partbounds.c

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/*-------------------------------------------------------------------------
 *
 * partbounds.c
 *      Support routines for manipulating partition bounds
 *
 * Portions Copyright (c) 1996-2019, 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/partition.h"
#include "catalog/pg_inherits.h"
#include "catalog/pg_type.h"
#include "commands/tablecmds.h"
#include "executor/executor.h"
#include "miscadmin.h"
#include "nodes/makefuncs.h"
#include "nodes/nodeFuncs.h"
#include "parser/parse_coerce.h"
#include "partitioning/partbounds.h"
#include "partitioning/partdesc.h"
#include "partitioning/partprune.h"
#include "utils/builtins.h"
#include "utils/datum.h"
#include "utils/fmgroids.h"
#include "utils/hashutils.h"
#include "utils/lsyscache.h"
#include "utils/partcache.h"
#include "utils/rel.h"
#include "utils/snapmgr.h"
#include "utils/ruleutils.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;

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 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, bool *is_equal);
static int  get_partition_bound_num_indexes(PartitionBoundInfo b);
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 rel, 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;

        default:
            elog(ERROR, "unexpected partition strategy: %d",
                 (int) key->strategy);
    }

    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 = (int *) palloc(sizeof(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);

        default:
            elog(ERROR, "unexpected partition strategy: %d",
                 (int) key->strategy);
            break;
    }

    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 = NULL;
    int         i;
    int         ndatums = 0;
    int         greatest_modulus;

    boundinfo = (PartitionBoundInfoData *)
        palloc0(sizeof(PartitionBoundInfoData));
    boundinfo->strategy = key->strategy;
    /* No special hash partitions. */
    boundinfo->null_index = -1;
    boundinfo->default_index = -1;

    ndatums = nparts;
    hbounds = (PartitionHashBound **)
        palloc(nparts * sizeof(PartitionHashBound *));

    /* 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] = (PartitionHashBound *) palloc(sizeof(PartitionHashBound));
        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[ndatums - 1]->modulus;

    boundinfo->ndatums = ndatums;
    boundinfo->datums = (Datum **) palloc0(ndatums * sizeof(Datum *));
    boundinfo->indexes = (int *) palloc(greatest_modulus * sizeof(int));
    for (i = 0; i < greatest_modulus; i++)
        boundinfo->indexes[i] = -1;

    /*
     * 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] = (Datum *) palloc(2 * sizeof(Datum));
        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[i]);
    }
    pfree(hbounds);

    return boundinfo;
}

/*
 * 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 = NULL;
    ListCell   *cell;
    int         i = 0;
    int         ndatums = 0;
    int         next_index = 0;
    int         default_index = -1;
    int         null_index = -1;
    List       *non_null_values = NIL;

    boundinfo = (PartitionBoundInfoData *)
        palloc0(sizeof(PartitionBoundInfoData));
    boundinfo->strategy = key->strategy;
    /* Will be set correctly below. */
    boundinfo->null_index = -1;
    boundinfo->default_index = -1;

    /* Create a unified list of non-null values across all partitions. */
    for (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 = castNode(Const, lfirst(c));
            PartitionListValue *list_value = NULL;

            if (!val->constisnull)
            {
                list_value = (PartitionListValue *)
                    palloc0(sizeof(PartitionListValue));
                list_value->index = i;
                list_value->value = val->constvalue;
            }
            else
            {
                /*
                 * Never put a null into the values array, flag instead for
                 * the code further down below where we construct the actual
                 * relcache struct.
                 */
                if (null_index != -1)
                    elog(ERROR, "found null more than once");
                null_index = i;
            }

            if (list_value)
                non_null_values = lappend(non_null_values, list_value);
        }
    }

    ndatums = list_length(non_null_values);

