartOid;
    bool        isSplitPartDefault;
    bool        createDefaultPart = false;
    int         default_index = -1;
    int         i;
    SinglePartitionSpec **new_parts;
    SinglePartitionSpec *spsPrev = NULL;
 
    /*
     * nparts counts the number of split partitions, but it exclude the
     * default partition.
     */
    int         nparts = 0;
 
    key = RelationGetPartitionKey(parent);
    strategy = get_partition_strategy(key);
 
    defaultPartOid =
        get_default_oid_from_partdesc(RelationGetPartitionDesc(parent, true));
 
    Assert(strategy == PARTITION_STRATEGY_RANGE ||
           strategy == PARTITION_STRATEGY_LIST);
 
    /*
     * Make an array new_parts with new partitions except the DEFAULT
     * partition.
     */
    new_parts = palloc0_array(SinglePartitionSpec *, list_length(partlist));
 
    /* isSplitPartDefault flag: is split partition a DEFAULT partition? */
    isSplitPartDefault = (defaultPartOid == splitPartOid);
 
    foreach_node(SinglePartitionSpec, sps, partlist)
    {
        if (sps->bound->is_default)
            default_index = foreach_current_index(sps);
        else
            new_parts[nparts++] = sps;
    }
 
    /* An indicator that the DEFAULT partition will be created. */
    if (default_index != -1)
    {
        createDefaultPart = true;
        Assert(nparts == list_length(partlist) - 1);
    }
 
    if (strategy == PARTITION_STRATEGY_RANGE)
    {
        PartitionRangeBound **lower_bounds;
        SinglePartitionSpec **tmp_new_parts;
 
        /*
         * To simplify the check for ranges of new partitions, we need to sort
         * all partitions in ascending order of their bounds (we compare the
         * lower bound only).
         */
        lower_bounds = palloc0_array(PartitionRangeBound *, nparts);
 
        /* Create an array of lower bounds. */
        for (i = 0; i < nparts; i++)
        {
            lower_bounds[i] = make_one_partition_rbound(key, i,
                                                        new_parts[i]->bound->lowerdatums, true);
        }
 
        /* Sort the array of lower bounds. */
        qsort_arg(lower_bounds, nparts, sizeof(PartitionRangeBound *),
                  qsort_partition_rbound_cmp, (void *) key);
 
        /* Reorder the array of partitions. */
        tmp_new_parts = new_parts;
        new_parts = palloc0_array(SinglePartitionSpec *, nparts);
        for (i = 0; i < nparts; i++)
            new_parts[i] = tmp_new_parts[lower_bounds[i]->index];
 
        pfree(tmp_new_parts);
        pfree(lower_bounds);
    }
 
    for (i = 0; i < nparts; i++)
    {
        SinglePartitionSpec *sps = new_parts[i];
 
        if (isSplitPartDefault)
        {
            /*
             * When the split partition is the DEFAULT partition, we can use
             * any free ranges - as when creating a new partition.
             */
            check_new_partition_bound(sps->name->relname, parent, sps->bound,
                                      pstate);
        }
        else
        {
            /*
             * Checks that the bounds of the current partition are inside the
             * bounds of the split partition. For range partitioning: checks
             * that the upper bound of the previous partition is equal to the
             * lower bound of the current partition. For list partitioning:
             * checks that the split partition contains all values of the
             * current partition.
             */
            if (strategy == PARTITION_STRATEGY_RANGE)
            {
                bool        first = (i == 0);
                bool        last = (i == (nparts - 1));
 
                check_partition_bounds_for_split_range(parent, sps->name->relname, sps->bound,
                                                       splitPartOid, first, last,
                                                       createDefaultPart, pstate);
            }
            else
                check_partition_bounds_for_split_list(parent, sps->name->relname,
                                                      sps->bound, splitPartOid, pstate);
        }
 
        /* Ranges of new partitions should not overlap. */
        if (strategy == PARTITION_STRATEGY_RANGE && spsPrev)
            check_two_partitions_bounds_range(parent, spsPrev->name, spsPrev->bound,
                                              sps->name, sps->bound,
                                              createDefaultPart,
                                              false,
                                              pstate);
 
        spsPrev = sps;
    }
 
    if (strategy == PARTITION_STRATEGY_LIST)
    {
        /* Values of new partitions should not overlap. */
        check_partitions_not_overlap_list(parent, new_parts, nparts,
                                          pstate);
 
        /*
         * Need to check that all values of the split partition are contained
         * in the new partitions. Skip this check if the DEFAULT partition
         * exists.
         */
        if (!createDefaultPart)
            check_parent_values_in_new_partitions(parent, splitPartOid,
                                                  new_parts, nparts, pstate);
    }
 
    pfree(new_parts);
}