path: root/src/backend/partitioning/partprune.c

/*-------------------------------------------------------------------------
 *
 * partprune.c
 *		Support for partition pruning during query planning and execution
 *
 * This module implements partition pruning using the information contained in
 * table's partition descriptor, query clauses, and run-time parameters.
 *
 * During planning, clauses that can be matched to the table's partition key
 * are turned into a set of "pruning steps", which are then executed to
 * produce a set of partitions (as indexes of the RelOptInfo->part_rels array)
 * that satisfy the constraints in the step.  Partitions not in the set are said
 * to have been pruned.
 *
 * A base pruning step may also consist of expressions whose values are only
 * known during execution, such as Params, in which case pruning cannot occur
 * entirely during planning.  In that case, such steps are included alongside
 * the plan, so that they can be used by the executor for further pruning.
 *
 * There are two kinds of pruning steps: a "base" pruning step, which contains
 * information extracted from one or more clauses that are matched to the
 * (possibly multi-column) partition key, such as the expressions whose values
 * to match against partition bounds and operator strategy to associate to
 * each expression.  The other kind is a "combine" pruning step, which combines
 * the outputs of some other steps using the appropriate combination method.
 * All steps that are constructed are executed in succession such that for any
 * "combine" step, all of the steps whose output it depends on are executed
 * first and their ouput preserved.
 *
 * See gen_partprune_steps_internal() for more details on step generation.
 *
 * Portions Copyright (c) 1996-2018, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * IDENTIFICATION
 *		  src/backend/partitioning/partprune.c
 *
 *-------------------------------------------------------------------------
*/
#include "postgres.h"

#include "access/hash.h"
#include "access/nbtree.h"
#include "catalog/pg_operator.h"
#include "catalog/pg_opfamily.h"
#include "catalog/pg_type.h"
#include "executor/executor.h"
#include "miscadmin.h"
#include "nodes/makefuncs.h"
#include "nodes/nodeFuncs.h"
#include "optimizer/clauses.h"
#include "optimizer/pathnode.h"
#include "optimizer/planner.h"
#include "optimizer/predtest.h"
#include "optimizer/prep.h"
#include "partitioning/partprune.h"
#include "partitioning/partbounds.h"
#include "rewrite/rewriteManip.h"
#include "utils/lsyscache.h"


/*
 * Information about a clause matched with a partition key.
 */
typedef struct PartClauseInfo
{
	int			keyno;			/* Partition key number (0 to partnatts - 1)  */
	Oid			opno;			/* operator used to compare partkey to 'expr' */
	bool		op_is_ne;		/* is clause's original operator <> ? */
	Expr	   *expr;			/* expr the partition key is compared to */
	Oid			cmpfn;			/* Oid of function to compare 'expr' to the
								 * partition key */
	int			op_strategy;	/* cached info. */
} PartClauseInfo;

/*
 * PartClauseMatchStatus
 *		Describes the result match_clause_to_partition_key produces for a
 *		given clause and the partition key to match with that are passed to it
 */
typedef enum PartClauseMatchStatus
{
	PARTCLAUSE_NOMATCH,
	PARTCLAUSE_MATCH_CLAUSE,
	PARTCLAUSE_MATCH_NULLNESS,
	PARTCLAUSE_MATCH_STEPS,
	PARTCLAUSE_MATCH_CONTRADICT,
	PARTCLAUSE_UNSUPPORTED
} PartClauseMatchStatus;

/*
 * GeneratePruningStepsContext
 *		Information about the current state of generation of "pruning steps"
 *		for a given set of clauses
 *
 * gen_partprune_steps() initializes an instance of this struct, which is used
 * throughout the step generation process.
 */
typedef struct GeneratePruningStepsContext
{
	int			next_step_id;
	List	   *steps;
} GeneratePruningStepsContext;

/* The result of performing one PartitionPruneStep */
typedef struct PruneStepResult
{
	/*
	 * The offsets of bounds (in a table's boundinfo) whose partition is
	 * selected by the pruning step.
	 */
	Bitmapset  *bound_offsets;

	bool		scan_default;	/* Scan the default partition? */
	bool		scan_null;		/* Scan the partition for NULL values? */
} PruneStepResult;


static List *gen_partprune_steps_internal(GeneratePruningStepsContext *context,
							 RelOptInfo *rel, List *clauses,
							 bool *contradictory);
static PartitionPruneStep *gen_prune_step_op(GeneratePruningStepsContext *context,
				  StrategyNumber opstrategy, bool op_is_ne,
				  List *exprs, List *cmpfns, Bitmapset *nullkeys);
static PartitionPruneStep *gen_prune_step_combine(GeneratePruningStepsContext *context,
					   List *source_stepids,
					   PartitionPruneCombineOp combineOp);
static PartitionPruneStep *gen_prune_steps_from_opexps(PartitionScheme part_scheme,
							GeneratePruningStepsContext *context,
							List **keyclauses, Bitmapset *nullkeys);
static PartClauseMatchStatus match_clause_to_partition_key(RelOptInfo *rel,
							  GeneratePruningStepsContext *context,
							  Expr *clause, Expr *partkey, int partkeyidx,
							  bool *clause_is_not_null,
							  PartClauseInfo **pc, List **clause_steps);
static List *get_steps_using_prefix(GeneratePruningStepsContext *context,
					   StrategyNumber step_opstrategy,
					   bool step_op_is_ne,
					   Expr *step_lastexpr,
					   Oid step_lastcmpfn,
					   int step_lastkeyno,
					   Bitmapset *step_nullkeys,
					   List *prefix);
static List *get_steps_using_prefix_recurse(GeneratePruningStepsContext *context,
							   StrategyNumber step_opstrategy,
							   bool step_op_is_ne,
							   Expr *step_lastexpr,
							   Oid step_lastcmpfn,
							   int step_lastkeyno,
							   Bitmapset *step_nullkeys,
							   ListCell *start,
							   List *step_exprs,
							   List *step_cmpfns);
static PruneStepResult *get_matching_hash_bounds(PartitionPruneContext *context,
						 StrategyNumber opstrategy, Datum *values, int nvalues,
						 FmgrInfo *partsupfunc, Bitmapset *nullkeys);
static PruneStepResult *get_matching_list_bounds(PartitionPruneContext *context,
						 StrategyNumber opstrategy, Datum value, int nvalues,
						 FmgrInfo *partsupfunc, Bitmapset *nullkeys);
static PruneStepResult *get_matching_range_bounds(PartitionPruneContext *context,
						  StrategyNumber opstrategy, Datum *values, int nvalues,
						  FmgrInfo *partsupfunc, Bitmapset *nullkeys);
static bool pull_partkey_params(PartitionPruneInfo *pinfo, List *steps);
static PruneStepResult *perform_pruning_base_step(PartitionPruneContext *context,
						  PartitionPruneStepOp *opstep);
static PruneStepResult *perform_pruning_combine_step(PartitionPruneContext *context,
							 PartitionPruneStepCombine *cstep,
							 PruneStepResult **step_results);
static bool match_boolean_partition_clause(Oid partopfamily, Expr *clause,
							   Expr *partkey, Expr **outconst);
static bool partkey_datum_from_expr(PartitionPruneContext *context,
						Expr *expr, int stateidx, Datum *value);

/*
 * make_partition_pruneinfo
 *		Build List of PartitionPruneInfos, one for each 'partitioned_rels'.
 *		These can be used in the executor to allow additional partition
 *		pruning to take place.
 *
 * Here we generate partition pruning steps for 'prunequal' and also build a
 * data stucture which allows mapping of partition indexes into 'subpaths'
 * indexes.
 *
 * If no Params were found to match the partition key in any of the
 * 'partitioned_rels', then we return NIL.  In such a case run-time partition
 * pruning would be useless.
 */
List *
make_partition_pruneinfo(PlannerInfo *root, List *partition_rels,
						 List *subpaths, List *prunequal)
{
	RelOptInfo *targetpart = NULL;
	ListCell   *lc;
	List	   *pinfolist = NIL;
	int		   *relid_subnode_map;
	int		   *relid_subpart_map;
	int			i;
	bool		gotparam = false;

	/*
	 * Allocate two arrays to store the 1-based indexes of the 'subpaths' and
	 * 'partitioned_rels' by relid.
	 */
	relid_subnode_map = palloc0(sizeof(int) * root->simple_rel_array_size);
	relid_subpart_map = palloc0(sizeof(int) * root->simple_rel_array_size);

	i = 1;
	foreach(lc, subpaths)
	{
		Path	   *path = (Path *) lfirst(lc);
		RelOptInfo *pathrel = path->parent;

		Assert(IS_SIMPLE_REL(pathrel));
		Assert(pathrel->relid < root->simple_rel_array_size);

		relid_subnode_map[pathrel->relid] = i++;
	}

	/* Likewise for the partition_rels */
	i = 1;
	foreach(lc, partition_rels)
	{
		Index		rti = lfirst_int(lc);

		Assert(rti < root->simple_rel_array_size);

		relid_subpart_map[rti] = i++;
	}

	/* We now build a PartitionPruneInfo for each partition_rels */
	foreach(lc, partition_rels)
	{
		Index		rti = lfirst_int(lc);
		RelOptInfo *subpart = find_base_rel(root, rti);
		PartitionPruneInfo *pinfo;
		RangeTblEntry *rte;
		Bitmapset  *present_parts;
		int			nparts = subpart->nparts;
		int		   *subnode_map;
		int		   *subpart_map;
		List	   *partprunequal;
		List	   *pruning_steps;
		bool		contradictory;

		/*
		 * The first item in the list is the target partitioned relation.  The
		 * quals belong to this relation, so require no translation.
		 */
		if (!targetpart)
		{
			targetpart = subpart;
			partprunequal = prunequal;
		}
		else
		{
			/*
			 * For sub-partitioned tables the columns may not be in the same
			 * order as the parent, so we must translate the prunequal to make
			 * it compatible with this relation.
			 */
			partprunequal = (List *)
				adjust_appendrel_attrs_multilevel(root,
												  (Node *) prunequal,
												  subpart->relids,
												  targetpart->relids);
		}

		pruning_steps = gen_partprune_steps(subpart, partprunequal,
											&contradictory);

		if (contradictory)
		{
			/*
			 * This shouldn't happen as the planner should have detected this
			 * earlier. However, we do use additional quals from parameterized
			 * paths here. These do only compare Params to the partition key,
			 * so this shouldn't cause the discovery of any new qual
			 * contradictions that were not previously discovered as the Param
			 * values are unknown during planning.  Anyway, we'd better do
			 * something sane here, so let's just disable run-time pruning.
			 */
			return NIL;
		}

		subnode_map = (int *) palloc(nparts * sizeof(int));
		subpart_map = (int *) palloc(nparts * sizeof(int));
		present_parts = NULL;

		/*
		 * Loop over each partition of the partitioned rel and record the
		 * subpath index for each.  Any partitions which are not present in
		 * the subpaths List will be set to -1, and any sub-partitioned table
		 * which is not present will also be set to -1.
		 */
		for (i = 0; i < nparts; i++)
		{
			RelOptInfo *partrel = subpart->part_rels[i];
			int			subnodeidx = relid_subnode_map[partrel->relid] - 1;
			int			subpartidx = relid_subpart_map[partrel->relid] - 1;

			subnode_map[i] = subnodeidx;
			subpart_map[i] = subpartidx;

			/*
			 * Record the indexes of all the partition indexes that we have
			 * subnodes or subparts for.  This allows an optimization to skip
			 * attempting any run-time pruning when no Params are found
			 * matching the partition key at this level.
			 */
			if (subnodeidx >= 0 || subpartidx >= 0)
				present_parts = bms_add_member(present_parts, i);
		}

		rte = root->simple_rte_array[subpart->relid];

		pinfo = makeNode(PartitionPruneInfo);
		pinfo->reloid = rte->relid;
		pinfo->pruning_steps = pruning_steps;
		pinfo->present_parts = present_parts;
		pinfo->nparts = nparts;
		pinfo->extparams = NULL;
		pinfo->execparams = NULL;
		pinfo->subnode_map = subnode_map;
		pinfo->subpart_map = subpart_map;

