postgres/src/backend/optimizer/path/indxpath.c

/*-------------------------------------------------------------------------
 *
 * indxpath.c
 *	  Routines to determine which indices are usable for scanning a
 *	  given relation, and create IndexPaths accordingly.
 *
 * Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *	  $Header: /cvsroot/pgsql/src/backend/optimizer/path/indxpath.c,v 1.76 2000/01/09 00:26:31 tgl Exp $
 *
 *-------------------------------------------------------------------------
 */
#include <ctype.h>
#include <math.h>

#include "postgres.h"

#include "access/heapam.h"
#include "access/nbtree.h"
#include "catalog/catname.h"
#include "catalog/pg_amop.h"
#include "catalog/pg_operator.h"
#include "executor/executor.h"
#include "mb/pg_wchar.h"
#include "nodes/makefuncs.h"
#include "nodes/nodeFuncs.h"
#include "optimizer/clauses.h"
#include "optimizer/cost.h"
#include "optimizer/pathnode.h"
#include "optimizer/paths.h"
#include "optimizer/plancat.h"
#include "optimizer/restrictinfo.h"
#include "optimizer/var.h"
#include "parser/parse_coerce.h"
#include "parser/parse_expr.h"
#include "parser/parse_oper.h"
#include "parser/parsetree.h"
#include "utils/builtins.h"
#include "utils/lsyscache.h"
#include "utils/syscache.h"


#define is_indexable_operator(clause,opclass,relam,indexkey_on_left) \
	(indexable_operator(clause,opclass,relam,indexkey_on_left) != InvalidOid)

typedef enum {
	Prefix_None, Prefix_Partial, Prefix_Exact
} Prefix_Status;

static void match_index_orclauses(RelOptInfo *rel, IndexOptInfo *index,
								  int indexkey, Oid opclass,
								  List *restrictinfo_list);
static List *match_index_orclause(RelOptInfo *rel, IndexOptInfo *index,
								  int indexkey, Oid opclass,
								  List *or_clauses,
								  List *other_matching_indices);
static bool match_or_subclause_to_indexkey(RelOptInfo *rel,
										   IndexOptInfo *index,
										   int indexkey, Oid opclass,
										   Expr *clause);
static List *group_clauses_by_indexkey(RelOptInfo *rel, IndexOptInfo *index,
									   int *indexkeys, Oid *classes,
									   List *restrictinfo_list);
static List *group_clauses_by_ikey_for_joins(RelOptInfo *rel,
											 IndexOptInfo *index,
											 int *indexkeys, Oid *classes,
											 List *join_cinfo_list,
											 List *restr_cinfo_list);
static bool match_clause_to_indexkey(RelOptInfo *rel, IndexOptInfo *index,
									 int indexkey, Oid opclass,
									 Expr *clause, bool join);
static bool pred_test(List *predicate_list, List *restrictinfo_list,
					  List *joininfo_list);
static bool one_pred_test(Expr *predicate, List *restrictinfo_list);
static bool one_pred_clause_expr_test(Expr *predicate, Node *clause);
static bool one_pred_clause_test(Expr *predicate, Node *clause);
static bool clause_pred_clause_test(Expr *predicate, Node *clause);
static void indexable_joinclauses(RelOptInfo *rel, IndexOptInfo *index,
								  List *joininfo_list, List *restrictinfo_list,
								  List **clausegroups, List **outerrelids);
static List *index_innerjoin(Query *root, RelOptInfo *rel, IndexOptInfo *index,
							 List *clausegroup_list, List *outerrelids_list);
static bool useful_for_mergejoin(RelOptInfo *rel, IndexOptInfo *index,
								 List *joininfo_list);
static bool useful_for_ordering(Query *root, RelOptInfo *rel,
								IndexOptInfo *index);
static bool match_index_to_operand(int indexkey, Var *operand,
								   RelOptInfo *rel, IndexOptInfo *index);
static bool function_index_operand(Expr *funcOpnd, RelOptInfo *rel,
								   IndexOptInfo *index);
static bool match_special_index_operator(Expr *clause, Oid opclass, Oid relam,
										 bool indexkey_on_left);
static Prefix_Status like_fixed_prefix(char *patt, char **prefix);
static Prefix_Status regex_fixed_prefix(char *patt, bool case_insensitive,
										char **prefix);
static List *prefix_quals(Var *leftop, Oid expr_op,
						  char *prefix, Prefix_Status pstatus);
static char *make_greater_string(const char * str, Oid datatype);
static Oid find_operator(const char * opname, Oid datatype);
static Datum string_to_datum(const char * str, Oid datatype);
static Const *string_to_const(const char * str, Oid datatype);
static bool string_lessthan(const char * str1, const char * str2,
							Oid datatype);


/*
 * create_index_paths()
 *	  Generate all interesting index paths for the given relation.
 *
 * To be considered for an index scan, an index must match one or more
 * restriction clauses or join clauses from the query's qual condition,
 * or match the query's ORDER BY condition.
 *
 * There are two basic kinds of index scans.  A "plain" index scan uses
 * only restriction clauses (possibly none at all) in its indexqual,
 * so it can be applied in any context.  An "innerjoin" index scan uses
 * join clauses (plus restriction clauses, if available) in its indexqual.
 * Therefore it can only be used as the inner relation of a nestloop
 * join against an outer rel that includes all the other rels mentioned
 * in its join clauses.  In that context, values for the other rels'
 * attributes are available and fixed during any one scan of the indexpath.
 *
 * This routine's return value is a list of plain IndexPaths for each
 * index the routine deems potentially interesting for the current query
 * (at most one IndexPath per index on the given relation).  An innerjoin
 * path is also generated for each interesting combination of outer join
 * relations.  The innerjoin paths are *not* in the return list, but are
 * appended to the "innerjoin" list of the relation itself.
 *
 * 'rel' is the relation for which we want to generate index paths
 * 'indices' is a list of available indexes for 'rel'
 * 'restrictinfo_list' is a list of restrictinfo nodes for 'rel'
 * 'joininfo_list' is a list of joininfo nodes for 'rel'
 *
 * Returns a list of IndexPath access path descriptors.  Additional
 * IndexPath nodes may also be added to the rel->innerjoin list.
 */
List *
create_index_paths(Query *root,
				   RelOptInfo *rel,
				   List *indices,
				   List *restrictinfo_list,
				   List *joininfo_list)
{
	List	   *retval = NIL;
	List	   *ilist;

	foreach(ilist, indices)
	{
		IndexOptInfo *index = (IndexOptInfo *) lfirst(ilist);
		List	   *restrictclauses;
		List	   *joinclausegroups;
		List	   *joinouterrelids;

		/*
		 * If this is a partial index, we can only use it if it passes
		 * the predicate test.
		 */
		if (index->indpred != NIL)
			if (!pred_test(index->indpred, restrictinfo_list, joininfo_list))
				continue;

		/*
		 * 1. Try matching the index against subclauses of restriction 'or'
		 * clauses (ie, 'or' clauses that reference only this relation).
		 * The restrictinfo nodes for the 'or' clauses are marked with lists
		 * of the matching indices.  No paths are actually created now;
		 * that will be done in orindxpath.c after all indexes for the rel
		 * have been examined.  (We need to do it that way because we can
		 * potentially use a different index for each subclause of an 'or',
		 * so we can't build a path for an 'or' clause until all indexes have
		 * been matched against it.)
		 *
		 * We currently only look to match the first key of each index against
		 * 'or' subclauses.  There are cases where a later key of a multi-key
		 * index could be used (if other top-level clauses match earlier keys
		 * of the index), but our poor brains are hurting already...
		 *
		 * We don't even think about special handling of 'or' clauses that
		 * involve more than one relation (ie, are join clauses).
		 * Can we do anything useful with those?
		 */
		match_index_orclauses(rel,
							  index,
							  index->indexkeys[0],
							  index->classlist[0],
							  restrictinfo_list);

		/*
		 * 2. If the keys of this index match any of the available non-'or'
		 * restriction clauses, then create a path using those clauses
		 * as indexquals.
		 */
		restrictclauses = group_clauses_by_indexkey(rel,
													index,
													index->indexkeys,
													index->classlist,
													restrictinfo_list);

		if (restrictclauses != NIL)
			retval = lappend(retval,
							 create_index_path(root, rel, index,
											   restrictclauses));