    /*
     * Collect all list values in one array. Alongside the value, we also save
     * the index of partition the value comes from.
     */
    all_values = (PartitionListValue **)
        palloc(ndatums * sizeof(PartitionListValue *));
    i = 0;
    foreach(cell, non_null_values)
    {
        PartitionListValue *src = lfirst(cell);

        all_values[i] = (PartitionListValue *)
            palloc(sizeof(PartitionListValue));
        all_values[i]->value = src->value;
        all_values[i]->index = src->index;
        i++;
    }

    qsort_arg(all_values, ndatums, sizeof(PartitionListValue *),
              qsort_partition_list_value_cmp, (void *) key);

    boundinfo->ndatums = ndatums;
    boundinfo->datums = (Datum **) palloc0(ndatums * sizeof(Datum *));
    boundinfo->indexes = (int *) palloc(ndatums * sizeof(int));

    /*
     * 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] = (Datum *) palloc(sizeof(Datum));
        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];
    }

    /*
     * 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];
    }

    /* 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;
    int         ndatums = 0;
    int         default_index = -1;
    int         next_index = 0;

    boundinfo = (PartitionBoundInfoData *)
        palloc0(sizeof(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 = (PartitionRangeBound **)
        palloc0(2 * nparts * sizeof(PartitionRangeBound *));

    /* 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,
              (void *) 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;
    }

    /* 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 = (Datum **) palloc0(ndatums * sizeof(Datum *));
    boundinfo->kind = (PartitionRangeDatumKind **)
        palloc(ndatums *
               sizeof(PartitionRangeDatumKind *));

    /*
     * For range partitioning, an additional value of -1 is stored as the last
     * element.
     */
    boundinfo->indexes = (int *) palloc((ndatums + 1) * sizeof(int));

    for (i = 0; i < ndatums; i++)
    {
        int         j;

        boundinfo->datums[i] = (Datum *) palloc(key->partnatts *
                                                sizeof(Datum));
        boundinfo->kind[i] = (PartitionRangeDatumKind *)
            palloc(key->partnatts *
                   sizeof(PartitionRangeDatumKind));
        for (j = 0; j < key->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];
        }
    }

    /* 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->null_index != b2->null_index)
        return false;

    if (b1->default_index != b2->default_index)
        return false;

    if (b1->strategy == PARTITION_STRATEGY_HASH)
    {
        int         greatest_modulus = get_hash_partition_greatest_modulus(b1);

        /*
         * If two hash partitioned tables have different greatest moduli,
         * their partition schemes don't match.
         */
        if (greatest_modulus != get_hash_partition_greatest_modulus(b2))
            return false;

        /*
         * 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
         * datums array from both the given bounds are same, if and only if
         * their indexes array will be same.  So, it suffices to compare
         * indexes array.
         */
        for (i = 0; i < greatest_modulus; i++)
            if (b1->indexes[i] != b2->indexes[i])
                return false;

#ifdef USE_ASSERT_CHECKING

        /*
         * Nonetheless make sure that the bounds are indeed same when the
         * indexes match.  Hash partition bound stores modulus and remainder
         * at b1->datums[i][0] and b1->datums[i][1] position respectively.
         */
        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;
            }

            if (b1->indexes[i] != b2->indexes[i])
                return false;
        }

        /* There are ndatums+1 indexes in case of range partitions */
        if (b1->strategy == PARTITION_STRATEGY_RANGE &&
            b1->indexes[i] != b2->indexes[i])
            return false;
    }
    return true;
}

/*
 * Return a copy of given PartitionBoundInfo structure. The data types of bounds
 * are described by given partition key specification.
 */
PartitionBoundInfo
partition_bounds_copy(PartitionBoundInfo src,
                      PartitionKey key)
{
    PartitionBoundInfo dest;
    int         i;
    int         ndatums;
    int         partnatts;
    int         num_indexes;

    dest = (PartitionBoundInfo) palloc(sizeof(PartitionBoundInfoData));

    dest->strategy = src->strategy;
    ndatums = dest->ndatums = src->ndatums;
    partnatts = key->partnatts;

    num_indexes = get_partition_bound_num_indexes(src);