		/*
		 * Extract Params matching partition key and record if we got any.
		 * We'll not bother enabling run-time pruning if no params matched the
		 * partition key at any level of partitioning.
		 */
		gotparam |= pull_partkey_params(pinfo, pruning_steps);

		pinfolist = lappend(pinfolist, pinfo);
	}

	pfree(relid_subnode_map);
	pfree(relid_subpart_map);

	if (gotparam)
		return pinfolist;

	/*
	 * If no Params were found to match the partition key on any of the
	 * partitioned relations then there's no point doing any run-time
	 * partition pruning.
	 */
	return NIL;
}

/*
 * gen_partprune_steps
 *		Process 'clauses' (a rel's baserestrictinfo list of clauses) and return
 *		a list of "partition pruning steps"
 *
 * If the clauses in the input list are contradictory or there is a
 * pseudo-constant "false", *contradictory is set to true upon return.
 */
List *
gen_partprune_steps(RelOptInfo *rel, List *clauses, bool *contradictory)
{
	GeneratePruningStepsContext context;

	context.next_step_id = 0;
	context.steps = NIL;

	/* The clauses list may be modified below, so better make a copy. */
	clauses = list_copy(clauses);

	/*
	 * For sub-partitioned tables there's a corner case where if the
	 * sub-partitioned table shares any partition keys with its parent, then
	 * it's possible that the partitioning hierarchy allows the parent
	 * partition to only contain a narrower range of values than the
	 * sub-partitioned table does.  In this case it is possible that we'd
	 * include partitions that could not possibly have any tuples matching
	 * 'clauses'.  The possibility of such a partition arrangement is perhaps
	 * unlikely for non-default partitions, but it may be more likely in the
	 * case of default partitions, so we'll add the parent partition table's
	 * partition qual to the clause list in this case only.  This may result
	 * in the default partition being eliminated.
	 */
	if (partition_bound_has_default(rel->boundinfo) &&
		rel->partition_qual != NIL)
	{
		List	   *partqual = rel->partition_qual;

		partqual = (List *) expression_planner((Expr *) partqual);

		/* Fix Vars to have the desired varno */
		if (rel->relid != 1)
			ChangeVarNodes((Node *) partqual, 1, rel->relid, 0);

		clauses = list_concat(clauses, partqual);
	}

	/* Down into the rabbit-hole. */
	gen_partprune_steps_internal(&context, rel, clauses, contradictory);

	return context.steps;
}

/*
 * prune_append_rel_partitions
 *		Returns RT indexes of the minimum set of child partitions which must
 *		be scanned to satisfy rel's baserestrictinfo quals.
 *
 * Callers must ensure that 'rel' is a partitioned table.
 */
Relids
prune_append_rel_partitions(RelOptInfo *rel)
{
	Relids		result;
	List	   *clauses = rel->baserestrictinfo;
	List	   *pruning_steps;
	bool		contradictory;
	PartitionPruneContext context;
	Bitmapset  *partindexes;
	int			i;

	Assert(clauses != NIL);
	Assert(rel->part_scheme != NULL);

	/* If there are no partitions, return the empty set */
	if (rel->nparts == 0)
		return NULL;

	/*
	 * Process clauses.  If the clauses are found to be contradictory, we can
	 * return the empty set.
	 */
	pruning_steps = gen_partprune_steps(rel, clauses, &contradictory);
	if (contradictory)
		return NULL;

	context.strategy = rel->part_scheme->strategy;
	context.partnatts = rel->part_scheme->partnatts;
	context.partopfamily = rel->part_scheme->partopfamily;
	context.partopcintype = rel->part_scheme->partopcintype;
	context.partcollation = rel->part_scheme->partcollation;
	context.partsupfunc = rel->part_scheme->partsupfunc;
	context.nparts = rel->nparts;
	context.boundinfo = rel->boundinfo;

	/* Not valid when being called from the planner */
	context.planstate = NULL;
	context.safeparams = NULL;
	context.exprstates = NULL;

	/* Actual pruning happens here. */
	partindexes = get_matching_partitions(&context, pruning_steps);

	/* Add selected partitions' RT indexes to result. */
	i = -1;
	result = NULL;
	while ((i = bms_next_member(partindexes, i)) >= 0)
		result = bms_add_member(result, rel->part_rels[i]->relid);

	return result;
}

/*
 * get_matching_partitions
 *		Determine partitions that survive partition pruning
 *
 * Returns a Bitmapset of the RelOptInfo->part_rels indexes of the surviving
 * partitions.
 */
Bitmapset *
get_matching_partitions(PartitionPruneContext *context, List *pruning_steps)
{
	Bitmapset  *result;
	int			num_steps = list_length(pruning_steps),
				i;
	PruneStepResult **results,
			   *final_result;
	ListCell   *lc;

	/* If there are no pruning steps then all partitions match. */
	if (num_steps == 0)
		return bms_add_range(NULL, 0, context->nparts - 1);

	/*
	 * Allocate space for individual pruning steps to store its result.  Each
	 * slot will hold a PruneStepResult after performing a given pruning step.
	 * Later steps may use the result of one or more earlier steps.  The
	 * result of applying all pruning steps is the value contained in the slot
	 * of the last pruning step.
	 */
	results = (PruneStepResult **)
		palloc0(num_steps * sizeof(PruneStepResult *));
	foreach(lc, pruning_steps)
	{
		PartitionPruneStep *step = lfirst(lc);

		switch (nodeTag(step))
		{
			case T_PartitionPruneStepOp:
				results[step->step_id] =
					perform_pruning_base_step(context,
											  (PartitionPruneStepOp *) step);
				break;

			case T_PartitionPruneStepCombine:
				results[step->step_id] =
					perform_pruning_combine_step(context,
												 (PartitionPruneStepCombine *) step,
												 results);
				break;

			default:
				elog(ERROR, "invalid pruning step type: %d",
					 (int) nodeTag(step));
		}
	}

	/*
	 * At this point we know the offsets of all the datums whose corresponding
	 * partitions need to be in the result, including special null-accepting
	 * and default partitions.  Collect the actual partition indexes now.
	 */
	final_result = results[num_steps - 1];
	Assert(final_result != NULL);
	i = -1;
	result = NULL;
	while ((i = bms_next_member(final_result->bound_offsets, i)) >= 0)
	{
		int			partindex = context->boundinfo->indexes[i];

		/*
		 * In range and hash partitioning cases, some slots may contain -1,
		 * indicating that no partition has been defined to accept a given
		 * range of data or for a given remainder, respectively. The default
		 * partition, if any, in case of range partitioning, will be added to
		 * the result, because the specified range still satisfies the query's
		 * conditions.
		 */
		if (partindex >= 0)
			result = bms_add_member(result, partindex);
	}

	/* Add the null and/or default partition if needed and if present. */
	if (final_result->scan_null)
	{
		Assert(context->strategy == PARTITION_STRATEGY_LIST);
		Assert(partition_bound_accepts_nulls(context->boundinfo));
		result = bms_add_member(result, context->boundinfo->null_index);
	}
	if (final_result->scan_default)
	{
		Assert(context->strategy == PARTITION_STRATEGY_LIST ||
			   context->strategy == PARTITION_STRATEGY_RANGE);
		Assert(partition_bound_has_default(context->boundinfo));
		result = bms_add_member(result, context->boundinfo->default_index);
	}

	return result;
}

/*
 * gen_partprune_steps_internal
 *		Processes 'clauses' to generate partition pruning steps.
 *
 * From OpExpr clauses that are mutually AND'd, we find combinations of those
 * that match to the partition key columns and for every such combination,
 * we emit a PartitionPruneStepOp containing a vector of expressions whose
 * values are used as a look up key to search partitions by comparing the
 * values with partition bounds.  Relevant details of the operator and a
 * vector of (possibly cross-type) comparison functions is also included with
 * each step.
 *
 * For BoolExpr clauses, we recursively generate steps for each argument, and
 * return a PartitionPruneStepCombine of their results.
 *
 * The generated steps are added to the context's steps list.  Each step is
 * assigned a step identifier, unique even across recursive calls.
 *
 * If we find clauses that are mutually contradictory, or a pseudoconstant
 * clause that contains false, we set *contradictory to true and return NIL
 * (that is, no pruning steps).  Caller should consider all partitions as
 * pruned in that case.  Otherwise, *contradictory is set to false.
 *
 * Note: the 'clauses' List may be modified inside this function. Callers may
 * like to make a copy of it before passing them to this function.
 */
static List *
gen_partprune_steps_internal(GeneratePruningStepsContext *context,
							 RelOptInfo *rel, List *clauses,
							 bool *contradictory)
{
	PartitionScheme part_scheme = rel->part_scheme;
	List	   *keyclauses[PARTITION_MAX_KEYS];
	Bitmapset  *nullkeys = NULL,
			   *notnullkeys = NULL;
	bool		generate_opsteps = false;
	List	   *result = NIL;
	ListCell   *lc;

	*contradictory = false;

	memset(keyclauses, 0, sizeof(keyclauses));
	foreach(lc, clauses)
	{
		Expr	   *clause = (Expr *) lfirst(lc);
		int			i;

		if (IsA(clause, RestrictInfo))
		{
			RestrictInfo *rinfo = (RestrictInfo *) clause;

			clause = rinfo->clause;
			if (rinfo->pseudoconstant &&
				IsA(rinfo->clause, Const) &&
				!DatumGetBool(((Const *) clause)->constvalue))
			{
				*contradictory = true;
				return NIL;
			}
		}

		/* Get the BoolExpr's out of the way. */
		if (IsA(clause, BoolExpr))
		{
			/*
			 * Generate steps for arguments.
			 *
			 * While steps generated for the arguments themselves will be
			 * added to context->steps during recursion and will be evaluated
			 * independently, collect their step IDs to be stored in the
			 * combine step we'll be creating.
			 */
			if (or_clause((Node *) clause))
			{
				List	   *arg_stepids = NIL;
				bool		all_args_contradictory = true;
				ListCell   *lc1;

				/*
				 * Get pruning step for each arg.  If we get contradictory for
				 * all args, it means the OR expression is false as a whole.
				 */
				foreach(lc1, ((BoolExpr *) clause)->args)
				{
					Expr	   *arg = lfirst(lc1);
					bool		arg_contradictory;
					List	   *argsteps;

					argsteps =
						gen_partprune_steps_internal(context, rel,
													 list_make1(arg),
													 &arg_contradictory);
					if (!arg_contradictory)
						all_args_contradictory = false;

					if (argsteps != NIL)
					{
						PartitionPruneStep *step;

						Assert(list_length(argsteps) == 1);
						step = (PartitionPruneStep *) linitial(argsteps);
						arg_stepids = lappend_int(arg_stepids, step->step_id);
					}
					else
					{
						/*
						 * No steps either means that arg_contradictory is
						 * true or the arg didn't contain a clause matching
						 * this partition key.
						 *
						 * In case of the latter, we cannot prune using such
						 * an arg.  To indicate that to the pruning code, we
						 * must construct a dummy PartitionPruneStepCombine
						 * whose source_stepids is set to an empty List.
						 * However, if we can prove using constraint exclusion
						 * that the clause refutes the table's partition
						 * constraint (if it's sub-partitioned), we need not
						 * bother with that.  That is, we effectively ignore
						 * this OR arm.
						 */
						List	   *partconstr = rel->partition_qual;
						PartitionPruneStep *orstep;