		/*
		 * 3. If this index can be used for a mergejoin, then create an
		 * index path for it even if there were no restriction clauses.
		 * (If there were, there is no need to make another index path.)
		 * This will allow the index to be considered as a base for a
		 * mergejoin in later processing.  Similarly, if the index matches
		 * the ordering that is needed for the overall query result, make
		 * an index path for it even if there is no other reason to do so.
		 */
		if (restrictclauses == NIL)
		{
			if (useful_for_mergejoin(rel, index, joininfo_list) ||
				useful_for_ordering(root, rel, index))
				retval = lappend(retval,
								 create_index_path(root, rel, index, NIL));
		}

		/*
		 * 4. Create an innerjoin index path for each combination of
		 * other rels used in available join clauses.  These paths will
		 * be considered as the inner side of nestloop joins against
		 * those sets of other rels.  indexable_joinclauses() finds sets
		 * of clauses that can be used with each combination of outer rels,
		 * and index_innerjoin builds the paths themselves.  We add the
		 * paths to the rel's innerjoin list, NOT to the result list.
		 */
		indexable_joinclauses(rel, index,
							  joininfo_list, restrictinfo_list,
							  &joinclausegroups,
							  &joinouterrelids);
		if (joinclausegroups != NIL)
		{
			rel->innerjoin = nconc(rel->innerjoin,
								   index_innerjoin(root, rel, index,
												   joinclausegroups,
												   joinouterrelids));
		}
	}

	return retval;
}


/****************************************************************************
 *		----  ROUTINES TO PROCESS 'OR' CLAUSES  ----
 ****************************************************************************/


/*
 * match_index_orclauses
 *	  Attempt to match an index against subclauses within 'or' clauses.
 *	  Each subclause that does match is marked with the index's node.
 *
 *	  Essentially, this adds 'index' to the list of subclause indices in
 *	  the RestrictInfo field of each of the 'or' clauses where it matches.
 *	  NOTE: we can use storage in the RestrictInfo for this purpose because
 *	  this processing is only done on single-relation restriction clauses.
 *	  Therefore, we will never have indexes for more than one relation
 *	  mentioned in the same RestrictInfo node's list.
 *
 * 'rel' is the node of the relation on which the index is defined.
 * 'index' is the index node.
 * 'indexkey' is the (single) key of the index that we will consider.
 * 'class' is the class of the operator corresponding to 'indexkey'.
 * 'restrictinfo_list' is the list of available restriction clauses.
 */
static void
match_index_orclauses(RelOptInfo *rel,
					  IndexOptInfo *index,
					  int indexkey,
					  Oid opclass,
					  List *restrictinfo_list)
{
	List	   *i;

	foreach(i, restrictinfo_list)
	{
		RestrictInfo *restrictinfo = (RestrictInfo *) lfirst(i);

		if (restriction_is_or_clause(restrictinfo))
		{
			/*
			 * Add this index to the subclause index list for each
			 * subclause that it matches.
			 */
			restrictinfo->subclauseindices =
				match_index_orclause(rel, index,
									 indexkey, opclass,
									 restrictinfo->clause->args,
									 restrictinfo->subclauseindices);
		}
	}
}

/*
 * match_index_orclause
 *	  Attempts to match an index against the subclauses of an 'or' clause.
 *
 *	  A match means that:
 *	  (1) the operator within the subclause can be used with the
 *				index's specified operator class, and
 *	  (2) one operand of the subclause matches the index key.
 *
 * 'or_clauses' is the list of subclauses within the 'or' clause
 * 'other_matching_indices' is the list of information on other indices
 *		that have already been matched to subclauses within this
 *		particular 'or' clause (i.e., a list previously generated by
 *		this routine), or NIL if this routine has not previously been
 *	    run for this 'or' clause.
 *
 * Returns a list of the form ((a b c) (d e f) nil (g h) ...) where
 * a,b,c are nodes of indices that match the first subclause in
 * 'or-clauses', d,e,f match the second subclause, no indices
 * match the third, g,h match the fourth, etc.
 */
static List *
match_index_orclause(RelOptInfo *rel,
					 IndexOptInfo *index,
					 int indexkey,
					 Oid opclass,
					 List *or_clauses,
					 List *other_matching_indices)
{
	List	   *matching_indices;
	List	   *index_list;
	List	   *clist;

	/* first time through, we create list of same length as OR clause,
	 * containing an empty sublist for each subclause.
	 */
	if (!other_matching_indices)
	{
		matching_indices = NIL;
		foreach(clist, or_clauses)
			matching_indices = lcons(NIL, matching_indices);
	}
	else
		matching_indices = other_matching_indices;

	index_list = matching_indices;

	foreach(clist, or_clauses)
	{
		Expr	   *clause = lfirst(clist);

		if (match_or_subclause_to_indexkey(rel, index, indexkey, opclass,
										   clause))
		{
			/* OK to add this index to sublist for this subclause */
			lfirst(matching_indices) = lcons(index,
											 lfirst(matching_indices));
		}

		matching_indices = lnext(matching_indices);
	}

	return index_list;
}

/*
 * See if a subclause of an OR clause matches an index.
 *
 * We accept the subclause if it is an operator clause that matches the
 * index, or if it is an AND clause all of whose members are operators
 * that match the index.  (XXX Would accepting a single match be useful?)
 */
static bool
match_or_subclause_to_indexkey(RelOptInfo *rel,
							   IndexOptInfo *index,
							   int indexkey,
							   Oid opclass,
							   Expr *clause)
{
	if (and_clause((Node *) clause))
	{
		List	   *item;

		foreach(item, clause->args)
		{
			if (! match_clause_to_indexkey(rel, index, indexkey, opclass,
										   lfirst(item), false))
				return false;
		}
		return true;
	}
	else
		return match_clause_to_indexkey(rel, index, indexkey, opclass,
										clause, false);
}


/****************************************************************************
 *				----  ROUTINES TO CHECK RESTRICTIONS  ----
 ****************************************************************************/


/*
 * DoneMatchingIndexKeys() - MACRO
 *
 * Determine whether we should continue matching index keys in a clause.
 * Depends on if there are more to match or if this is a functional index.
 * In the latter case we stop after the first match since the there can
 * be only key (i.e. the function's return value) and the attributes in
 * keys list represent the arguments to the function.  -mer 3 Oct. 1991
 */
#define DoneMatchingIndexKeys(indexkeys, index) \
		(indexkeys[0] == 0 || \
		 (index->indproc != InvalidOid))

/*
 * group_clauses_by_indexkey
 *	  Generates a list of restriction clauses that can be used with an index.
 *
 * 'rel' is the node of the relation itself.
 * 'index' is a index on 'rel'.
 * 'indexkeys' are the index keys to be matched.
 * 'classes' are the classes of the index operators on those keys.
 * 'restrictinfo_list' is the list of available restriction clauses for 'rel'.
 *
 * Returns a list of all the RestrictInfo nodes for clauses that can be
 * used with this index.
 *
 * The list is ordered by index key (but as far as I can tell, this is
 * an implementation artifact of this routine, and is not depended on by
 * any user of the returned list --- tgl 7/99).
 *
 * Note that in a multi-key index, we stop if we find a key that cannot be
 * used with any clause.  For example, given an index on (A,B,C), we might
 * return (C1 C2 C3 C4) if we find that clauses C1 and C2 use column A,
 * clauses C3 and C4 use column B, and no clauses use column C.  But if
 * no clauses match B we will return (C1 C2), whether or not there are
 * clauses matching column C, because the executor couldn't use them anyway.
 */
static List *
group_clauses_by_indexkey(RelOptInfo *rel,
						  IndexOptInfo *index,
						  int *indexkeys,
						  Oid *classes,
						  List *restrictinfo_list)
{
	List	   *clausegroup_list = NIL;

	if (restrictinfo_list == NIL || indexkeys[0] == 0)
		return NIL;

	do
	{
		int			curIndxKey = indexkeys[0];
		Oid			curClass = classes[0];
		List	   *clausegroup = NIL;
		List	   *curCinfo;

		foreach(curCinfo, restrictinfo_list)
		{
			RestrictInfo *rinfo = (RestrictInfo *) lfirst(curCinfo);

			if (match_clause_to_indexkey(rel,
										 index,
										 curIndxKey,
										 curClass,
										 rinfo->clause,
										 false))
				clausegroup = lappend(clausegroup, rinfo);
		}

		/* If no clauses match this key, we're done; we don't want to
		 * look at keys to its right.
		 */
		if (clausegroup == NIL)
			break;

		clausegroup_list = nconc(clausegroup_list, clausegroup);

		indexkeys++;
		classes++;

	} while (!DoneMatchingIndexKeys(indexkeys, index));

	/* clausegroup_list holds all matched clauses ordered by indexkeys */
	return clausegroup_list;
}