    /* List partitioned tables have only a single partition key. */
    Assert(key->strategy != PARTITION_STRATEGY_LIST || partnatts == 1);

    dest->datums = (Datum **) palloc(sizeof(Datum *) * ndatums);

    if (src->kind != NULL)
    {
        dest->kind = (PartitionRangeDatumKind **) palloc(ndatums *
                                                         sizeof(PartitionRangeDatumKind *));
        for (i = 0; i < ndatums; i++)
        {
            dest->kind[i] = (PartitionRangeDatumKind *) palloc(partnatts *
                                                               sizeof(PartitionRangeDatumKind));

            memcpy(dest->kind[i], src->kind[i],
                   sizeof(PartitionRangeDatumKind) * key->partnatts);
        }
    }
    else
        dest->kind = NULL;

    for (i = 0; i < ndatums; i++)
    {
        int         j;

        /*
         * For a corresponding to hash partition, datums array will have two
         * elements - modulus and remainder.
         */
        bool        hash_part = (key->strategy == PARTITION_STRATEGY_HASH);
        int         natts = hash_part ? 2 : partnatts;

        dest->datums[i] = (Datum *) palloc(sizeof(Datum) * natts);

        for (j = 0; j < natts; j++)
        {
            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];
            }

            if (dest->kind == NULL ||
                dest->kind[i][j] == PARTITION_RANGE_DATUM_VALUE)
                dest->datums[i][j] = datumCopy(src->datums[i][j],
                                               byval, typlen);
        }
    }

    dest->indexes = (int *) palloc(sizeof(int) * num_indexes);
    memcpy(dest->indexes, src->indexes, sizeof(int) * num_indexes);

    dest->null_index = src->null_index;
    dest->default_index = src->default_index;

    return dest;
}

/*
 * 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.
 *
 * If out of order, or there is insufficient info to know the order,
 * then we return false.
 */
bool
partitions_are_ordered(PartitionBoundInfo boundinfo, int nparts)
{
    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 then it doesn't work, as
             * that could contain tuples from either below or above the
             * defined range, or tuples belonging to gaps between partitions.
             */
            if (!partition_bound_has_default(boundinfo))
                return true;
            break;

        case PARTITION_STRATEGY_LIST:

            /*
             * LIST partitioning can also guarantee ordering, but only if the
             * partitions don't accept interleaved values.  We could likely
             * check for this by looping over the PartitionBound's indexes
             * array to check that the indexes are in order.  For now, let's
             * just keep it simple and just accept LIST partitioning when
             * there's no DEFAULT partition, exactly one value per partition,
             * and optionally a NULL partition that does not accept any other
             * values.  Such a NULL partition will come last in the
             * PartitionDesc, and the other partitions will be properly
             * ordered.  This is a cheap test to make as it does not require
             * any per-partition processing.  Maybe we'd like to handle more
             * complex cases in the future.
             */
            if (partition_bound_has_default(boundinfo))
                return false;

            if (boundinfo->ndatums + partition_bound_accepts_nulls(boundinfo)
                == nparts)
                return true;
            break;

        default:
            /* HASH, or some other strategy */
            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)
{
    PartitionKey key = RelationGetPartitionKey(parent);
    PartitionDesc partdesc = RelationGetPartitionDesc(parent);
    PartitionBoundInfo boundinfo = partdesc->boundinfo;
    ParseState *pstate = make_parsestate(NULL);
    int         with = -1;
    bool        overlap = false;

    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)
                {
                    Datum     **datums = boundinfo->datums;
                    int         ndatums = boundinfo->ndatums;
                    int         greatest_modulus;
                    int         remainder;
                    int         offset;
                    bool        valid_modulus = true;
                    int         prev_modulus,   /* Previous largest modulus */
                                next_modulus;   /* Next largest modulus */