						/* Just ignore this argument. */
						if (arg_contradictory)
							continue;

						if (partconstr)
						{
							partconstr = (List *)
								expression_planner((Expr *) partconstr);
							if (rel->relid != 1)
								ChangeVarNodes((Node *) partconstr, 1,
											   rel->relid, 0);
							if (predicate_refuted_by(partconstr,
													 list_make1(arg),
													 false))
								continue;
						}

						orstep = gen_prune_step_combine(context, NIL,
														PARTPRUNE_COMBINE_UNION);
						arg_stepids = lappend_int(arg_stepids, orstep->step_id);
					}
				}

				*contradictory = all_args_contradictory;

				/* Check if any contradicting clauses were found */
				if (*contradictory)
					return NIL;

				if (arg_stepids != NIL)
				{
					PartitionPruneStep *step;

					step = gen_prune_step_combine(context, arg_stepids,
												  PARTPRUNE_COMBINE_UNION);
					result = lappend(result, step);
				}
				continue;
			}
			else if (and_clause((Node *) clause))
			{
				List	   *args = ((BoolExpr *) clause)->args;
				List	   *argsteps,
						   *arg_stepids = NIL;
				ListCell   *lc1;

				/*
				 * args may itself contain clauses of arbitrary type, so just
				 * recurse and later combine the component partitions sets
				 * using a combine step.
				 */
				argsteps = gen_partprune_steps_internal(context, rel, args,
														contradictory);
				if (*contradictory)
					return NIL;

				foreach(lc1, argsteps)
				{
					PartitionPruneStep *step = lfirst(lc1);

					arg_stepids = lappend_int(arg_stepids, step->step_id);
				}

				if (arg_stepids != NIL)
				{
					PartitionPruneStep *step;

					step = gen_prune_step_combine(context, arg_stepids,
												  PARTPRUNE_COMBINE_INTERSECT);
					result = lappend(result, step);
				}
				continue;
			}

			/*
			 * Fall-through for a NOT clause, which if it's a Boolean clause,
			 * will be handled in match_clause_to_partition_key(). We
			 * currently don't perform any pruning for more complex NOT
			 * clauses.
			 */
		}

		/*
		 * Must be a clause for which we can check if one of its args matches
		 * the partition key.
		 */
		for (i = 0; i < part_scheme->partnatts; i++)
		{
			Expr	   *partkey = linitial(rel->partexprs[i]);
			bool		clause_is_not_null = false;
			PartClauseInfo *pc = NULL;
			List	   *clause_steps = NIL;

			switch (match_clause_to_partition_key(rel, context,
												  clause, partkey, i,
												  &clause_is_not_null,
												  &pc, &clause_steps))
			{
				case PARTCLAUSE_MATCH_CLAUSE:
					Assert(pc != NULL);

					/*
					 * Since we only allow strict operators, check for any
					 * contradicting IS NULL.
					 */
					if (bms_is_member(i, nullkeys))
					{
						*contradictory = true;
						return NIL;
					}
					generate_opsteps = true;
					keyclauses[i] = lappend(keyclauses[i], pc);
					break;

				case PARTCLAUSE_MATCH_NULLNESS:
					if (!clause_is_not_null)
					{
						/* check for conflicting IS NOT NULL */
						if (bms_is_member(i, notnullkeys))
						{
							*contradictory = true;
							return NIL;
						}
						nullkeys = bms_add_member(nullkeys, i);
					}
					else
					{
						/* check for conflicting IS NULL */
						if (bms_is_member(i, nullkeys))
						{
							*contradictory = true;
							return NIL;
						}
						notnullkeys = bms_add_member(notnullkeys, i);
					}
					break;

				case PARTCLAUSE_MATCH_STEPS:
					Assert(clause_steps != NIL);
					result = list_concat(result, clause_steps);
					break;

				case PARTCLAUSE_MATCH_CONTRADICT:
					/* We've nothing more to do if a contradiction was found. */
					*contradictory = true;
					return NIL;

				case PARTCLAUSE_NOMATCH:

					/*
					 * Clause didn't match this key, but it might match the
					 * next one.
					 */
					continue;

				case PARTCLAUSE_UNSUPPORTED:
					/* This clause cannot be used for pruning. */
					break;
			}

			/* done; go check the next clause. */
			break;
		}
	}

	/*
	 * If generate_opsteps is set to false it means no OpExprs were directly
	 * present in the input list.
	 */
	if (!generate_opsteps)
	{
		/*
		 * Generate one prune step for the information derived from IS NULL,
		 * if any.  To prune hash partitions, we must have found IS NULL
		 * clauses for all partition keys.
		 */
		if (!bms_is_empty(nullkeys) &&
			(part_scheme->strategy != PARTITION_STRATEGY_HASH ||
			 bms_num_members(nullkeys) == part_scheme->partnatts))
		{
			PartitionPruneStep *step;

			step = gen_prune_step_op(context, InvalidStrategy,
									 false, NIL, NIL, nullkeys);
			result = lappend(result, step);
		}

		/*
		 * Note that for IS NOT NULL clauses, simply having step suffices;
		 * there is no need to propagate the exact details of which keys are
		 * required to be NOT NULL.  Hash partitioning expects to see actual
		 * values to perform any pruning.
		 */
		if (!bms_is_empty(notnullkeys) &&
			part_scheme->strategy != PARTITION_STRATEGY_HASH)
		{
			PartitionPruneStep *step;

			step = gen_prune_step_op(context, InvalidStrategy,
									 false, NIL, NIL, NULL);
			result = lappend(result, step);
		}
	}
	else
	{
		PartitionPruneStep *step;

		/* Generate pruning steps from OpExpr clauses in keyclauses. */
		step = gen_prune_steps_from_opexps(part_scheme, context,
										   keyclauses, nullkeys);
		if (step != NULL)
			result = lappend(result, step);
	}

	/*
	 * Finally, results from all entries appearing in result should be
	 * combined using an INTERSECT combine step, if more than one.
	 */
	if (list_length(result) > 1)
	{
		List	   *step_ids = NIL;

		foreach(lc, result)
		{
			PartitionPruneStep *step = lfirst(lc);

			step_ids = lappend_int(step_ids, step->step_id);
		}

		if (step_ids != NIL)
		{
			PartitionPruneStep *step;

			step = gen_prune_step_combine(context, step_ids,
										  PARTPRUNE_COMBINE_INTERSECT);
			result = lappend(result, step);
		}
	}

	return result;
}

/*
 * gen_prune_step_op
 *		Generate a pruning step for a specific operator
 *
 * The step is assigned a unique step identifier and added to context's 'steps'
 * list.
 */
static PartitionPruneStep *
gen_prune_step_op(GeneratePruningStepsContext *context,
				  StrategyNumber opstrategy, bool op_is_ne,
				  List *exprs, List *cmpfns,
				  Bitmapset *nullkeys)
{
	PartitionPruneStepOp *opstep = makeNode(PartitionPruneStepOp);

	opstep->step.step_id = context->next_step_id++;

	/*
	 * For clauses that contain an <> operator, set opstrategy to
	 * InvalidStrategy to signal get_matching_list_bounds to do the right
	 * thing.
	 */
	opstep->opstrategy = op_is_ne ? InvalidStrategy : opstrategy;
	Assert(list_length(exprs) == list_length(cmpfns));
	opstep->exprs = exprs;
	opstep->cmpfns = cmpfns;
	opstep->nullkeys = nullkeys;

	context->steps = lappend(context->steps, opstep);

	return (PartitionPruneStep *) opstep;
}

/*
 * gen_prune_step_combine
 *		Generate a pruning step for a combination of several other steps
 *
 * The step is assigned a unique step identifier and added to context's
 * 'steps' list.
 */
static PartitionPruneStep *
gen_prune_step_combine(GeneratePruningStepsContext *context,
					   List *source_stepids,
					   PartitionPruneCombineOp combineOp)
{
	PartitionPruneStepCombine *cstep = makeNode(PartitionPruneStepCombine);

	cstep->step.step_id = context->next_step_id++;
	cstep->combineOp = combineOp;
	cstep->source_stepids = source_stepids;

	context->steps = lappend(context->steps, cstep);

	return (PartitionPruneStep *) cstep;
}

/*
 * gen_prune_steps_from_opexps
 *		Generate pruning steps based on clauses for partition keys
 *
 * 'keyclauses' contains one list of clauses per partition key.  We check here
 * if we have found clauses for a valid subset of the partition key. In some
 * cases, (depending on the type of partitioning being used) if we didn't
 * find clauses for a given key, we discard clauses that may have been
 * found for any subsequent keys; see specific notes below.
 */
static PartitionPruneStep *
gen_prune_steps_from_opexps(PartitionScheme part_scheme,
							GeneratePruningStepsContext *context,
							List **keyclauses, Bitmapset *nullkeys)
{
	ListCell   *lc;
	List	   *opsteps = NIL;
	List	   *btree_clauses[BTMaxStrategyNumber + 1],
			   *hash_clauses[HTMaxStrategyNumber + 1];
	bool		need_next_less,
				need_next_eq,
				need_next_greater;
	int			i;

	memset(btree_clauses, 0, sizeof(btree_clauses));
	memset(hash_clauses, 0, sizeof(hash_clauses));
	for (i = 0; i < part_scheme->partnatts; i++)
	{
		List	   *clauselist = keyclauses[i];
		bool		consider_next_key = true;

		/*
		 * To be useful for pruning, we must have clauses for a prefix of
		 * partition keys in the case of range partitioning.  So, ignore
		 * clauses for keys after this one.
		 */
		if (part_scheme->strategy == PARTITION_STRATEGY_RANGE &&
			clauselist == NIL)
			break;

		/*
		 * For hash partitioning, if a column doesn't have the necessary
		 * equality clause, there should be an IS NULL clause, otherwise
		 * pruning is not possible.
		 */
		if (part_scheme->strategy == PARTITION_STRATEGY_HASH &&
			clauselist == NIL && !bms_is_member(i, nullkeys))
			return NULL;

		need_next_eq = need_next_less = need_next_greater = true;
		foreach(lc, clauselist)
		{
			PartClauseInfo *pc = (PartClauseInfo *) lfirst(lc);
			Oid			lefttype,
						righttype;

			/* Look up the operator's btree/hash strategy number. */
			if (pc->op_strategy == InvalidStrategy)
				get_op_opfamily_properties(pc->opno,
										   part_scheme->partopfamily[i],
										   false,
										   &pc->op_strategy,
										   &lefttype,
										   &righttype);

			switch (part_scheme->strategy)
			{
				case PARTITION_STRATEGY_LIST:
				case PARTITION_STRATEGY_RANGE:
					{
						PartClauseInfo *last = NULL;
						bool		inclusive = false;

						/*
						 * Add this clause to the list of clauses to be used
						 * for pruning if this is the first such key for this
						 * operator strategy or if it is consecutively next to
						 * the last column for which a clause with this
						 * operator strategy was matched.
						 */
						if (btree_clauses[pc->op_strategy] != NIL)
							last = llast(btree_clauses[pc->op_strategy]);

						if (last == NULL ||
							i == last->keyno || i == last->keyno + 1)
							btree_clauses[pc->op_strategy] =
								lappend(btree_clauses[pc->op_strategy], pc);

						/*
						 * We may not need the next clause if they're of
						 * certain strategy.
						 */
						switch (pc->op_strategy)
						{
							case BTLessEqualStrategyNumber:
								inclusive = true;
								/* fall through */
							case BTLessStrategyNumber:
								if (!inclusive)
									need_next_eq = need_next_less = false;
								break;
							case BTEqualStrategyNumber:
								/* always accept clauses for the next key. */
								break;
							case BTGreaterEqualStrategyNumber:
								inclusive = true;
								/* fall through */
							case BTGreaterStrategyNumber:
								if (!inclusive)
									need_next_eq = need_next_greater = false;
								break;
						}