/*
 * group_clauses_by_ikey_for_joins
 *    Generates a list of join clauses that can be used with an index
 *	  to scan the inner side of a nestloop join.
 *
 * This is much like group_clauses_by_indexkey(), but we consider both
 * join and restriction clauses.  For each indexkey in the index, we
 * accept both join and restriction clauses that match it, since both
 * will make useful indexquals if the index is being used to scan the
 * inner side of a nestloop join.  But there must be at least one matching
 * join clause, or we return NIL indicating that this index isn't useful
 * for nestloop joining.
 */
static List *
group_clauses_by_ikey_for_joins(RelOptInfo *rel,
								IndexOptInfo *index,
								int *indexkeys,
								Oid *classes,
								List *join_cinfo_list,
								List *restr_cinfo_list)
{
	List	   *clausegroup_list = NIL;
	bool		jfound = false;

	if (join_cinfo_list == NIL || indexkeys[0] == 0)
		return NIL;

	do
	{
		int			curIndxKey = indexkeys[0];
		Oid			curClass = classes[0];
		List	   *clausegroup = NIL;
		List	   *curCinfo;

		foreach(curCinfo, join_cinfo_list)
		{
			RestrictInfo *rinfo = (RestrictInfo *) lfirst(curCinfo);

			if (match_clause_to_indexkey(rel,
										 index,
										 curIndxKey,
										 curClass,
										 rinfo->clause,
										 true))
			{
				clausegroup = lappend(clausegroup, rinfo);
				jfound = true;
			}
		}
		foreach(curCinfo, restr_cinfo_list)
		{
			RestrictInfo *rinfo = (RestrictInfo *) lfirst(curCinfo);

			if (match_clause_to_indexkey(rel,
										 index,
										 curIndxKey,
										 curClass,
										 rinfo->clause,
										 false))
				clausegroup = lappend(clausegroup, rinfo);
		}

		/* If no clauses match this key, we're done; we don't want to
		 * look at keys to its right.
		 */
		if (clausegroup == NIL)
			break;

		clausegroup_list = nconc(clausegroup_list, clausegroup);

		indexkeys++;
		classes++;

	} while (!DoneMatchingIndexKeys(indexkeys, index));

	/*
	 * if no join clause was matched then there ain't clauses for
	 * joins at all.
	 */
	if (!jfound)
	{
		freeList(clausegroup_list);
		return NIL;
	}

	/* clausegroup_list holds all matched clauses ordered by indexkeys */
	return clausegroup_list;
}


/*
 * match_clause_to_indexkey()
 *    Determines whether a restriction or join clause matches
 *    a key of an index.
 *
 *	  To match, the clause:

 *	  (1a) for a restriction clause: must be in the form (indexkey op const)
 *		   or (const op indexkey), or
 *	  (1b) for a join clause: must be in the form (indexkey op others)
 *		   or (others op indexkey), where others is an expression involving
 *		   only vars of the other relation(s); and
 *	  (2)  must contain an operator which is in the same class as the index
 *		   operator for this key, or is a "special" operator as recognized
 *		   by match_special_index_operator().
 *
 *	  Presently, the executor can only deal with indexquals that have the
 *	  indexkey on the left, so we can only use clauses that have the indexkey
 *	  on the right if we can commute the clause to put the key on the left.
 *	  We do not actually do the commuting here, but we check whether a
 *	  suitable commutator operator is available.
 *
 *	  Note that in the join case, we already know that the clause as a
 *	  whole uses vars from the interesting set of relations.  But we need
 *	  to defend against expressions like (a.f1 OP (b.f2 OP a.f3)); that's
 *	  not processable by an indexscan nestloop join, whereas
 *	  (a.f1 OP (b.f2 OP c.f3)) is.
 *
 * 'rel' is the relation of interest.
 * 'index' is an index on 'rel'.
 * 'indexkey' is a key of 'index'.
 * 'opclass' is the corresponding operator class.
 * 'clause' is the clause to be tested.
 * 'join' is true if we are considering this clause for joins.
 *
 * Returns true if the clause can be used with this index key.
 *
 * NOTE:  returns false if clause is an OR or AND clause; to the extent
 * we cope with those at all, it is done by higher-level routines.
 */
static bool
match_clause_to_indexkey(RelOptInfo *rel,
						 IndexOptInfo *index,
						 int indexkey,
						 Oid opclass,
						 Expr *clause,
						 bool join)
{
	Var		   *leftop,
			   *rightop;

	/* Clause must be a binary opclause. */
	if (! is_opclause((Node *) clause))
		return false;
	leftop = get_leftop(clause);
	rightop = get_rightop(clause);
	if (! leftop || ! rightop)
		return false;

	if (!join)
	{
		/*
		 * Not considering joins, so check for clauses of the form:
		 * (indexkey operator constant) or (constant operator indexkey).
		 * We will accept a Param as being constant.
		 */

		if ((IsA(rightop, Const) || IsA(rightop, Param)) &&
			match_index_to_operand(indexkey, leftop, rel, index))
		{
			if (is_indexable_operator(clause, opclass, index->relam, true))
				return true;
			/*
			 * If we didn't find a member of the index's opclass,
			 * see whether it is a "special" indexable operator.
			 */
			if (match_special_index_operator(clause, opclass, index->relam,
											 true))
				return true;
			return false;
		}
		if ((IsA(leftop, Const) || IsA(leftop, Param)) &&
			match_index_to_operand(indexkey, rightop, rel, index))
		{
			if (is_indexable_operator(clause, opclass, index->relam, false))
				return true;
			/*
			 * If we didn't find a member of the index's opclass,
			 * see whether it is a "special" indexable operator.
			 */
			if (match_special_index_operator(clause, opclass, index->relam,
											 false))
				return true;
			return false;
		}
	}
	else
	{
		/*
		 * Check for an indexqual that could be handled by a nestloop join.
		 * We need the index key to be compared against an expression
		 * that uses none of the indexed relation's vars.
		 */
		if (match_index_to_operand(indexkey, leftop, rel, index))
		{
			List	   *othervarnos = pull_varnos((Node *) rightop);
			bool		isIndexable;

			isIndexable = ! intMember(lfirsti(rel->relids), othervarnos);
			freeList(othervarnos);
			if (isIndexable &&
				is_indexable_operator(clause, opclass, index->relam, true))
				return true;
		}
		else if (match_index_to_operand(indexkey, rightop, rel, index))
		{
			List	   *othervarnos = pull_varnos((Node *) leftop);
			bool		isIndexable;

			isIndexable = ! intMember(lfirsti(rel->relids), othervarnos);
			freeList(othervarnos);
			if (isIndexable &&
				is_indexable_operator(clause, opclass, index->relam, false))
				return true;
		}
	}

	return false;
}

/*
 * indexable_operator
 *	  Does a binary opclause contain an operator matching the index's
 *	  access method?
 *
 * If the indexkey is on the right, what we actually want to know
 * is whether the operator has a commutator operator that matches
 * the index's access method.
 *
 * We try both the straightforward match and matches that rely on
 * recognizing binary-compatible datatypes.  For example, if we have
 * an expression like "oid = 123", the operator will be oideqint4,
 * which we need to replace with oideq in order to recognize it as
 * matching an oid_ops index on the oid field.
 *
 * Returns the OID of the matching operator, or InvalidOid if no match.
 * Note that the returned OID will be different from the one in the given
 * expression if we used a binary-compatible substitution.  Also note that
 * if indexkey_on_left is FALSE (meaning we need to commute), the returned
 * OID is *not* commuted; it can be plugged directly into the given clause.
 */
Oid
indexable_operator(Expr *clause, Oid opclass, Oid relam,
				   bool indexkey_on_left)
{
	Oid			expr_op = ((Oper *) clause->oper)->opno;
	Oid			commuted_op;
	Oid			ltype,
				rtype;

	/* Get the commuted operator if necessary */
	if (indexkey_on_left)
		commuted_op = expr_op;
	else
		commuted_op = get_commutator(expr_op);
	if (commuted_op == InvalidOid)
		return InvalidOid;

	/* Done if the (commuted) operator is a member of the index's AM */
	if (op_class(commuted_op, opclass, relam))
		return expr_op;

	/*
	 * Maybe the index uses a binary-compatible operator set.
	 */
	ltype = exprType((Node *) get_leftop(clause));
	rtype = exprType((Node *) get_rightop(clause));