                    /*
                     * 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.
                     *
                     * 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)
                    {
                        next_modulus = DatumGetInt32(datums[0][0]);
                        valid_modulus = (next_modulus % spec->modulus) == 0;
                    }
                    else
                    {
                        prev_modulus = DatumGetInt32(datums[offset][0]);
                        valid_modulus = (spec->modulus % prev_modulus) == 0;

                        if (valid_modulus && (offset + 1) < ndatums)
                        {
                            next_modulus = DatumGetInt32(datums[offset + 1][0]);
                            valid_modulus = (next_modulus % spec->modulus) == 0;
                        }
                    }

                    if (!valid_modulus)
                        ereport(ERROR,
                                (errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
                                 errmsg("every hash partition modulus must be a factor of the next larger modulus")));

                    greatest_modulus = get_hash_partition_greatest_modulus(boundinfo);
                    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;
                            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 = castNode(Const, lfirst(cell));

                        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;

                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
                 */
                if (partition_rbound_cmp(key->partnatts, key->partsupfunc,
                                         key->partcollation, lower->datums,
                                         lower->kind, true, upper) >= 0)
                {
                    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, spec->location)));
                }

                if (partdesc->nparts > 0)
                {
                    int         offset;
                    bool        equal;

                    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,
                                                     &equal);

                    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)
                        {
                            int32       cmpval;
                            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)
                            {
                                /*
                                 * The new partition overlaps with the
                                 * existing partition between offset + 1 and
                                 * offset + 2.
                                 */
                                overlap = true;
                                with = boundinfo->indexes[offset + 2];
                            }
                        }
                    }
                    else
                    {
                        /*
                         * The new partition overlaps with the existing
                         * partition between offset and offset + 1.
                         */
                        overlap = true;
                        with = boundinfo->indexes[offset + 1];
                    }
                }

                break;
            }

        default:
            elog(ERROR, "unexpected partition strategy: %d",
                 (int) key->strategy);
    }

    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, spec->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, NULL);

    /*
     * 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("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, NULL);

            /*
             * 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("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))));

            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. The greatest
 * modulus will be at the end of the datums array because hash partitions are
 * arranged in the ascending order of their moduli and remainders.
 */
int
get_hash_partition_greatest_modulus(PartitionBoundInfo bound)
{
    Assert(bound && bound->strategy == PARTITION_STRATEGY_HASH);
    Assert(bound->datums && bound->ndatums > 0);
    Assert(DatumGetInt32(bound->datums[bound->ndatums - 1][0]) > 0);

    return DatumGetInt32(bound->datums[bound->ndatums - 1][0]);
}

/*
 * 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 = (PartitionRangeBound *) palloc0(sizeof(PartitionRangeBound));
    bound->index = index;
    bound->datums = (Datum *) palloc0(key->partnatts * sizeof(Datum));
    bound->kind = (PartitionRangeDatumKind *) palloc0(key->partnatts *
                                                      sizeof(PartitionRangeDatumKind));
    bound->lower = lower;

    i = 0;
    foreach(lc, datums)
    {
        PartitionRangeDatum *datum = castNode(PartitionRangeDatum, lfirst(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
 *
 * Return for two range bounds whether the 1st one (specified in datums1,
 * kind1, and lower1) is <, =, or > the bound specified in *b2.
 *
 * 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       cmpval = 0;     /* placate compiler */
    int         i;
    Datum      *datums2 = b2->datums;
    PartitionRangeDatumKind *kind2 = b2->kind;
    bool        lower2 = b2->lower;

    for (i = 0; i < partnatts; i++)
    {
        /*
         * 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 -1;
        else if (kind1[i] > kind2[i])
            return 1;
        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;
}