						/* We may want to change our mind. */
						if (consider_next_key)
							consider_next_key = (need_next_eq ||
												 need_next_less ||
												 need_next_greater);
						break;
					}

				case PARTITION_STRATEGY_HASH:
					if (pc->op_strategy != HTEqualStrategyNumber)
						elog(ERROR, "invalid clause for hash partitioning");
					hash_clauses[pc->op_strategy] =
						lappend(hash_clauses[pc->op_strategy], pc);
					break;

				default:
					elog(ERROR, "invalid partition strategy: %c",
						 part_scheme->strategy);
					break;
			}
		}

		/*
		 * If we've decided that clauses for subsequent partition keys
		 * wouldn't be useful for pruning, don't search any further.
		 */
		if (!consider_next_key)
			break;
	}

	/*
	 * Now, we have divided clauses according to their operator strategies.
	 * Check for each strategy if we can generate pruning step(s) by
	 * collecting a list of expressions whose values will constitute a vector
	 * that can be used as a lookup key by a partition bound searching
	 * function.
	 */
	switch (part_scheme->strategy)
	{
		case PARTITION_STRATEGY_LIST:
		case PARTITION_STRATEGY_RANGE:
			{
				List	   *eq_clauses = btree_clauses[BTEqualStrategyNumber];
				List	   *le_clauses = btree_clauses[BTLessEqualStrategyNumber];
				List	   *ge_clauses = btree_clauses[BTGreaterEqualStrategyNumber];
				int			strat;

				/*
				 * For each clause under consideration for a given strategy,
				 * we collect expressions from clauses for earlier keys, whose
				 * operator strategy is inclusive, into a list called
				 * 'prefix'. By appending the clause's own expression to the
				 * 'prefix', we'll generate one step using the so generated
				 * vector and assign the current strategy to it.  Actually,
				 * 'prefix' might contain multiple clauses for the same key,
				 * in which case, we must generate steps for various
				 * combinations of expressions of different keys, which
				 * get_steps_using_prefix takes care of for us.
				 */
				for (strat = 1; strat <= BTMaxStrategyNumber; strat++)
				{
					foreach(lc, btree_clauses[strat])
					{
						PartClauseInfo *pc = lfirst(lc);
						ListCell   *lc1;
						List	   *prefix = NIL;
						List	   *pc_steps;

						/*
						 * Expressions from = clauses can always be in the
						 * prefix, provided they're from an earlier key.
						 */
						foreach(lc1, eq_clauses)
						{
							PartClauseInfo *eqpc = lfirst(lc1);

							if (eqpc->keyno == pc->keyno)
								break;
							if (eqpc->keyno < pc->keyno)
								prefix = lappend(prefix, eqpc);
						}

						/*
						 * If we're generating steps for </<= strategy, we can
						 * add other <= clauses to the prefix, provided
						 * they're from an earlier key.
						 */
						if (strat == BTLessStrategyNumber ||
							strat == BTLessEqualStrategyNumber)
						{
							foreach(lc1, le_clauses)
							{
								PartClauseInfo *lepc = lfirst(lc1);

								if (lepc->keyno == pc->keyno)
									break;
								if (lepc->keyno < pc->keyno)
									prefix = lappend(prefix, lepc);
							}
						}

						/*
						 * If we're generating steps for >/>= strategy, we can
						 * add other >= clauses to the prefix, provided
						 * they're from an earlier key.
						 */
						if (strat == BTGreaterStrategyNumber ||
							strat == BTGreaterEqualStrategyNumber)
						{
							foreach(lc1, ge_clauses)
							{
								PartClauseInfo *gepc = lfirst(lc1);

								if (gepc->keyno == pc->keyno)
									break;
								if (gepc->keyno < pc->keyno)
									prefix = lappend(prefix, gepc);
							}
						}

						/*
						 * As mentioned above, if 'prefix' contains multiple
						 * expressions for the same key, the following will
						 * generate multiple steps, one for each combination
						 * of the expressions for different keys.
						 *
						 * Note that we pass NULL for step_nullkeys, because
						 * we don't search list/range partition bounds where
						 * some keys are NULL.
						 */
						Assert(pc->op_strategy == strat);
						pc_steps = get_steps_using_prefix(context, strat,
														  pc->op_is_ne,
														  pc->expr,
														  pc->cmpfn,
														  pc->keyno,
														  NULL,
														  prefix);
						opsteps = list_concat(opsteps, list_copy(pc_steps));
					}
				}
				break;
			}

		case PARTITION_STRATEGY_HASH:
			{
				List	   *eq_clauses = hash_clauses[HTEqualStrategyNumber];

				/* For hash partitioning, we have just the = strategy. */
				if (eq_clauses != NIL)
				{
					PartClauseInfo *pc;
					List	   *pc_steps;
					List	   *prefix = NIL;
					int			last_keyno;
					ListCell   *lc1;

					/*
					 * Locate the clause for the greatest column.  This may
					 * not belong to the last partition key, but it is the
					 * clause belonging to the last partition key we found a
					 * clause for above.
					 */
					pc = llast(eq_clauses);

					/*
					 * There might be multiple clauses which matched to that
					 * partition key; find the first such clause.  While at
					 * it, add all the clauses before that one to 'prefix'.
					 */
					last_keyno = pc->keyno;
					foreach(lc, eq_clauses)
					{
						pc = lfirst(lc);
						if (pc->keyno == last_keyno)
							break;
						prefix = lappend(prefix, pc);
					}

					/*
					 * For each clause for the "last" column, after appending
					 * the clause's own expression to the 'prefix', we'll
					 * generate one step using the so generated vector and and
					 * assign = as its strategy.  Actually, 'prefix' might
					 * contain multiple clauses for the same key, in which
					 * case, we must generate steps for various combinations
					 * of expressions of different keys, which
					 * get_steps_using_prefix will take care of for us.
					 */
					for_each_cell(lc1, lc)
					{
						pc = lfirst(lc1);

						/*
						 * Note that we pass nullkeys for step_nullkeys,
						 * because we need to tell hash partition bound search
						 * function which of the keys we found IS NULL clauses
						 * for.
						 */
						Assert(pc->op_strategy == HTEqualStrategyNumber);
						pc_steps =
							get_steps_using_prefix(context,
												   HTEqualStrategyNumber,
												   false,
												   pc->expr,
												   pc->cmpfn,
												   pc->keyno,
												   nullkeys,
												   prefix);
						opsteps = list_concat(opsteps, list_copy(pc_steps));
					}
				}
				break;
			}

		default:
			elog(ERROR, "invalid partition strategy: %c",
				 part_scheme->strategy);
			break;
	}

	/* Lastly, add a combine step to mutually AND these op steps, if needed */
	if (list_length(opsteps) > 1)
	{
		List	   *opstep_ids = NIL;

		foreach(lc, opsteps)
		{
			PartitionPruneStep *step = lfirst(lc);

			opstep_ids = lappend_int(opstep_ids, step->step_id);
		}

		if (opstep_ids != NIL)
			return gen_prune_step_combine(context, opstep_ids,
										  PARTPRUNE_COMBINE_INTERSECT);
		return NULL;
	}
	else if (opsteps != NIL)
		return linitial(opsteps);

	return NULL;
}

/*
 * If the partition key has a collation, then the clause must have the same
 * input collation.  If the partition key is non-collatable, we assume the
 * collation doesn't matter, because while collation wasn't considered when
 * performing partitioning, the clause still may have a collation assigned
 * due to the other input being of a collatable type.
 *
 * See also IndexCollMatchesExprColl.
 */
#define PartCollMatchesExprColl(partcoll, exprcoll) \
	((partcoll) == InvalidOid || (partcoll) == (exprcoll))

/*
 * match_clause_to_partition_key
 *		Attempt to match the given 'clause' with the specified partition key.
 *
 * Return value is:
 * * PARTCLAUSE_NOMATCH if the clause doesn't match this partition key (but
 *   caller should keep trying, because it might match a subsequent key).
 *   Output arguments: none set.
 *
 * * PARTCLAUSE_MATCH_CLAUSE if there is a match.
 *   Output arguments: *pc is set to a PartClauseInfo constructed for the
 *   matched clause.
 *
 * * PARTCLAUSE_MATCH_NULLNESS if there is a match, and the matched clause was
 *   either a "a IS NULL" or "a IS NOT NULL" clause.
 *   Output arguments: *clause_is_not_null is set to false in the former case
 *   true otherwise.
 *
 * * PARTCLAUSE_MATCH_STEPS if there is a match.
 *   Output arguments: *clause_steps is set to a list of PartitionPruneStep
 *   generated for the clause.
 *
 * * PARTCLAUSE_MATCH_CONTRADICT if the clause is self-contradictory.  This can
 *   only happen if it's a BoolExpr whose arguments are self-contradictory.
 *   Output arguments: none set.
 *
 * * PARTCLAUSE_UNSUPPORTED if the clause cannot be used for pruning at all
 *   due to one of its properties, such as argument volatility, even if it may
 *   have been matched with a key.
 *   Output arguments: none set.
 */
static PartClauseMatchStatus
match_clause_to_partition_key(RelOptInfo *rel,
							  GeneratePruningStepsContext *context,
							  Expr *clause, Expr *partkey, int partkeyidx,
							  bool *clause_is_not_null, PartClauseInfo **pc,
							  List **clause_steps)
{
	PartitionScheme part_scheme = rel->part_scheme;
	Expr	   *expr;
	Oid			partopfamily = part_scheme->partopfamily[partkeyidx],
				partcoll = part_scheme->partcollation[partkeyidx];

	/*
	 * Recognize specially shaped clauses that match with the Boolean
	 * partition key.
	 */
	if (match_boolean_partition_clause(partopfamily, clause, partkey, &expr))
	{
		PartClauseInfo *partclause;

		partclause = (PartClauseInfo *) palloc(sizeof(PartClauseInfo));
		partclause->keyno = partkeyidx;
		/* Do pruning with the Boolean equality operator. */
		partclause->opno = BooleanEqualOperator;
		partclause->op_is_ne = false;
		partclause->expr = expr;
		/* We know that expr is of Boolean type. */
		partclause->cmpfn = rel->part_scheme->partsupfunc[partkeyidx].fn_oid;
		partclause->op_strategy = InvalidStrategy;

		*pc = partclause;

		return PARTCLAUSE_MATCH_CLAUSE;
	}
	else if (IsA(clause, OpExpr) &&
			 list_length(((OpExpr *) clause)->args) == 2)
	{
		OpExpr	   *opclause = (OpExpr *) clause;
		Expr	   *leftop,
				   *rightop;
		Oid			op_lefttype,
					op_righttype,
					commutator = InvalidOid,
					negator = InvalidOid;
		Oid			cmpfn;
		int			op_strategy;
		bool		is_opne_listp = false;
		PartClauseInfo *partclause;

		leftop = (Expr *) get_leftop(clause);
		if (IsA(leftop, RelabelType))
			leftop = ((RelabelType *) leftop)->arg;
		rightop = (Expr *) get_rightop(clause);
		if (IsA(rightop, RelabelType))
			rightop = ((RelabelType *) rightop)->arg;

		/* check if the clause matches this partition key */
		if (equal(leftop, partkey))
			expr = rightop;
		else if (equal(rightop, partkey))
		{
			expr = leftop;
			commutator = get_commutator(opclause->opno);

			/* nothing we can do unless we can swap the operands */
			if (!OidIsValid(commutator))
				return PARTCLAUSE_UNSUPPORTED;
		}
		else
			/* clause does not match this partition key, but perhaps next. */
			return PARTCLAUSE_NOMATCH;

		/*
		 * Partition key also consists of a collation that's specified for it,
		 * so try to match it too.  There may be multiple keys with the same
		 * expression but different collations.
		 */
		if (!PartCollMatchesExprColl(partcoll, opclause->inputcollid))
			return PARTCLAUSE_NOMATCH;