	/*
	 * make sure we have two different binary-compatible types...
	 */
	if (ltype != rtype && IS_BINARY_COMPATIBLE(ltype, rtype))
	{
		char	   *opname = get_opname(expr_op);
		Operator	newop;

		if (opname == NULL)
			return InvalidOid;	/* probably shouldn't happen */

		/* Use the datatype of the index key */
		if (indexkey_on_left)
			newop = oper(opname, ltype, ltype, TRUE);
		else
			newop = oper(opname, rtype, rtype, TRUE);

		if (HeapTupleIsValid(newop))
		{
			Oid		new_expr_op = oprid(newop);

			if (new_expr_op != expr_op)
			{
				/*
				 * OK, we found a binary-compatible operator of the same name;
				 * now does it match the index?
				 */
				if (indexkey_on_left)
					commuted_op = new_expr_op;
				else
					commuted_op = get_commutator(new_expr_op);
				if (commuted_op == InvalidOid)
					return InvalidOid;

				if (op_class(commuted_op, opclass, relam))
					return new_expr_op;
			}
		}
	}

	return InvalidOid;
}

/*
 * useful_for_mergejoin
 *	  Determine whether the given index can support a mergejoin based
 *	  on any available join clause.
 *
 *	  We look to see whether the first indexkey of the index matches the
 *	  left or right sides of any of the mergejoinable clauses and provides
 *	  the ordering needed for that side.  If so, the index is useful.
 *	  Matching a second or later indexkey is not useful unless there is
 *	  also a mergeclause for the first indexkey, so we need not consider
 *	  secondary indexkeys at this stage.
 *
 * 'rel' is the relation for which 'index' is defined
 * 'joininfo_list' is the list of JoinInfo nodes for 'rel'
 */
static bool
useful_for_mergejoin(RelOptInfo *rel,
					 IndexOptInfo *index,
					 List *joininfo_list)
{
	int		   *indexkeys = index->indexkeys;
	Oid		   *ordering = index->ordering;
	List	   *i;

	if (!indexkeys || indexkeys[0] == 0 ||
		!ordering || ordering[0] == InvalidOid)
		return false;			/* unordered index is not useful */

	foreach(i, joininfo_list)
	{
		JoinInfo   *joininfo = (JoinInfo *) lfirst(i);
		List	   *j;

		foreach(j, joininfo->jinfo_restrictinfo)
		{
			RestrictInfo *restrictinfo = (RestrictInfo *) lfirst(j);

			if (restrictinfo->mergejoinoperator)
			{
				if (restrictinfo->left_sortop == ordering[0] &&
					match_index_to_operand(indexkeys[0],
										   get_leftop(restrictinfo->clause),
										   rel, index))
					return true;
				if (restrictinfo->right_sortop == ordering[0] &&
					match_index_to_operand(indexkeys[0],
										   get_rightop(restrictinfo->clause),
										   rel, index))
					return true;
			}
		}
	}
	return false;
}

/*
 * useful_for_ordering
 *	  Determine whether the given index can produce an ordering matching
 *	  the order that is wanted for the query result.
 *
 * We check to see whether either forward or backward scan direction can
 * match the specified pathkeys.
 *
 * 'rel' is the relation for which 'index' is defined
 */
static bool
useful_for_ordering(Query *root,
					RelOptInfo *rel,
					IndexOptInfo *index)
{
	List	   *index_pathkeys;

	if (root->query_pathkeys == NIL)
		return false;			/* no special ordering requested */

	index_pathkeys = build_index_pathkeys(root, rel, index);

	if (index_pathkeys == NIL)
		return false;			/* unordered index */

	if (pathkeys_contained_in(root->query_pathkeys, index_pathkeys))
		return true;

	/* caution: commute_pathkeys destructively modifies its argument;
	 * safe because we just built the index_pathkeys for local use here.
	 */
	if (commute_pathkeys(index_pathkeys))
	{
		if (pathkeys_contained_in(root->query_pathkeys, index_pathkeys))
			return true;		/* useful as a reverse-order path */
	}

	return false;
}

/****************************************************************************
 *				----  ROUTINES TO DO PARTIAL INDEX PREDICATE TESTS	----
 ****************************************************************************/

/*
 * pred_test
 *	  Does the "predicate inclusion test" for partial indexes.
 *
 *	  Recursively checks whether the clauses in restrictinfo_list imply
 *	  that the given predicate is true.
 *
 *	  This routine (together with the routines it calls) iterates over
 *	  ANDs in the predicate first, then reduces the qualification
 *	  clauses down to their constituent terms, and iterates over ORs
 *	  in the predicate last.  This order is important to make the test
 *	  succeed whenever possible (assuming the predicate has been
 *	  successfully cnfify()-ed). --Nels, Jan '93
 */
static bool
pred_test(List *predicate_list, List *restrictinfo_list, List *joininfo_list)
{
	List	   *pred,
			   *items,
			   *item;

	/*
	 * Note: if Postgres tried to optimize queries by forming equivalence
	 * classes over equi-joined attributes (i.e., if it recognized that a
	 * qualification such as "where a.b=c.d and a.b=5" could make use of
	 * an index on c.d), then we could use that equivalence class info
	 * here with joininfo_list to do more complete tests for the usability
	 * of a partial index.	For now, the test only uses restriction
	 * clauses (those in restrictinfo_list). --Nels, Dec '92
	 */

	if (predicate_list == NULL)
		return true;			/* no predicate: the index is usable */
	if (restrictinfo_list == NULL)
		return false;			/* no restriction clauses: the test must
								 * fail */

	foreach(pred, predicate_list)
	{

		/*
		 * if any clause is not implied, the whole predicate is not
		 * implied
		 */
		if (and_clause(lfirst(pred)))
		{
			items = ((Expr *) lfirst(pred))->args;
			foreach(item, items)
			{
				if (!one_pred_test(lfirst(item), restrictinfo_list))
					return false;
			}
		}
		else if (!one_pred_test(lfirst(pred), restrictinfo_list))
			return false;
	}
	return true;
}


/*
 * one_pred_test
 *	  Does the "predicate inclusion test" for one conjunct of a predicate
 *	  expression.
 */
static bool
one_pred_test(Expr *predicate, List *restrictinfo_list)
{
	RestrictInfo *restrictinfo;
	List	   *item;

	Assert(predicate != NULL);
	foreach(item, restrictinfo_list)
	{
		restrictinfo = (RestrictInfo *) lfirst(item);
		/* if any clause implies the predicate, return true */
		if (one_pred_clause_expr_test(predicate, (Node *) restrictinfo->clause))
			return true;
	}
	return false;
}


/*
 * one_pred_clause_expr_test
 *	  Does the "predicate inclusion test" for a general restriction-clause
 *	  expression.
 */
static bool
one_pred_clause_expr_test(Expr *predicate, Node *clause)
{
	List	   *items,
			   *item;

	if (is_opclause(clause))
		return one_pred_clause_test(predicate, clause);
	else if (or_clause(clause))
	{
		items = ((Expr *) clause)->args;
		foreach(item, items)
		{
			/* if any OR item doesn't imply the predicate, clause doesn't */
			if (!one_pred_clause_expr_test(predicate, lfirst(item)))
				return false;
		}
		return true;
	}
	else if (and_clause(clause))
	{
		items = ((Expr *) clause)->args;
		foreach(item, items)
		{

			/*
			 * if any AND item implies the predicate, the whole clause
			 * does
			 */
			if (one_pred_clause_expr_test(predicate, lfirst(item)))
				return true;
		}
		return false;
	}
	else
	{
		/* unknown clause type never implies the predicate */
		return false;
	}
}


/*
 * one_pred_clause_test
 *	  Does the "predicate inclusion test" for one conjunct of a predicate
 *	  expression for a simple restriction clause.
 */
static bool
one_pred_clause_test(Expr *predicate, Node *clause)
{
	List	   *items,
			   *item;

	if (is_opclause((Node *) predicate))
		return clause_pred_clause_test(predicate, clause);
	else if (or_clause((Node *) predicate))
	{
		items = predicate->args;
		foreach(item, items)
		{
			/* if any item is implied, the whole predicate is implied */
			if (one_pred_clause_test(lfirst(item), clause))
				return true;
		}
		return false;
	}
	else if (and_clause((Node *) predicate))
	{
		items = predicate->args;
		foreach(item, items)
		{

			/*
			 * if any item is not implied, the whole predicate is not
			 * implied
			 */
			if (!one_pred_clause_test(lfirst(item), clause))
				return false;
		}
		return true;
	}
	else
	{
		elog(DEBUG, "Unsupported predicate type, index will not be used");
		return false;
	}
}