/*
 * 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,
                           Datum *rb_datums, PartitionRangeDatumKind *rb_kind,
                           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
 *
 * *is_equal is set to true if the range bound at the returned index is equal
 * to the input range bound
 */
static int
partition_range_bsearch(int partnatts, FmgrInfo *partsupfunc,
                        Oid *partcollation,
                        PartitionBoundInfo boundinfo,
                        PartitionRangeBound *probe, 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_cmp(partnatts, partsupfunc,
                                      partcollation,
                                      boundinfo->datums[mid],
                                      boundinfo->kind[mid],
                                      (boundinfo->indexes[mid] == -1),
                                      probe);
        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 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, 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)
{
    PartitionHashBound *h1 = (*(PartitionHashBound *const *) a);
    PartitionHashBound *h2 = (*(PartitionHashBound *const *) 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 = (*(PartitionListValue *const *) a)->value,
                val2 = (*(PartitionListValue *const *) 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 partition_rbound_cmp(key->partnatts, key->partsupfunc,
                                key->partcollation, b1->datums, b1->kind,
                                b1->lower, b2);
}

/*
 * get_partition_bound_num_indexes
 *
 * Returns the number of the entries in the partition bound indexes array.
 */
static int
get_partition_bound_num_indexes(PartitionBoundInfo bound)
{
    int         num_indexes;

    Assert(bound);

    switch (bound->strategy)
    {
        case PARTITION_STRATEGY_HASH:

            /*
             * The number of the entries in the indexes array is same as the
             * greatest modulus.
             */
            num_indexes = get_hash_partition_greatest_modulus(bound);
            break;

        case PARTITION_STRATEGY_LIST:
            num_indexes = bound->ndatums;
            break;

        case PARTITION_STRATEGY_RANGE:
            /* Range partitioned table has an extra index. */
            num_indexes = bound->ndatums + 1;
            break;

        default:
            elog(ERROR, "unexpected partition strategy: %d",
                 (int) bound->strategy);
    }

    return num_indexes;
}

/*
 * 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->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;

        default:
            elog(ERROR, "invalid partitioning strategy");
            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);
        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 = castNode(Const, lfirst(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 AND'd 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);
        Oid        *inhoids = pdesc->oids;
        int         nparts = pdesc->nparts,
                    i;

        for (i = 0; i < nparts; i++)
        {
            Oid         inhrelid = inhoids[i];
            HeapTuple   tuple;
            Datum       datum;
            bool        isnull;
            PartitionBoundSpec *bspec;

            tuple = SearchSysCache1(RELOID, inhrelid);
            if (!HeapTupleIsValid(tuple))
                elog(ERROR, "cache lookup failed for relation %u", inhrelid);

            datum = SysCacheGetAttr(RELOID, tuple,
                                    Anum_pg_class_relpartbound,
                                    &isnull);
            if (isnull)
                elog(ERROR, "null relpartbound for relation %u", inhrelid);

            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;
    }

    lower_or_start_datum = list_head(spec->lowerdatums);
    upper_or_start_datum = list_head(spec->upperdatums);
    num_or_arms = key->partnatts;

    /*
     * 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 = castNode(PartitionRangeDatum, lfirst(cell1));
        udatum = castNode(PartitionRangeDatum, lfirst(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 = castNode(PartitionRangeDatum, lfirst(cell1));
            if (lnext(spec->lowerdatums, cell1))
                ldatum_next = castNode(PartitionRangeDatum,
                                       lfirst(lnext(spec->lowerdatums, cell1)));
            udatum = castNode(PartitionRangeDatum, lfirst(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, Oid *partcollation,
                             Datum *values, 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.
 *
 * 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 null if the parent OID, modulus, or remainder is NULL. */
    if (PG_ARGISNULL(0) || PG_ARGISNULL(1) || PG_ARGISNULL(2))
        PG_RETURN_NULL();
    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 a positive integer")));
    if (remainder < 0)
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                 errmsg("remainder for hash partition must be a non-negative integer")));
    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 = try_relation_open(parentId, AccessShareLock);
        if (parent == NULL)
            PG_RETURN_NULL();
        key = RelationGetPartitionKey(parent);

        /* Reject parent table that is not hash-partitioned. */
        if (parent->rd_rel->relkind != RELKIND_PARTITIONED_TABLE ||
            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);
}