		/*
		 * Matched with this key.  Now check various properties of the clause
		 * to see if it's sane to use it for pruning.  If any of the
		 * properties makes it unsuitable for pruning, then the clause is
		 * useless no matter which key it's matched to.
		 */

		/*
		 * Only allow strict operators.  This will guarantee nulls are
		 * filtered.
		 */
		if (!op_strict(opclause->opno))
			return PARTCLAUSE_UNSUPPORTED;

		/* We can't use any volatile expressions to prune partitions. */
		if (contain_volatile_functions((Node *) expr))
			return PARTCLAUSE_UNSUPPORTED;

		/*
		 * Determine the input types of the operator we're considering.
		 *
		 * Normally we only care about operators that are listed as being part
		 * of the partitioning operator family.  But there is one exception:
		 * the not-equals operators are not listed in any operator family
		 * whatsoever, but their negators (equality) are.  We can use one of
		 * those if we find it, but only for list partitioning.
		 */
		if (op_in_opfamily(opclause->opno, partopfamily))
		{
			Oid		oper;

			oper = OidIsValid(commutator) ? commutator : opclause->opno;
			get_op_opfamily_properties(oper, partopfamily, false,
									   &op_strategy, &op_lefttype,
									   &op_righttype);
		}
		else
		{
			/* Not good unless list partitioning */
			if (part_scheme->strategy != PARTITION_STRATEGY_LIST)
				return PARTCLAUSE_UNSUPPORTED;

			/* See if the negator is equality */
			negator = get_negator(opclause->opno);
			if (OidIsValid(negator) && op_in_opfamily(negator, partopfamily))
			{
				get_op_opfamily_properties(negator, partopfamily, false,
										   &op_strategy, &op_lefttype,
										   &op_righttype);
				if (op_strategy == BTEqualStrategyNumber)
					is_opne_listp = true;	/* bingo */
			}

			/* Operator isn't really what we were hoping it'd be. */
			if (!is_opne_listp)
				return PARTCLAUSE_UNSUPPORTED;
		}

		/*
		 * Now find the procedure to use, based on the types.  If the clause's
		 * other argument is of the same type as the partitioning opclass's
		 * declared input type, we can use the procedure cached in
		 * PartitionKey.  If not, search for a cross-type one in the same
		 * opfamily; if one doesn't exist, give up on pruning for this clause.
		 */
		if (op_righttype == part_scheme->partopcintype[partkeyidx])
			cmpfn = part_scheme->partsupfunc[partkeyidx].fn_oid;
		else
		{
			switch (part_scheme->strategy)
			{
				/*
				 * For range and list partitioning, we need the ordering
				 * procedure with lefttype being the partition key's type, and
				 * righttype the clause's operator's right type.
				 */
				case PARTITION_STRATEGY_LIST:
				case PARTITION_STRATEGY_RANGE:
					cmpfn =
						get_opfamily_proc(part_scheme->partopfamily[partkeyidx],
										  part_scheme->partopcintype[partkeyidx],
										  op_righttype, BTORDER_PROC);
					break;

				/*
				 * For hash partitioning, we need the hashing procedure for
				 * the clause's type.
				 */
				case PARTITION_STRATEGY_HASH:
					cmpfn =
						get_opfamily_proc(part_scheme->partopfamily[partkeyidx],
										  op_righttype, op_righttype,
										  HASHEXTENDED_PROC);
					break;

				default:
					elog(ERROR, "invalid partition strategy: %c",
						 part_scheme->strategy);
					break;
			}

			/* If we couldn't find one, we cannot use this expression. */
			if (!OidIsValid(cmpfn))
				return PARTCLAUSE_UNSUPPORTED;
		}

		/*
		 * Build the clause, passing the negator or commutator if applicable.
		 */
		partclause = (PartClauseInfo *) palloc(sizeof(PartClauseInfo));
		partclause->keyno = partkeyidx;
		if (is_opne_listp)
		{
			Assert(OidIsValid(negator));
			partclause->opno = negator;
			partclause->op_is_ne = true;
			partclause->op_strategy = InvalidStrategy;
		}
		else
		{
			partclause->opno = OidIsValid(commutator) ?
				commutator : opclause->opno;
			partclause->op_is_ne = false;
			partclause->op_strategy = op_strategy;
		}
		partclause->expr = expr;
		partclause->cmpfn = cmpfn;

		*pc = partclause;

		return PARTCLAUSE_MATCH_CLAUSE;
	}
	else if (IsA(clause, ScalarArrayOpExpr))
	{
		ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) clause;
		Oid			saop_op = saop->opno;
		Oid			saop_coll = saop->inputcollid;
		Expr	   *leftop = (Expr *) linitial(saop->args),
				   *rightop = (Expr *) lsecond(saop->args);
		List	   *elem_exprs,
				   *elem_clauses;
		ListCell   *lc1;

		if (IsA(leftop, RelabelType))
			leftop = ((RelabelType *) leftop)->arg;

		/* Check it matches this partition key */
		if (!equal(leftop, partkey) ||
			!PartCollMatchesExprColl(partcoll, saop->inputcollid))
			return PARTCLAUSE_NOMATCH;

		/*
		 * Matched with this key.  Check various properties of the clause to
		 * see if it can sanely be used for partition pruning.
		 */

		/*
		 * Only allow strict operators.  This will guarantee nulls are
		 * filtered.
		 */
		if (!op_strict(saop->opno))
			return PARTCLAUSE_UNSUPPORTED;

		/* Useless if the array has any volatile functions. */
		if (contain_volatile_functions((Node *) rightop))
			return PARTCLAUSE_UNSUPPORTED;

		/*
		 * In case of NOT IN (..), we get a '<>', which we handle if list
		 * partitioning is in use and we're able to confirm that it's negator
		 * is a btree equality operator belonging to the partitioning operator
		 * family.
		 */
		if (!op_in_opfamily(saop_op, partopfamily))
		{
			Oid			negator;

			if (part_scheme->strategy != PARTITION_STRATEGY_LIST)
				return PARTCLAUSE_UNSUPPORTED;

			negator = get_negator(saop_op);
			if (OidIsValid(negator) && op_in_opfamily(negator, partopfamily))
			{
				int			strategy;
				Oid			lefttype,
							righttype;

				get_op_opfamily_properties(negator, partopfamily,
										   false, &strategy,
										   &lefttype, &righttype);
				if (strategy != BTEqualStrategyNumber)
					return PARTCLAUSE_UNSUPPORTED;
			}
		}

		/*
		 * First generate a list of Const nodes, one for each array element
		 * (excepting nulls).
		 */
		elem_exprs = NIL;
		if (IsA(rightop, Const))
		{
			Const	   *arr = castNode(Const, rightop);
			ArrayType  *arrval = DatumGetArrayTypeP(arr->constvalue);
			int16		elemlen;
			bool		elembyval;
			char		elemalign;
			Datum	   *elem_values;
			bool	   *elem_nulls;
			int			num_elems,
						i;

			get_typlenbyvalalign(ARR_ELEMTYPE(arrval),
								 &elemlen, &elembyval, &elemalign);
			deconstruct_array(arrval,
							  ARR_ELEMTYPE(arrval),
							  elemlen, elembyval, elemalign,
							  &elem_values, &elem_nulls,
							  &num_elems);
			for (i = 0; i < num_elems; i++)
			{
				Const	   *elem_expr;

				/* Only consider non-null values. */
				if (elem_nulls[i])
					continue;

				elem_expr = makeConst(ARR_ELEMTYPE(arrval), -1,
									  arr->constcollid, elemlen,
									  elem_values[i], false, elembyval);
				elem_exprs = lappend(elem_exprs, elem_expr);
			}
		}
		else
		{
			ArrayExpr  *arrexpr = castNode(ArrayExpr, rightop);

			/*
			 * For a nested ArrayExpr, we don't know how to get the actual
			 * scalar values out into a flat list, so we give up doing
			 * anything with this ScalarArrayOpExpr.
			 */
			if (arrexpr->multidims)
				return PARTCLAUSE_UNSUPPORTED;

			elem_exprs = arrexpr->elements;
		}

		/*
		 * Now generate a list of clauses, one for each array element, of the
		 * form saop_leftop saop_op elem_expr
		 */
		elem_clauses = NIL;
		foreach(lc1, elem_exprs)
		{
			Expr	   *rightop = (Expr *) lfirst(lc1),
					   *elem_clause;

			elem_clause = make_opclause(saop_op, BOOLOID, false,
										leftop, rightop,
										InvalidOid, saop_coll);
			elem_clauses = lappend(elem_clauses, elem_clause);
		}

		/*
		 * Build a combine step as if for an OR clause or add the clauses to
		 * the end of the list that's being processed currently.
		 */
		if (saop->useOr && list_length(elem_clauses) > 1)
		{
			Expr	   *orexpr;
			bool		contradictory;

			orexpr = makeBoolExpr(OR_EXPR, elem_clauses, -1);
			*clause_steps =
				gen_partprune_steps_internal(context, rel, list_make1(orexpr),
											 &contradictory);
			if (contradictory)
				return PARTCLAUSE_MATCH_CONTRADICT;

			Assert(list_length(*clause_steps) == 1);
			return PARTCLAUSE_MATCH_STEPS;
		}
		else
		{
			bool		contradictory;

			*clause_steps =
				gen_partprune_steps_internal(context, rel, elem_clauses,
											 &contradictory);
			if (contradictory)
				return PARTCLAUSE_MATCH_CONTRADICT;
			Assert(list_length(*clause_steps) >= 1);
			return PARTCLAUSE_MATCH_STEPS;
		}
	}
	else if (IsA(clause, NullTest))
	{
		NullTest   *nulltest = (NullTest *) clause;
		Expr	   *arg = nulltest->arg;

		if (IsA(arg, RelabelType))
			arg = ((RelabelType *) arg)->arg;

		/* Does arg match with this partition key column? */
		if (!equal(arg, partkey))
			return PARTCLAUSE_NOMATCH;

		*clause_is_not_null = nulltest->nulltesttype == IS_NOT_NULL;

		return PARTCLAUSE_MATCH_NULLNESS;
	}

	return PARTCLAUSE_UNSUPPORTED;
}

/*
 * get_steps_using_prefix
 *		Generate list of PartitionPruneStepOp steps each consisting of given
 *		opstrategy
 *
 * To generate steps, step_lastexpr and step_lastcmpfn are appended to
 * expressions and cmpfns, respectively, extracted from the clauses in
 * 'prefix'.  Actually, since 'prefix' may contain multiple clauses for the
 * same partition key column, we must generate steps for various combinations
 * of the clauses of different keys.
 */
static List *
get_steps_using_prefix(GeneratePruningStepsContext *context,
					   StrategyNumber step_opstrategy,
					   bool step_op_is_ne,
					   Expr *step_lastexpr,
					   Oid step_lastcmpfn,
					   int step_lastkeyno,
					   Bitmapset *step_nullkeys,
					   List *prefix)
{
	/* Quick exit if there are no values to prefix with. */
	if (list_length(prefix) == 0)
	{
		PartitionPruneStep *step;

		step = gen_prune_step_op(context,
								 step_opstrategy,
								 step_op_is_ne,
								 list_make1(step_lastexpr),
								 list_make1_oid(step_lastcmpfn),
								 step_nullkeys);
		return list_make1(step);
	}

	/* Recurse to generate steps for various combinations. */
	return get_steps_using_prefix_recurse(context,
										  step_opstrategy,
										  step_op_is_ne,
										  step_lastexpr,
										  step_lastcmpfn,
										  step_lastkeyno,
										  step_nullkeys,
										  list_head(prefix),
										  NIL, NIL);
}