/*
 * Define an "operator implication table" for btree operators ("strategies").
 * The "strategy numbers" are:	(1) <	(2) <=	 (3) =	 (4) >=   (5) >
 *
 * The interpretation of:
 *
 *		test_op = BT_implic_table[given_op-1][target_op-1]
 *
 * where test_op, given_op and target_op are strategy numbers (from 1 to 5)
 * of btree operators, is as follows:
 *
 *	 If you know, for some ATTR, that "ATTR given_op CONST1" is true, and you
 *	 want to determine whether "ATTR target_op CONST2" must also be true, then
 *	 you can use "CONST1 test_op CONST2" as a test.  If this test returns true,
 *	 then the target expression must be true; if the test returns false, then
 *	 the target expression may be false.
 *
 * An entry where test_op==0 means the implication cannot be determined, i.e.,
 * this test should always be considered false.
 */

static StrategyNumber
BT_implic_table[BTMaxStrategyNumber][BTMaxStrategyNumber] = {
	{2, 2, 0, 0, 0},
	{1, 2, 0, 0, 0},
	{1, 2, 3, 4, 5},
	{0, 0, 0, 4, 5},
	{0, 0, 0, 4, 4}
};


/*
 * clause_pred_clause_test
 *	  Use operator class info to check whether clause implies predicate.
 *
 *	  Does the "predicate inclusion test" for a "simple clause" predicate
 *	  for a single "simple clause" restriction.  Currently, this only handles
 *	  (binary boolean) operators that are in some btree operator class.
 *	  Eventually, rtree operators could also be handled by defining an
 *	  appropriate "RT_implic_table" array.
 */
static bool
clause_pred_clause_test(Expr *predicate, Node *clause)
{
	Var		   *pred_var,
			   *clause_var;
	Const	   *pred_const,
			   *clause_const;
	Oid			pred_op,
				clause_op,
				test_op;
	Oid			opclass_id;
	StrategyNumber pred_strategy,
				clause_strategy,
				test_strategy;
	Oper	   *test_oper;
	Expr	   *test_expr;
	bool		test_result,
				isNull;
	Relation	relation;
	HeapScanDesc scan;
	HeapTuple	tuple;
	ScanKeyData entry[3];
	Form_pg_amop aform;

	pred_var = (Var *) get_leftop(predicate);
	pred_const = (Const *) get_rightop(predicate);
	clause_var = (Var *) get_leftop((Expr *) clause);
	clause_const = (Const *) get_rightop((Expr *) clause);

	/* Check the basic form; for now, only allow the simplest case */
	if (!is_opclause(clause) ||
		!IsA(clause_var, Var) ||
		clause_const == NULL ||
		!IsA(clause_const, Const) ||
		!IsA(predicate->oper, Oper) ||
		!IsA(pred_var, Var) ||
		!IsA(pred_const, Const))
		return false;

	/*
	 * The implication can't be determined unless the predicate and the
	 * clause refer to the same attribute.
	 */
	if (clause_var->varattno != pred_var->varattno)
		return false;

	/* Get the operators for the two clauses we're comparing */
	pred_op = ((Oper *) ((Expr *) predicate)->oper)->opno;
	clause_op = ((Oper *) ((Expr *) clause)->oper)->opno;


	/*
	 * 1. Find a "btree" strategy number for the pred_op
	 */
	ScanKeyEntryInitialize(&entry[0], 0,
						   Anum_pg_amop_amopid,
						   F_OIDEQ,
						   ObjectIdGetDatum(BTREE_AM_OID));

	ScanKeyEntryInitialize(&entry[1], 0,
						   Anum_pg_amop_amopopr,
						   F_OIDEQ,
						   ObjectIdGetDatum(pred_op));

	relation = heap_openr(AccessMethodOperatorRelationName, AccessShareLock);

	/*
	 * The following assumes that any given operator will only be in a
	 * single btree operator class.  This is true at least for all the
	 * pre-defined operator classes.  If it isn't true, then whichever
	 * operator class happens to be returned first for the given operator
	 * will be used to find the associated strategy numbers for the test.
	 * --Nels, Jan '93
	 */
	scan = heap_beginscan(relation, false, SnapshotNow, 2, entry);
	tuple = heap_getnext(scan, 0);
	if (!HeapTupleIsValid(tuple))
	{
		elog(DEBUG, "clause_pred_clause_test: unknown pred_op");
		heap_endscan(scan);
		heap_close(relation, AccessShareLock);
		return false;
	}
	aform = (Form_pg_amop) GETSTRUCT(tuple);

	/* Get the predicate operator's strategy number (1 to 5) */
	pred_strategy = (StrategyNumber) aform->amopstrategy;

	/* Remember which operator class this strategy number came from */
	opclass_id = aform->amopclaid;

	heap_endscan(scan);


	/*
	 * 2. From the same opclass, find a strategy num for the clause_op
	 */
	ScanKeyEntryInitialize(&entry[1], 0,
						   Anum_pg_amop_amopclaid,
						   F_OIDEQ,
						   ObjectIdGetDatum(opclass_id));

	ScanKeyEntryInitialize(&entry[2], 0,
						   Anum_pg_amop_amopopr,
						   F_OIDEQ,
						   ObjectIdGetDatum(clause_op));

	scan = heap_beginscan(relation, false, SnapshotNow, 3, entry);
	tuple = heap_getnext(scan, 0);
	if (!HeapTupleIsValid(tuple))
	{
		elog(DEBUG, "clause_pred_clause_test: unknown clause_op");
		heap_endscan(scan);
		heap_close(relation, AccessShareLock);
		return false;
	}
	aform = (Form_pg_amop) GETSTRUCT(tuple);

	/* Get the restriction clause operator's strategy number (1 to 5) */
	clause_strategy = (StrategyNumber) aform->amopstrategy;
	heap_endscan(scan);


	/*
	 * 3. Look up the "test" strategy number in the implication table
	 */

	test_strategy = BT_implic_table[clause_strategy - 1][pred_strategy - 1];
	if (test_strategy == 0)
	{
		heap_close(relation, AccessShareLock);
		return false;			/* the implication cannot be determined */
	}

	/*
	 * 4. From the same opclass, find the operator for the test strategy
	 */

	ScanKeyEntryInitialize(&entry[2], 0,
						   Anum_pg_amop_amopstrategy,
						   F_INT2EQ,
						   Int16GetDatum(test_strategy));

	scan = heap_beginscan(relation, false, SnapshotNow, 3, entry);
	tuple = heap_getnext(scan, 0);
	if (!HeapTupleIsValid(tuple))
	{
		elog(DEBUG, "clause_pred_clause_test: unknown test_op");
		heap_endscan(scan);
		heap_close(relation, AccessShareLock);
		return false;
	}
	aform = (Form_pg_amop) GETSTRUCT(tuple);

	/* Get the test operator */
	test_op = aform->amopopr;

	heap_endscan(scan);

	heap_close(relation, AccessShareLock);

	/*
	 * 5. Evaluate the test
	 */
	test_oper = makeOper(test_op,		/* opno */
						 InvalidOid,	/* opid */
						 BOOLOID,		/* opresulttype */
						 0,		/* opsize */
						 NULL); /* op_fcache */
	replace_opid(test_oper);

	test_expr = make_opclause(test_oper,
							  copyObject(clause_const),
							  copyObject(pred_const));

#ifndef OMIT_PARTIAL_INDEX
	test_result = ExecEvalExpr((Node *) test_expr, NULL, &isNull, NULL);
#endif	 /* OMIT_PARTIAL_INDEX */
	if (isNull)
	{
		elog(DEBUG, "clause_pred_clause_test: null test result");
		return false;
	}
	return test_result;
}


/****************************************************************************
 *				----  ROUTINES TO CHECK JOIN CLAUSES  ----
 ****************************************************************************/