/*
 * get_steps_using_prefix_recurse
 *		Recursively generate combinations of clauses for different partition
 *		keys and start generating steps upon reaching clauses for the greatest
 *		column that is less than the one for which we're currently generating
 *		steps (that is, step_lastkeyno)
 *
 * 'start' is where we should start iterating for the current invocation.
 * 'step_exprs' and 'step_cmpfns' each contains the expressions and cmpfns
 * we've generated so far from the clauses for the previous part keys.
 */
static List *
get_steps_using_prefix_recurse(GeneratePruningStepsContext *context,
							   StrategyNumber step_opstrategy,
							   bool step_op_is_ne,
							   Expr *step_lastexpr,
							   Oid step_lastcmpfn,
							   int step_lastkeyno,
							   Bitmapset *step_nullkeys,
							   ListCell *start,
							   List *step_exprs,
							   List *step_cmpfns)
{
	List	   *result = NIL;
	ListCell   *lc;
	int			cur_keyno;

	/* Actually, recursion would be limited by PARTITION_MAX_KEYS. */
	check_stack_depth();

	/* Check if we need to recurse. */
	Assert(start != NULL);
	cur_keyno = ((PartClauseInfo *) lfirst(start))->keyno;
	if (cur_keyno < step_lastkeyno - 1)
	{
		PartClauseInfo *pc;
		ListCell   *next_start;

		/*
		 * For each clause with cur_keyno, adds its expr and cmpfn to
		 * step_exprs and step_cmpfns, respectively, and recurse after setting
		 * next_start to the ListCell of the first clause for the next
		 * partition key.
		 */
		for_each_cell(lc, start)
		{
			pc = lfirst(lc);

			if (pc->keyno > cur_keyno)
				break;
		}
		next_start = lc;

		for_each_cell(lc, start)
		{
			List	   *moresteps;

			pc = lfirst(lc);
			if (pc->keyno == cur_keyno)
			{
				/* clean up before starting a new recursion cycle. */
				if (cur_keyno == 0)
				{
					list_free(step_exprs);
					list_free(step_cmpfns);
					step_exprs = list_make1(pc->expr);
					step_cmpfns = list_make1_oid(pc->cmpfn);
				}
				else
				{
					step_exprs = lappend(step_exprs, pc->expr);
					step_cmpfns = lappend_oid(step_cmpfns, pc->cmpfn);
				}
			}
			else
			{
				Assert(pc->keyno > cur_keyno);
				break;
			}

			moresteps = get_steps_using_prefix_recurse(context,
													   step_opstrategy,
													   step_op_is_ne,
													   step_lastexpr,
													   step_lastcmpfn,
													   step_lastkeyno,
													   step_nullkeys,
													   next_start,
													   step_exprs,
													   step_cmpfns);
			result = list_concat(result, moresteps);
		}
	}
	else
	{
		/*
		 * End the current recursion cycle and start generating steps, one for
		 * each clause with cur_keyno, which is all clauses from here onward
		 * till the end of the list.
		 */
		Assert(list_length(step_exprs) == cur_keyno);
		for_each_cell(lc, start)
		{
			PartClauseInfo *pc = lfirst(lc);
			PartitionPruneStep *step;
			List	   *step_exprs1,
					   *step_cmpfns1;

			Assert(pc->keyno == cur_keyno);

			/* Leave the original step_exprs unmodified. */
			step_exprs1 = list_copy(step_exprs);
			step_exprs1 = lappend(step_exprs1, pc->expr);
			step_exprs1 = lappend(step_exprs1, step_lastexpr);

			/* Leave the original step_cmpfns unmodified. */
			step_cmpfns1 = list_copy(step_cmpfns);
			step_cmpfns1 = lappend_oid(step_cmpfns1, pc->cmpfn);
			step_cmpfns1 = lappend_oid(step_cmpfns1, step_lastcmpfn);

			step = gen_prune_step_op(context,
									 step_opstrategy, step_op_is_ne,
									 step_exprs1, step_cmpfns1,
									 step_nullkeys);
			result = lappend(result, step);
		}
	}

	return result;
}

/*
 * get_matching_hash_bounds
 *		Determine offset of the hash bound matching the specified values,
 *		considering that all the non-null values come from clauses containing
 *		a compatible hash equality operator and any keys that are null come
 *		from an IS NULL clause.
 *
 * Generally this function will return a single matching bound offset,
 * although if a partition has not been setup for a given modulus then we may
 * return no matches.  If the number of clauses found don't cover the entire
 * partition key, then we'll need to return all offsets.
 *
 * 'opstrategy' if non-zero must be HTEqualStrategyNumber.
 *
 * 'values' contains Datums indexed by the partition key to use for pruning.
 *
 * 'nvalues', the number of Datums in the 'values' array.
 *
 * 'partsupfunc' contains partition hashing functions that can produce correct
 * hash for the type of the values contained in 'values'.
 *
 * 'nullkeys' is the set of partition keys that are null.
 */
static PruneStepResult *
get_matching_hash_bounds(PartitionPruneContext *context,
						 StrategyNumber opstrategy, Datum *values, int nvalues,
						 FmgrInfo *partsupfunc, Bitmapset *nullkeys)
{
	PruneStepResult *result = (PruneStepResult *) palloc0(sizeof(PruneStepResult));
	PartitionBoundInfo boundinfo = context->boundinfo;
	int		   *partindices = boundinfo->indexes;
	int			partnatts = context->partnatts;
	bool		isnull[PARTITION_MAX_KEYS];
	int			i;
	uint64		rowHash;
	int			greatest_modulus;

	Assert(context->strategy == PARTITION_STRATEGY_HASH);

	/*
	 * For hash partitioning we can only perform pruning based on equality
	 * clauses to the partition key or IS NULL clauses.  We also can only
	 * prune if we got values for all keys.
	 */
	if (nvalues + bms_num_members(nullkeys) == partnatts)
	{
		/*
		 * If there are any values, they must have come from clauses
		 * containing an equality operator compatible with hash partitioning.
		 */
		Assert(opstrategy == HTEqualStrategyNumber || nvalues == 0);

		for (i = 0; i < partnatts; i++)
			isnull[i] = bms_is_member(i, nullkeys);

		greatest_modulus = get_hash_partition_greatest_modulus(boundinfo);
		rowHash = compute_hash_value(partnatts, partsupfunc, values, isnull);

		if (partindices[rowHash % greatest_modulus] >= 0)
			result->bound_offsets =
				bms_make_singleton(rowHash % greatest_modulus);
	}
	else
		result->bound_offsets = bms_add_range(NULL, 0,
											  boundinfo->ndatums - 1);

	/*
	 * There is neither a special hash null partition or the default hash
	 * partition.
	 */
	result->scan_null = result->scan_default = false;

	return result;
}

/*
 * get_matching_list_bounds
 *		Determine the offsets of list bounds matching the specified value,
 *		according to the semantics of the given operator strategy
 * 'opstrategy' if non-zero must be a btree strategy number.
 *
 * 'value' contains the value to use for pruning.
 *
 * 'nvalues', if non-zero, should be exactly 1, because of list partitioning.
 *
 * 'partsupfunc' contains the list partitioning comparison function to be used
 * to perform partition_list_bsearch
 *
 * 'nullkeys' is the set of partition keys that are null.
 */
static PruneStepResult *
get_matching_list_bounds(PartitionPruneContext *context,
						 StrategyNumber opstrategy, Datum value, int nvalues,
						 FmgrInfo *partsupfunc, Bitmapset *nullkeys)
{
	PruneStepResult *result = (PruneStepResult *) palloc0(sizeof(PruneStepResult));
	PartitionBoundInfo boundinfo = context->boundinfo;
	int			off,
				minoff,
				maxoff;
	bool		is_equal;
	bool		inclusive = false;
	Oid		   *partcollation = context->partcollation;

	Assert(context->strategy == PARTITION_STRATEGY_LIST);
	Assert(context->partnatts == 1);

	result->scan_null = result->scan_default = false;

	if (!bms_is_empty(nullkeys))
	{
		/*
		 * Nulls may exist in only one partition - the partition whose
		 * accepted set of values includes null or the default partition if
		 * the former doesn't exist.
		 */
		if (partition_bound_accepts_nulls(boundinfo))
			result->scan_null = true;
		else
			result->scan_default = partition_bound_has_default(boundinfo);
		return result;
	}

	/*
	 * If there are no datums to compare keys with, but there are partitions,
	 * just return the default partition if one exists.
	 */
	if (boundinfo->ndatums == 0)
	{
		result->scan_default = partition_bound_has_default(boundinfo);
		return result;
	}

	minoff = 0;
	maxoff = boundinfo->ndatums - 1;

	/*
	 * If there are no values to compare with the datums in boundinfo, it
	 * means the caller asked for partitions for all non-null datums.  Add
	 * indexes of *all* partitions, including the default if any.
	 */
	if (nvalues == 0)
	{
		result->bound_offsets = bms_add_range(NULL, 0,
											  boundinfo->ndatums - 1);
		result->scan_default = partition_bound_has_default(boundinfo);
		return result;
	}

	/* Special case handling of values coming from a <> operator clause. */
	if (opstrategy == InvalidStrategy)
	{
		/*
		 * First match to all bounds.  We'll remove any matching datums below.
		 */
		result->bound_offsets = bms_add_range(NULL, 0,
											  boundinfo->ndatums - 1);

		off = partition_list_bsearch(partsupfunc, partcollation, boundinfo,
									 value, &is_equal);
		if (off >= 0 && is_equal)
		{

			/* We have a match. Remove from the result. */
			Assert(boundinfo->indexes[off] >= 0);
			result->bound_offsets = bms_del_member(result->bound_offsets,
												   off);
		}

		/* Always include the default partition if any. */
		result->scan_default = partition_bound_has_default(boundinfo);

		return result;
	}

	/*
	 * With range queries, always include the default list partition, because
	 * list partitions divide the key space in a discontinuous manner, not all
	 * values in the given range will have a partition assigned.  This may not
	 * technically be true for some data types (e.g. integer types), however,
	 * we currently lack any sort of infrastructure to provide us with proofs
	 * that would allow us to do anything smarter here.
	 */
	if (opstrategy != BTEqualStrategyNumber)
		result->scan_default = partition_bound_has_default(boundinfo);

	switch (opstrategy)
	{
		case BTEqualStrategyNumber:
			off = partition_list_bsearch(partsupfunc,
										 partcollation,
										 boundinfo, value,
										 &is_equal);
			if (off >= 0 && is_equal)
			{
				Assert(boundinfo->indexes[off] >= 0);
				result->bound_offsets = bms_make_singleton(off);
			}
			else
				result->scan_default = partition_bound_has_default(boundinfo);
			return result;

		case BTGreaterEqualStrategyNumber:
			inclusive = true;
			/* fall through */
		case BTGreaterStrategyNumber:
			off = partition_list_bsearch(partsupfunc,
										 partcollation,
										 boundinfo, value,
										 &is_equal);
			if (off >= 0)
			{
				/* We don't want the matched datum to be in the result. */
				if (!is_equal || !inclusive)
					off++;
			}
			else
			{
				/*
				 * This case means all partition bounds are greater, which in
				 * turn means that all partitions satisfy this key.
				 */
				off = 0;
			}

			/*
			 * off is greater than the numbers of datums we have partitions
			 * for.  The only possible partition that could contain a match is
			 * the default partition, but we must've set context->scan_default
			 * above anyway if one exists.
			 */
			if (off > boundinfo->ndatums - 1)
				return result;

			minoff = off;
			break;

		case BTLessEqualStrategyNumber:
			inclusive = true;
			/* fall through */
		case BTLessStrategyNumber:
			off = partition_list_bsearch(partsupfunc,
										 partcollation,
										 boundinfo, value,
										 &is_equal);
			if (off >= 0 && is_equal && !inclusive)
				off--;