/*
 * indexable_joinclauses
 *	  Finds all groups of join clauses from among 'joininfo_list' that can
 *	  be used in conjunction with 'index' for the inner scan of a nestjoin.
 *
 *	  Each clause group comes from a single joininfo node plus the current
 *	  rel's restrictinfo list.  Therefore, every clause in the group references
 *	  the current rel plus the same set of other rels (except for the restrict
 *	  clauses, which only reference the current rel).  Therefore, this set
 *    of clauses could be used as an indexqual if the relation is scanned
 *	  as the inner side of a nestloop join when the outer side contains
 *	  (at least) all those "other rels".
 *
 *	  XXX Actually, given that we are considering a join that requires an
 *	  outer rel set (A,B,C), we should use all qual clauses that reference
 *	  any subset of these rels, not just the full set or none.  This is
 *	  doable with a doubly nested loop over joininfo_list; is it worth it?
 *
 * Returns two parallel lists of the same length: the clause groups,
 * and the required outer rel set for each one.
 *
 * 'rel' is the relation for which 'index' is defined
 * 'joininfo_list' is the list of JoinInfo nodes for 'rel'
 * 'restrictinfo_list' is the list of restriction clauses for 'rel'
 * '*clausegroups' receives a list of clause sublists
 * '*outerrelids' receives a list of relid lists
 */
static void
indexable_joinclauses(RelOptInfo *rel, IndexOptInfo *index,
					  List *joininfo_list, List *restrictinfo_list,
					  List **clausegroups, List **outerrelids)
{
	List	   *cg_list = NIL;
	List	   *relid_list = NIL;
	List	   *i;

	foreach(i, joininfo_list)
	{
		JoinInfo   *joininfo = (JoinInfo *) lfirst(i);
		List	   *clausegroup;

		clausegroup = group_clauses_by_ikey_for_joins(rel,
													  index,
													  index->indexkeys,
													  index->classlist,
											joininfo->jinfo_restrictinfo,
													  restrictinfo_list);

		if (clausegroup != NIL)
		{
			cg_list = lappend(cg_list, clausegroup);
			relid_list = lappend(relid_list, joininfo->unjoined_relids);
		}
	}

	*clausegroups = cg_list;
	*outerrelids = relid_list;
}

/****************************************************************************
 *				----  PATH CREATION UTILITIES  ----
 ****************************************************************************/

/*
 * index_innerjoin
 *	  Creates index path nodes corresponding to paths to be used as inner
 *	  relations in nestloop joins.
 *
 * 'rel' is the relation for which 'index' is defined
 * 'clausegroup_list' is a list of lists of restrictinfo nodes which can use
 * 'index'.  Each sublist refers to the same set of outer rels.
 * 'outerrelids_list' is a list of the required outer rels for each sublist
 * of join clauses.
 *
 * Returns a list of index pathnodes.
 */
static List *
index_innerjoin(Query *root, RelOptInfo *rel, IndexOptInfo *index,
				List *clausegroup_list, List *outerrelids_list)
{
	List	   *path_list = NIL;
	List	   *i;

	foreach(i, clausegroup_list)
	{
		List	   *clausegroup = lfirst(i);
		IndexPath  *pathnode = makeNode(IndexPath);
		List	   *indexquals;
		long		npages;
		Selectivity	selec;

		indexquals = get_actual_clauses(clausegroup);
		/* expand special operators to indexquals the executor can handle */
		indexquals = expand_indexqual_conditions(indexquals);

		index_selectivity(root,
						  rel,
						  index,
						  indexquals,
						  &npages,
						  &selec);

		/* XXX this code ought to be merged with create_index_path? */

		pathnode->path.pathtype = T_IndexScan;
		pathnode->path.parent = rel;
		pathnode->path.pathkeys = build_index_pathkeys(root, rel, index);

		/* Note that we are making a pathnode for a single-scan indexscan;
		 * therefore, both indexid and indexqual should be single-element
		 * lists.
		 */
		pathnode->indexid = lconsi(index->indexoid, NIL);
		pathnode->indexqual = lcons(indexquals, NIL);

		/* joinrelids saves the rels needed on the outer side of the join */
		pathnode->joinrelids = lfirst(outerrelids_list);

		pathnode->path.path_cost = cost_index(rel, index,
											  npages, selec,
											  true);

		path_list = lappend(path_list, pathnode);
		outerrelids_list = lnext(outerrelids_list);
	}
	return path_list;
}

/****************************************************************************
 *				----  ROUTINES TO CHECK OPERANDS  ----
 ****************************************************************************/

/*
 * match_index_to_operand()
 *	  Generalized test for a match between an index's key
 *	  and the operand on one side of a restriction or join clause.
 *    Now check for functional indices as well.
 */
static bool
match_index_to_operand(int indexkey,
					   Var *operand,
					   RelOptInfo *rel,
					   IndexOptInfo *index)
{
	if (index->indproc == InvalidOid)
	{
		/*
		 * Normal index.
		 */
		if (IsA(operand, Var) &&
			lfirsti(rel->relids) == operand->varno &&
			indexkey == operand->varattno)
			return true;
		else
			return false;
	}

	/*
	 * functional index check
	 */
	return function_index_operand((Expr *) operand, rel, index);
}

static bool
function_index_operand(Expr *funcOpnd, RelOptInfo *rel, IndexOptInfo *index)
{
	int			relvarno = lfirsti(rel->relids);
	Func	   *function;
	List	   *funcargs;
	int		   *indexKeys = index->indexkeys;
	List	   *arg;
	int			i;

	/*
	 * sanity check, make sure we know what we're dealing with here.
	 */
	if (funcOpnd == NULL ||	! IsA(funcOpnd, Expr) ||
		funcOpnd->opType != FUNC_EXPR ||
		funcOpnd->oper == NULL || indexKeys == NULL)
		return false;

	function = (Func *) funcOpnd->oper;
	funcargs = funcOpnd->args;

	if (function->funcid != index->indproc)
		return false;

	/*
	 * Check that the arguments correspond to the same arguments used to
	 * create the functional index.  To do this we must check that 1.
	 * refer to the right relation. 2. the args have the right attr.
	 * numbers in the right order.
	 */
	i = 0;
	foreach(arg, funcargs)
	{
		Var	   *var = (Var *) lfirst(arg);

		if (! IsA(var, Var))
			return false;
		if (indexKeys[i] == 0)
			return false;
		if (var->varno != relvarno || var->varattno != indexKeys[i])
			return false;

		i++;
	}

	if (indexKeys[i] != 0)
		return false;			/* not enough arguments */

	return true;
}

/****************************************************************************
 *			----  ROUTINES FOR "SPECIAL" INDEXABLE OPERATORS  ----
 ****************************************************************************/

/*----------
 * These routines handle special optimization of operators that can be
 * used with index scans even though they are not known to the executor's
 * indexscan machinery.  The key idea is that these operators allow us
 * to derive approximate indexscan qual clauses, such that any tuples
 * that pass the operator clause itself must also satisfy the simpler
 * indexscan condition(s).  Then we can use the indexscan machinery
 * to avoid scanning as much of the table as we'd otherwise have to,
 * while applying the original operator as a qpqual condition to ensure
 * we deliver only the tuples we want.  (In essence, we're using a regular
 * index as if it were a lossy index.)
 *
 * An example of what we're doing is
 *			textfield LIKE 'abc%'
 * from which we can generate the indexscanable conditions
 *			textfield >= 'abc' AND textfield < 'abd'
 * which allow efficient scanning of an index on textfield.
 * (In reality, character set and collation issues make the transformation
 * from LIKE to indexscan limits rather harder than one might think ...
 * but that's the basic idea.)
 *
 * Two routines are provided here, match_special_index_operator() and
 * expand_indexqual_conditions().  match_special_index_operator() is
 * just an auxiliary function for match_clause_to_indexkey(); after
 * the latter fails to recognize a restriction opclause's operator
 * as a member of an index's opclass, it asks match_special_index_operator()
 * whether the clause should be considered an indexqual anyway.
 * expand_indexqual_conditions() converts a list of "raw" indexqual
 * conditions (with implicit AND semantics across list elements) into
 * a list that the executor can actually handle.  For operators that
 * are members of the index's opclass this transformation is a no-op,
 * but operators recognized by match_special_index_operator() must be
 * converted into one or more "regular" indexqual conditions.
 *----------
 */

/*
 * match_special_index_operator
 *	  Recognize restriction clauses that can be used to generate
 *	  additional indexscanable qualifications.
 *
 * The given clause is already known to be a binary opclause having
 * the form (indexkey OP const/param) or (const/param OP indexkey),
 * but the OP proved not to be one of the index's opclass operators.
 * Return 'true' if we can do something with it anyway.
 */
static bool
match_special_index_operator(Expr *clause, Oid opclass, Oid relam,
							 bool indexkey_on_left)
{
	bool		isIndexable = false;
	Var		   *leftop,
			   *rightop;
	Oid			expr_op;
	Datum		constvalue;
	char	   *patt;
	char	   *prefix;

	/* Currently, all known special operators require the indexkey
	 * on the left, but this test could be pushed into the switch statement
	 * if some are added that do not...
	 */
	if (! indexkey_on_left)
		return false;

	/* we know these will succeed */
	leftop = get_leftop(clause);
	rightop = get_rightop(clause);
	expr_op = ((Oper *) clause->oper)->opno;

	/* again, required for all current special ops: */
	if (! IsA(rightop, Const) ||
		((Const *) rightop)->constisnull)
		return false;
	constvalue = ((Const *) rightop)->constvalue;

	switch (expr_op)
	{
		case OID_TEXT_LIKE_OP:
		case OID_BPCHAR_LIKE_OP:
		case OID_VARCHAR_LIKE_OP:
		case OID_NAME_LIKE_OP:
			/* the right-hand const is type text for all of these */
			patt = textout((text *) DatumGetPointer(constvalue));
			isIndexable = like_fixed_prefix(patt, &prefix) != Prefix_None;
			if (prefix) pfree(prefix);
			pfree(patt);
			break;

		case OID_TEXT_REGEXEQ_OP:
		case OID_BPCHAR_REGEXEQ_OP:
		case OID_VARCHAR_REGEXEQ_OP:
		case OID_NAME_REGEXEQ_OP:
			/* the right-hand const is type text for all of these */
			patt = textout((text *) DatumGetPointer(constvalue));
			isIndexable = regex_fixed_prefix(patt, false, &prefix) != Prefix_None;
			if (prefix) pfree(prefix);
			pfree(patt);
			break;

		case OID_TEXT_ICREGEXEQ_OP:
		case OID_BPCHAR_ICREGEXEQ_OP:
		case OID_VARCHAR_ICREGEXEQ_OP:
		case OID_NAME_ICREGEXEQ_OP:
			/* the right-hand const is type text for all of these */
			patt = textout((text *) DatumGetPointer(constvalue));
			isIndexable = regex_fixed_prefix(patt, true, &prefix) != Prefix_None;
			if (prefix) pfree(prefix);
			pfree(patt);
			break;
	}

	/* done if the expression doesn't look indexable */
	if (! isIndexable)
		return false;

	/*
	 * Must also check that index's opclass supports the operators we will
	 * want to apply.  (A hash index, for example, will not support ">=".)
	 * We cheat a little by not checking for availability of "=" ... any
	 * index type should support "=", methinks.
	 */
	switch (expr_op)
	{
		case OID_TEXT_LIKE_OP:
		case OID_TEXT_REGEXEQ_OP:
		case OID_TEXT_ICREGEXEQ_OP:
			if (! op_class(find_operator(">=", TEXTOID), opclass, relam) ||
				! op_class(find_operator("<", TEXTOID), opclass, relam))
				isIndexable = false;
			break;

		case OID_BPCHAR_LIKE_OP:
		case OID_BPCHAR_REGEXEQ_OP:
		case OID_BPCHAR_ICREGEXEQ_OP:
			if (! op_class(find_operator(">=", BPCHAROID), opclass, relam) ||
				! op_class(find_operator("<", BPCHAROID), opclass, relam))
				isIndexable = false;
			break;

		case OID_VARCHAR_LIKE_OP:
		case OID_VARCHAR_REGEXEQ_OP:
		case OID_VARCHAR_ICREGEXEQ_OP:
			if (! op_class(find_operator(">=", VARCHAROID), opclass, relam) ||
				! op_class(find_operator("<", VARCHAROID), opclass, relam))
				isIndexable = false;
			break;

		case OID_NAME_LIKE_OP:
		case OID_NAME_REGEXEQ_OP:
		case OID_NAME_ICREGEXEQ_OP:
			if (! op_class(find_operator(">=", NAMEOID), opclass, relam) ||
				! op_class(find_operator("<", NAMEOID), opclass, relam))
				isIndexable = false;
			break;
	}

	return isIndexable;
}

/*
 * expand_indexqual_conditions
 *	  Given a list of (implicitly ANDed) indexqual clauses,
 *	  expand any "special" index operators into clauses that the indexscan
 *	  machinery will know what to do with.  Clauses that were not
 *	  recognized by match_special_index_operator() must be passed through
 *	  unchanged.
 */
List *
expand_indexqual_conditions(List *indexquals)
{
	List	   *resultquals = NIL;
	List	   *q;

	foreach(q, indexquals)
	{
		Expr	   *clause = (Expr *) lfirst(q);
		/* we know these will succeed */
		Var		   *leftop = get_leftop(clause);
		Var		   *rightop = get_rightop(clause);
		Oid			expr_op = ((Oper *) clause->oper)->opno;
		Datum		constvalue;
		char	   *patt;
		char	   *prefix;
		Prefix_Status pstatus;

		switch (expr_op)
		{
			/*
			 * LIKE and regex operators are not members of any index opclass,
			 * so if we find one in an indexqual list we can assume that
			 * it was accepted by match_special_index_operator().
			 */
			case OID_TEXT_LIKE_OP:
			case OID_BPCHAR_LIKE_OP:
			case OID_VARCHAR_LIKE_OP:
			case OID_NAME_LIKE_OP:
				/* the right-hand const is type text for all of these */
				constvalue = ((Const *) rightop)->constvalue;
				patt = textout((text *) DatumGetPointer(constvalue));
				pstatus = like_fixed_prefix(patt, &prefix);
				resultquals = nconc(resultquals,
									prefix_quals(leftop, expr_op,
												 prefix, pstatus));
				if (prefix) pfree(prefix);
				pfree(patt);
				break;

			case OID_TEXT_REGEXEQ_OP:
			case OID_BPCHAR_REGEXEQ_OP:
			case OID_VARCHAR_REGEXEQ_OP:
			case OID_NAME_REGEXEQ_OP:
				/* the right-hand const is type text for all of these */
				constvalue = ((Const *) rightop)->constvalue;
				patt = textout((text *) DatumGetPointer(constvalue));
				pstatus = regex_fixed_prefix(patt, false, &prefix);
				resultquals = nconc(resultquals,
									prefix_quals(leftop, expr_op,
												 prefix, pstatus));
				if (prefix) pfree(prefix);
				pfree(patt);
				break;

			case OID_TEXT_ICREGEXEQ_OP:
			case OID_BPCHAR_ICREGEXEQ_OP:
			case OID_VARCHAR_ICREGEXEQ_OP:
			case OID_NAME_ICREGEXEQ_OP:
				/* the right-hand const is type text for all of these */
				constvalue = ((Const *) rightop)->constvalue;
				patt = textout((text *) DatumGetPointer(constvalue));
				pstatus = regex_fixed_prefix(patt, true, &prefix);
				resultquals = nconc(resultquals,
									prefix_quals(leftop, expr_op,
												 prefix, pstatus));
				if (prefix) pfree(prefix);
				pfree(patt);
				break;

			default:
				resultquals = lappend(resultquals, clause);
				break;
		}
	}

	return resultquals;
}

/*
 * Extract the fixed prefix, if any, for a LIKE pattern.
 * *prefix is set to a palloc'd prefix string,
 * or to NULL if no fixed prefix exists for the pattern.
 * The return value distinguishes no fixed prefix, a partial prefix,
 * or an exact-match-only pattern.
 */
static Prefix_Status
like_fixed_prefix(char *patt, char **prefix)
{
	char	   *match;
	int			pos,
				match_pos;

	*prefix = match = palloc(strlen(patt)+1);
	match_pos = 0;

	for (pos = 0; patt[pos]; pos++)
	{
		/* % and _ are wildcard characters in LIKE */
		if (patt[pos] == '%' ||
			patt[pos] == '_')
			break;
		/* Backslash quotes the next character */
		if (patt[pos] == '\\')
		{
			pos++;
			if (patt[pos] == '\0')
				break;
		}
		/*
		 * NOTE: this code used to think that %% meant a literal %,
		 * but textlike() itself does not think that, and the SQL92
		 * spec doesn't say any such thing either.
		 */
		match[match_pos++] = patt[pos];
	}
	
	match[match_pos] = '\0';

	/* in LIKE, an empty pattern is an exact match! */
	if (patt[pos] == '\0')
		return Prefix_Exact;	/* reached end of pattern, so exact */

	if (match_pos > 0)
		return Prefix_Partial;
	return Prefix_None;
}

/*
 * Extract the fixed prefix, if any, for a regex pattern.
 * *prefix is set to a palloc'd prefix string,
 * or to NULL if no fixed prefix exists for the pattern.
 * The return value distinguishes no fixed prefix, a partial prefix,
 * or an exact-match-only pattern.
 */
static Prefix_Status
regex_fixed_prefix(char *patt, bool case_insensitive,
				   char **prefix)
{
	char	   *match;
	int			pos,
				match_pos;

	*prefix = NULL;

	/* Pattern must be anchored left */
	if (patt[0] != '^')
		return Prefix_None;