			/*
			 * off is smaller than the datums of all non-default partitions.
			 * The only possible partition that could contain a match is the
			 * default partition, but we must've set context->scan_default
			 * above anyway if one exists.
			 */
			if (off < 0)
				return result;

			maxoff = off;
			break;

		default:
			elog(ERROR, "invalid strategy number %d", opstrategy);
			break;
	}

	result->bound_offsets = bms_add_range(NULL, minoff, maxoff);
	return result;
}


/*
 * get_matching_range_datums
 *		Determine the offsets of range bounds matching the specified values,
 *		according to the semantics of the given operator strategy
 *
 * Each datum whose offset is in result is to be treated as the upper bound of
 * the partition that will contain the desired values.
 *
 * If default partition needs to be scanned for given values, set scan_default
 * in result if present.
 *
 * 'opstrategy' if non-zero must be a btree strategy number.
 *
 * 'values' contains Datums indexed by the partition key to use for pruning.
 *
 * 'nvalues', number of Datums in 'values' array. Must be <= context->partnatts.
 *
 * 'partsupfunc' contains the range partitioning comparison functions to be
 * used to perform partition_range_datum_bsearch or partition_rbound_datum_cmp
 * using.
 *
 * 'nullkeys' is the set of partition keys that are null.
 */
static PruneStepResult *
get_matching_range_bounds(PartitionPruneContext *context,
						  StrategyNumber opstrategy, Datum *values, int nvalues,
						  FmgrInfo *partsupfunc, Bitmapset *nullkeys)
{
	PruneStepResult *result = (PruneStepResult *) palloc0(sizeof(PruneStepResult));
	PartitionBoundInfo boundinfo = context->boundinfo;
	Oid		   *partcollation = context->partcollation;
	int			partnatts = context->partnatts;
	int		   *partindices = boundinfo->indexes;
	int			off,
				minoff,
				maxoff,
				i;
	bool		is_equal;
	bool		inclusive = false;

	Assert(context->strategy == PARTITION_STRATEGY_RANGE);
	Assert(nvalues <= partnatts);

	result->scan_null = result->scan_default = false;

	/*
	 * If there are no datums to compare keys with, or if we got an IS NULL
	 * clause just return the default partition, if it exists.
	 */
	if (boundinfo->ndatums == 0 || !bms_is_empty(nullkeys))
	{
		result->scan_default = partition_bound_has_default(boundinfo);
		return result;
	}

	minoff = 0;
	maxoff = boundinfo->ndatums;

	/*
	 * If there are no values to compare with the datums in boundinfo, it
	 * means the caller asked for partitions for all non-null datums.  Add
	 * indexes of *all* partitions, including the default partition if one
	 * exists.
	 */
	if (nvalues == 0)
	{
		if (partindices[minoff] < 0)
			minoff++;
		if (partindices[maxoff] < 0)
			maxoff--;

		result->scan_default = partition_bound_has_default(boundinfo);
		result->bound_offsets = bms_add_range(NULL, minoff, maxoff);

		return result;
	}

	/*
	 * If the query does not constrain all key columns, we'll need to scan the
	 * the default partition, if any.
	 */
	if (nvalues < partnatts)
		result->scan_default = partition_bound_has_default(boundinfo);

	switch (opstrategy)
	{
		case BTEqualStrategyNumber:
			/* Look for the smallest bound that is = lookup value. */
			off = partition_range_datum_bsearch(partsupfunc,
												partcollation,
												boundinfo,
												nvalues, values,
												&is_equal);

			if (off >= 0 && is_equal)
			{
				if (nvalues == partnatts)
				{
					/* There can only be zero or one matching partition. */
					if (partindices[off + 1] >= 0)
						result->bound_offsets = bms_make_singleton(off + 1);
					else
						result->scan_default =
							partition_bound_has_default(boundinfo);
					return result;
				}
				else
				{
					int			saved_off = off;

					/*
					 * Since the lookup value contains only a prefix of keys,
					 * we must find other bounds that may also match the
					 * prefix.  partition_range_datum_bsearch() returns the
					 * offset of one of them, find others by checking adjacent
					 * bounds.
					 */

					/*
					 * First find greatest bound that's smaller than the
					 * lookup value.
					 */
					while (off >= 1)
					{
						int32		cmpval;

						cmpval =
							partition_rbound_datum_cmp(partsupfunc,
													   partcollation,
													   boundinfo->datums[off - 1],
													   boundinfo->kind[off - 1],
													   values, nvalues);
						if (cmpval != 0)
							break;
						off--;
					}

					Assert(0 ==
						   partition_rbound_datum_cmp(partsupfunc,
													  partcollation,
													  boundinfo->datums[off],
													  boundinfo->kind[off],
													  values, nvalues));

					/*
					 * We can treat 'off' as the offset of the smallest bound
					 * to be included in the result, if we know it is the
					 * upper bound of the partition in which the lookup value
					 * could possibly exist.  One case it couldn't is if the
					 * bound, or precisely the matched portion of its prefix,
					 * is not inclusive.
					 */
					if (boundinfo->kind[off][nvalues] ==
						PARTITION_RANGE_DATUM_MINVALUE)
						off++;

					minoff = off;

					/*
					 * Now find smallest bound that's greater than the lookup
					 * value.
					 */
					off = saved_off;
					while (off < boundinfo->ndatums - 1)
					{
						int32		cmpval;

						cmpval = partition_rbound_datum_cmp(partsupfunc,
															partcollation,
															boundinfo->datums[off + 1],
															boundinfo->kind[off + 1],
															values, nvalues);
						if (cmpval != 0)
							break;
						off++;
					}

					Assert(0 ==
						   partition_rbound_datum_cmp(partsupfunc,
													  partcollation,
													  boundinfo->datums[off],
													  boundinfo->kind[off],
													  values, nvalues));

					/*
					 * off + 1, then would be the offset of the greatest bound
					 * to be included in the result.
					 */
					maxoff = off + 1;
				}

				/*
				 * Skip if minoff/maxoff are actually the upper bound of a
				 * un-assigned portion of values.
				 */
				if (partindices[minoff] < 0 && minoff < boundinfo->ndatums)
					minoff++;
				if (partindices[maxoff] < 0 && maxoff >= 1)
					maxoff--;

				/*
				 * There may exist a range of values unassigned to any
				 * non-default partition between the datums at minoff and
				 * maxoff.  Add the default partition in that case.
				 */
				if (partition_bound_has_default(boundinfo))
				{
					for (i = minoff; i <= maxoff; i++)
					{
						if (partindices[i] < 0)
						{
							result->scan_default = true;
							break;
						}
					}
				}

				Assert(minoff >= 0 && maxoff >= 0);
				result->bound_offsets = bms_add_range(NULL, minoff, maxoff);
			}
			else if (off >= 0)	/* !is_equal */
			{
				/*
				 * The lookup value falls in the range between some bounds in
				 * boundinfo.  'off' would be the offset of the greatest bound
				 * that is <= lookup value, so add off + 1 to the result
				 * instead as the offset of the upper bound of the only
				 * partition that may contain the lookup value.
				 */
				if (partindices[off + 1] >= 0)
					result->bound_offsets = bms_make_singleton(off + 1);
				else
					result->scan_default =
						partition_bound_has_default(boundinfo);
			}
			else
			{
				/*
				 * off < 0: the lookup value is smaller than all bounds, so
				 * only the default partition qualifies, if there is one.
				 */
				result->scan_default = partition_bound_has_default(boundinfo);
			}

			return result;

		case BTGreaterEqualStrategyNumber:
			inclusive = true;
			/* fall through */
		case BTGreaterStrategyNumber:

			/*
			 * Look for the smallest bound that is > or >= lookup value and
			 * set minoff to its offset.
			 */
			off = partition_range_datum_bsearch(partsupfunc,
												partcollation,
												boundinfo,
												nvalues, values,
												&is_equal);
			if (off < 0)
			{
				/*
				 * All bounds are greater than the lookup value, so include
				 * all of them in the result.
				 */
				minoff = 0;
			}
			else
			{
				if (is_equal && nvalues < partnatts)
				{
					/*
					 * Since the lookup value contains only a prefix of keys,
					 * we must find other bounds that may also match the
					 * prefix.  partition_range_datum_bsearch() returns the
					 * offset of one of them, find others by checking adjacent
					 * bounds.
					 *
					 * Based on whether the lookup values are inclusive or
					 * not, we must either include the indexes of all such
					 * bounds in the result (that is, set minoff to the index
					 * of smallest such bound) or find the smallest one that's
					 * greater than the lookup values and set minoff to that.
					 */
					while (off >= 1 && off < boundinfo->ndatums - 1)
					{
						int32		cmpval;
						int			nextoff;

						nextoff = inclusive ? off - 1 : off + 1;
						cmpval =
							partition_rbound_datum_cmp(partsupfunc,
													   partcollation,
													   boundinfo->datums[nextoff],
													   boundinfo->kind[nextoff],
													   values, nvalues);
						if (cmpval != 0)
							break;

						off = nextoff;
					}

					Assert(0 ==
						   partition_rbound_datum_cmp(partsupfunc,
													  partcollation,
													  boundinfo->datums[off],
													  boundinfo->kind[off],
													  values, nvalues));

					minoff = inclusive ? off : off + 1;
				}

				/*
				 * lookup value falls in the range between some bounds in
				 * boundinfo.  off would be the offset of the greatest bound
				 * that is <= lookup value, so add off + 1 to the result
				 * instead as the offset of the upper bound of the smallest
				 * partition that may contain the lookup value.
				 */
				else
					minoff = off + 1;
			}
			break;

		case BTLessEqualStrategyNumber:
			inclusive = true;
			/* fall through */
		case BTLessStrategyNumber:

			/*
			 * Look for the greatest bound that is < or <= lookup value and
			 * set minoff to its offset.
			 */
			off = partition_range_datum_bsearch(partsupfunc,
												partcollation,
												boundinfo,
												nvalues, values,
												&is_equal);
			if (off < 0)
			{
				/*
				 * All bounds are greater than the key, so we could only
				 * expect to find the lookup key in the default partition.
				 */
				result->scan_default = partition_bound_has_default(boundinfo);
				return result;
			}
			else
			{
				/*
				 * See the comment above.
				 */
				if (is_equal && nvalues < partnatts)
				{
					while (off >= 1 && off < boundinfo->ndatums - 1)
					{
						int32		cmpval;
						int			nextoff;

						nextoff = inclusive ? off + 1 : off - 1;
						cmpval = partition_rbound_datum_cmp(partsupfunc,
															partcollation,
															boundinfo->datums[nextoff],
															boundinfo->kind[nextoff],
															values, nvalues);
						if (cmpval != 0)
							break;

						off = nextoff;
					}

					Assert(0 ==
						   partition_rbound_datum_cmp(partsupfunc,
													  partcollation,
													  boundinfo->datums[off],
													  boundinfo->kind[off],
													  values, nvalues));

					maxoff = inclusive ? off + 1 : off;
				}

				/*
				 * The lookup value falls in the range between some bounds in
				 * boundinfo.  'off' would be the offset of the greatest bound
				 * that is <= lookup value, so add off + 1 to the result
				 * instead as the offset of the upper bound of the greatest
				 * partition that may contain lookup value.  If the lookup
				 * value had exactly matched the bound, but it isn't
				 * inclusive, no need add the adjacent partition.
				 */
				else if (!is_equal || inclusive)
					maxoff = off + 1;
				else
					maxoff = off;
			}
			break;

		default:
			elog(ERROR, "invalid strategy number %d", opstrategy);
			break;
	}

	/*
	 * Skip a gap and when doing so, check if the bound contains a finite
	 * value to decide if we need to add the default partition.  If it's an
	 * infinite bound, we need not add the default partition, as having an
	 * infinite bound means the partition in question catches any values that
	 * would otherwise be in the default partition.
	 */
	if (partindices[minoff] < 0)
	{
		int			lastkey = nvalues - 1;

		if (minoff >= 0 &&
			minoff < boundinfo->ndatums &&
			boundinfo->kind[minoff][lastkey] ==
			PARTITION_RANGE_DATUM_VALUE)
			result->scan_default = partition_bound_has_default(boundinfo);

		minoff++;
	}

	/*
	 * Skip a gap.  See the above comment about how we decide whether or or
	 * not to scan the default partition based whether the datum that will
	 * become the maximum datum is finite or not.
	 */
	if (maxoff >= 1 && partindices[maxoff] < 0)
	{
		int			lastkey = nvalues - 1;

		if (maxoff >= 0 &&
			maxoff <= boundinfo->ndatums &&
			boundinfo->kind[maxoff - 1][lastkey] ==
			PARTITION_RANGE_DATUM_VALUE)
			result->scan_default = partition_bound_has_default(boundinfo);

		maxoff--;
	}

	if (partition_bound_has_default(boundinfo))
	{
		/*
		 * There may exist a range of values unassigned to any non-default
		 * partition between the datums at minoff and maxoff.  Add the default
		 * partition in that case.
		 */
		for (i = minoff; i <= maxoff; i++)
		{
			if (partindices[i] < 0)
			{
				result->scan_default = true;
				break;
			}
		}
	}

	Assert(minoff >= 0 && maxoff >= 0);
	if (minoff <= maxoff)
		result->bound_offsets = bms_add_range(NULL, minoff, maxoff);

	return result;
}

/*
 * pull_partkey_params
 *		Loop through each pruning step and record each external and exec
 *		Params being compared to the partition keys.
 */
static bool
pull_partkey_params(PartitionPruneInfo *pinfo, List *steps)
{
	ListCell   *lc;
	bool		gotone = false;

	foreach(lc, steps)
	{
		PartitionPruneStepOp *stepop = lfirst(lc);
		ListCell   *lc2;

		if (!IsA(stepop, PartitionPruneStepOp))
			continue;

		foreach(lc2, stepop->exprs)
		{
			Expr	   *expr = lfirst(lc2);

			if (IsA(expr, Param))
			{
				Param	   *param = (Param *) expr;

				switch (param->paramkind)
				{
					case PARAM_EXTERN:
						pinfo->extparams = bms_add_member(pinfo->extparams,
														  param->paramid);
						break;
					case PARAM_EXEC:
						pinfo->execparams = bms_add_member(pinfo->execparams,
														   param->paramid);
						break;

					default:
						elog(ERROR, "unrecognized paramkind: %d",
							 (int) param->paramkind);
						break;
				}
				gotone = true;
			}
		}
	}

	return gotone;
}

/*
 * perform_pruning_base_step
 *		Determines the indexes of datums that satisfy conditions specified in
 *		'opstep'.
 *
 * Result also contains whether special null-accepting and/or default
 * partition need to be scanned.
 */
static PruneStepResult *
perform_pruning_base_step(PartitionPruneContext *context,
						  PartitionPruneStepOp *opstep)
{
	ListCell   *lc1,
			   *lc2;
	int			keyno,
				nvalues;
	Datum		values[PARTITION_MAX_KEYS];
	FmgrInfo	partsupfunc[PARTITION_MAX_KEYS];

	/*
	 * There better be the same number of expressions and compare functions.
	 */
	Assert(list_length(opstep->exprs) == list_length(opstep->cmpfns));

	nvalues = 0;
	lc1 = list_head(opstep->exprs);
	lc2 = list_head(opstep->cmpfns);

	/*
	 * Generate the partition lookup key that will be used by one of the
	 * get_matching_*_bounds functions called below.
	 */
	for (keyno = 0; keyno < context->partnatts; keyno++)
	{
		/*
		 * For hash partitioning, it is possible that values of some keys are
		 * not provided in operator clauses, but instead the planner found
		 * that they appeared in a IS NULL clause.
		 */
		if (bms_is_member(keyno, opstep->nullkeys))
			continue;

		/*
		 * For range partitioning, we must only perform pruning with values
		 * for either all partition keys or a prefix thereof.
		 */
		if (keyno > nvalues && context->strategy == PARTITION_STRATEGY_RANGE)
			break;

		if (lc1 != NULL)
		{
			Expr	   *expr;
			int			stateidx;
			Datum		datum;

			expr = lfirst(lc1);
			stateidx = PruneCxtStateIdx(context->partnatts,
										opstep->step.step_id, keyno);
			if (partkey_datum_from_expr(context, expr, stateidx, &datum))
			{
				Oid			cmpfn;

				/*
				 * If we're going to need a different comparison function than
				 * the one cached in the PartitionKey, we'll need to look up
				 * the FmgrInfo.
				 */
				cmpfn = lfirst_oid(lc2);
				Assert(OidIsValid(cmpfn));
				if (cmpfn != context->partsupfunc[keyno].fn_oid)
					fmgr_info(cmpfn, &partsupfunc[keyno]);
				else
					fmgr_info_copy(&partsupfunc[keyno],
								   &context->partsupfunc[keyno],
								   CurrentMemoryContext);

				values[keyno] = datum;
				nvalues++;
			}

			lc1 = lnext(lc1);
			lc2 = lnext(lc2);
		}
	}

	switch (context->strategy)
	{
		case PARTITION_STRATEGY_HASH:
			return get_matching_hash_bounds(context,
											opstep->opstrategy,
											values, nvalues,
											partsupfunc,
											opstep->nullkeys);

		case PARTITION_STRATEGY_LIST:
			return get_matching_list_bounds(context,
											opstep->opstrategy,
											values[0], nvalues,
											&partsupfunc[0],
											opstep->nullkeys);

		case PARTITION_STRATEGY_RANGE:
			return get_matching_range_bounds(context,
											 opstep->opstrategy,
											 values, nvalues,
											 partsupfunc,
											 opstep->nullkeys);

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

	return NULL;
}

/*
 * perform_pruning_combine_step
 *		Determines the indexes of datums obtained by combining those given
 *		by the steps identified by cstep->source_stepids using the specified
 *		combination method
 *
 * Since cstep may refer to the result of earlier steps, we also receive
 * step_results here.
 */
static PruneStepResult *
perform_pruning_combine_step(PartitionPruneContext *context,
							 PartitionPruneStepCombine *cstep,
							 PruneStepResult **step_results)
{
	ListCell   *lc1;
	PruneStepResult *result = NULL;
	bool		firststep;

	/*
	 * A combine step without any source steps is an indication to not perform
	 * any partition pruning, we just return all partitions.
	 */
	result = (PruneStepResult *) palloc0(sizeof(PruneStepResult));
	if (list_length(cstep->source_stepids) == 0)
	{
		PartitionBoundInfo boundinfo = context->boundinfo;

		result->bound_offsets = bms_add_range(NULL, 0, boundinfo->ndatums - 1);
		result->scan_default = partition_bound_has_default(boundinfo);
		result->scan_null = partition_bound_accepts_nulls(boundinfo);
		return result;
	}

	switch (cstep->combineOp)
	{
		case PARTPRUNE_COMBINE_UNION:
			foreach(lc1, cstep->source_stepids)
			{
				int			step_id = lfirst_int(lc1);
				PruneStepResult *step_result;

				/*
				 * step_results[step_id] must contain a valid result, which is
				 * confirmed by the fact that cstep's step_id is greater than
				 * step_id and the fact that results of the individual steps
				 * are evaluated in sequence of their step_ids.
				 */
				if (step_id >= cstep->step.step_id)
					elog(ERROR, "invalid pruning combine step argument");
				step_result = step_results[step_id];
				Assert(step_result != NULL);

				/* Record any additional datum indexes from this step */
				result->bound_offsets = bms_add_members(result->bound_offsets,
														step_result->bound_offsets);

				/* Update whether to scan null and default partitions. */
				if (!result->scan_null)
					result->scan_null = step_result->scan_null;
				if (!result->scan_default)
					result->scan_default = step_result->scan_default;
			}
			break;

		case PARTPRUNE_COMBINE_INTERSECT:
			firststep = true;
			foreach(lc1, cstep->source_stepids)
			{
				int			step_id = lfirst_int(lc1);
				PruneStepResult *step_result;

				if (step_id >= cstep->step.step_id)
					elog(ERROR, "invalid pruning combine step argument");
				step_result = step_results[step_id];
				Assert(step_result != NULL);

				if (firststep)
				{
					/* Copy step's result the first time. */
					result->bound_offsets =
						bms_copy(step_result->bound_offsets);
					result->scan_null = step_result->scan_null;
					result->scan_default = step_result->scan_default;
					firststep = false;
				}
				else
				{
					/* Record datum indexes common to both steps */
					result->bound_offsets =
						bms_int_members(result->bound_offsets,
										step_result->bound_offsets);

					/* Update whether to scan null and default partitions. */
					if (result->scan_null)
						result->scan_null = step_result->scan_null;
					if (result->scan_default)
						result->scan_default = step_result->scan_default;
				}
			}
			break;

		default:
			elog(ERROR, "invalid pruning combine op: %d",
				 (int) cstep->combineOp);
	}

	return result;
}

/*
 * match_boolean_partition_clause
 *
 * Sets *outconst to a Const containing true or false value and returns true if
 * we're able to match the clause to the partition key as specially-shaped
 * Boolean clause.  Returns false otherwise with *outconst set to NULL.
 */
static bool
match_boolean_partition_clause(Oid partopfamily, Expr *clause, Expr *partkey,
							   Expr **outconst)
{
	Expr	   *leftop;

	*outconst = NULL;

	if (!IsBooleanOpfamily(partopfamily))
		return false;

	if (IsA(clause, BooleanTest))
	{
		BooleanTest *btest = (BooleanTest *) clause;

		/* Only IS [NOT] TRUE/FALSE are any good to us */
		if (btest->booltesttype == IS_UNKNOWN ||
			btest->booltesttype == IS_NOT_UNKNOWN)
			return false;

		leftop = btest->arg;
		if (IsA(leftop, RelabelType))
			leftop = ((RelabelType *) leftop)->arg;

		if (equal(leftop, partkey))
			*outconst = (btest->booltesttype == IS_TRUE ||
						 btest->booltesttype == IS_NOT_FALSE)
				? (Expr *) makeBoolConst(true, false)
				: (Expr *) makeBoolConst(false, false);

		if (*outconst)
			return true;
	}
	else
	{
		bool		is_not_clause = not_clause((Node *) clause);

		leftop = is_not_clause ? get_notclausearg(clause) : clause;

		if (IsA(leftop, RelabelType))
			leftop = ((RelabelType *) leftop)->arg;

		/* Compare to the partition key, and make up a clause ... */
		if (equal(leftop, partkey))
			*outconst = is_not_clause ?
				(Expr *) makeBoolConst(false, false) :
				(Expr *) makeBoolConst(true, false);
		else if (equal(negate_clause((Node *) leftop), partkey))
			*outconst = (Expr *) makeBoolConst(false, false);

		if (*outconst)
			return true;
	}

	return false;
}

/*
 * partkey_datum_from_expr
 *		Evaluate expression for potential partition pruning
 *
 * Evaluate 'expr', whose ExprState is stateidx of the context exprstate
 * array; set *value to the resulting Datum.  Return true if evaluation was
 * possible, otherwise false.
 */
static bool
partkey_datum_from_expr(PartitionPruneContext *context,
						Expr *expr, int stateidx, Datum *value)
{
	switch (nodeTag(expr))
	{
		case T_Const:
			*value = ((Const *) expr)->constvalue;
			return true;

		case T_Param:

			/*
			 * When being called from the executor we may be able to evaluate
			 * the Param's value.
			 */
			if (context->planstate &&
				bms_is_member(((Param *) expr)->paramid, context->safeparams))
			{
				ExprState  *exprstate;
				ExprContext *ectx;
				bool		isNull;

				exprstate = context->exprstates[stateidx];
				ectx = context->planstate->ps_ExprContext;
				*value = ExecEvalExprSwitchContext(exprstate, ectx, &isNull);
				if (isNull)
					return false;

				return true;
			}
			break;

		default:
			break;
	}

	return false;
}