	/* Cannot optimize if unquoted | { } is present in pattern */
	for (pos = 1; patt[pos]; pos++)
	{
		if (patt[pos] == '|' ||
			patt[pos] == '{' ||
			patt[pos] == '}')
			return Prefix_None;
		if (patt[pos] == '\\')
		{
			pos++;
			if (patt[pos] == '\0')
				break;
		}
	}

	/* OK, allocate space for pattern */
	*prefix = match = palloc(strlen(patt)+1);
	match_pos = 0;

	/* note start at pos 1 to skip leading ^ */
	for (pos = 1; patt[pos]; pos++)
	{
		if (patt[pos] == '.' ||
			patt[pos] == '?' ||
			patt[pos] == '*' ||
			patt[pos] == '[' ||
			patt[pos] == '$' ||
			/* XXX I suspect isalpha() is not an adequately locale-sensitive
			 * test for characters that can vary under case folding?
			 */
			(case_insensitive && isalpha(patt[pos])))
			break;
		if (patt[pos] == '\\')
		{
			pos++;
			if (patt[pos] == '\0')
				break;
		}
		match[match_pos++] = patt[pos];
	}

	match[match_pos] = '\0';

	if (patt[pos] == '$' && patt[pos+1] == '\0')
		return Prefix_Exact;	/* pattern specifies exact match */
	
	if (match_pos > 0)
		return Prefix_Partial;
	return Prefix_None;
}

/*
 * Given a fixed prefix that all the "leftop" values must have,
 * generate suitable indexqual condition(s).  expr_op is the original
 * LIKE or regex operator; we use it to deduce the appropriate comparison
 * operators.
 */
static List *
prefix_quals(Var *leftop, Oid expr_op,
			 char *prefix, Prefix_Status pstatus)
{
	List	   *result;
	Oid			datatype;
	Oid			oproid;
	Const	   *con;
	Oper	   *op;
	Expr	   *expr;
	char	   *greaterstr;

	Assert(pstatus != Prefix_None);

	switch (expr_op)
	{
		case OID_TEXT_LIKE_OP:
		case OID_TEXT_REGEXEQ_OP:
		case OID_TEXT_ICREGEXEQ_OP:
			datatype = TEXTOID;
			break;

		case OID_BPCHAR_LIKE_OP:
		case OID_BPCHAR_REGEXEQ_OP:
		case OID_BPCHAR_ICREGEXEQ_OP:
			datatype = BPCHAROID;
			break;

		case OID_VARCHAR_LIKE_OP:
		case OID_VARCHAR_REGEXEQ_OP:
		case OID_VARCHAR_ICREGEXEQ_OP:
			datatype = VARCHAROID;
			break;

		case OID_NAME_LIKE_OP:
		case OID_NAME_REGEXEQ_OP:
		case OID_NAME_ICREGEXEQ_OP:
			datatype = NAMEOID;
			break;

		default:
			elog(ERROR, "prefix_quals: unexpected operator %u", expr_op);
			return NIL;
	}

	/*
	 * If we found an exact-match pattern, generate an "=" indexqual.
	 */
	if (pstatus == Prefix_Exact)
	{
		oproid = find_operator("=", datatype);
		if (oproid == InvalidOid)
			elog(ERROR, "prefix_quals: no = operator for type %u", datatype);
		con = string_to_const(prefix, datatype);
		op = makeOper(oproid, InvalidOid, BOOLOID, 0, NULL);
		expr = make_opclause(op, leftop, (Var *) con);
		result = lcons(expr, NIL);
		return result;
	}

	/*
	 * Otherwise, we have a nonempty required prefix of the values.
	 *
	 * We can always say "x >= prefix".
	 */
	oproid = find_operator(">=", datatype);
	if (oproid == InvalidOid)
		elog(ERROR, "prefix_quals: no >= operator for type %u", datatype);
	con = string_to_const(prefix, datatype);
	op = makeOper(oproid, InvalidOid, BOOLOID, 0, NULL);
	expr = make_opclause(op, leftop, (Var *) con);
	result = lcons(expr, NIL);

	/*
	 * If we can create a string larger than the prefix, say "x < greaterstr".
	 */
	greaterstr = make_greater_string(prefix, datatype);
	if (greaterstr)
	{
		oproid = find_operator("<", datatype);
		if (oproid == InvalidOid)
			elog(ERROR, "prefix_quals: no < operator for type %u", datatype);
		con = string_to_const(greaterstr, datatype);
		op = makeOper(oproid, InvalidOid, BOOLOID, 0, NULL);
		expr = make_opclause(op, leftop, (Var *) con);
		result = lappend(result, expr);
		pfree(greaterstr);
	}

	return result;
}

/*
 * Try to generate a string greater than the given string or any string it is
 * a prefix of.  If successful, return a palloc'd string; else return NULL.
 *
 * To work correctly in non-ASCII locales with weird collation orders,
 * we cannot simply increment "foo" to "fop" --- we have to check whether
 * we actually produced a string greater than the given one.  If not,
 * increment the righthand byte again and repeat.  If we max out the righthand
 * byte, truncate off the last character and start incrementing the next.
 * For example, if "z" were the last character in the sort order, then we
 * could produce "foo" as a string greater than "fonz".
 *
 * This could be rather slow in the worst case, but in most cases we won't
 * have to try more than one or two strings before succeeding.
 *
 * XXX in a sufficiently weird locale, this might produce incorrect results?
 * For example, in German I believe "ss" is treated specially --- if we are
 * given "foos" and return "foot", will this actually be greater than "fooss"?
 */
static char *
make_greater_string(const char * str, Oid datatype)
{
	char	   *workstr;
	int			len;

	/* Make a modifiable copy, which will be our return value if successful */
	workstr = pstrdup((char *) str);

	while ((len = strlen(workstr)) > 0)
	{
		unsigned char  *lastchar = (unsigned char *) (workstr + len - 1);

		/*
		 * Try to generate a larger string by incrementing the last byte.
		 */
		while (*lastchar < (unsigned char) 255)
		{
			(*lastchar)++;
			if (string_lessthan(str, workstr, datatype))
				return workstr;			/* Success! */
		}
		/*
		 * Truncate off the last character, which might be more than 1 byte
		 * in MULTIBYTE case.
		 */
#ifdef MULTIBYTE
		len = pg_mbcliplen((const unsigned char *) workstr, len, len-1);
		workstr[len] = '\0';
#else
		*lastchar = '\0';
#endif
	}

	/* Failed... */
	pfree(workstr);
	return NULL;
}

/*
 * Handy subroutines for match_special_index_operator() and friends.
 */

/* See if there is a binary op of the given name for the given datatype */
static Oid
find_operator(const char * opname, Oid datatype)
{
	HeapTuple	optup;

	optup = SearchSysCacheTuple(OPERNAME,
								PointerGetDatum(opname),
								ObjectIdGetDatum(datatype),
								ObjectIdGetDatum(datatype),
								CharGetDatum('b'));
	if (!HeapTupleIsValid(optup))
		return InvalidOid;
	return optup->t_data->t_oid;
}

/*
 * Generate a Datum of the appropriate type from a C string.
 * Note that all of the supported types are pass-by-ref, so the
 * returned value should be pfree'd if no longer needed.
 */
static Datum
string_to_datum(const char * str, Oid datatype)
{
	/* We cheat a little by assuming that textin() will do for
	 * bpchar and varchar constants too...
	 */
	if (datatype == NAMEOID)
		return PointerGetDatum(namein((char *) str));
	else
		return PointerGetDatum(textin((char *) str));
}

/*
 * Generate a Const node of the appropriate type from a C string.
 */
static Const *
string_to_const(const char * str, Oid datatype)
{
	Datum		conval = string_to_datum(str, datatype);

	return makeConst(datatype, ((datatype == NAMEOID) ? NAMEDATALEN : -1),
					 conval, false, false, false, false);
}

/*
 * Test whether two strings are "<" according to the rules of the given
 * datatype.  We do this the hard way, ie, actually calling the type's
 * "<" operator function, to ensure we get the right result...
 */
static bool
string_lessthan(const char * str1, const char * str2, Oid datatype)
{
	Datum		datum1 = string_to_datum(str1, datatype);
	Datum		datum2 = string_to_datum(str2, datatype);
	bool		result;

	switch (datatype)
	{
		case TEXTOID:
			result = text_lt((text *) datum1, (text *) datum2);
			break;

		case BPCHAROID:
			result = bpcharlt((char *) datum1, (char *) datum2);
			break;

		case VARCHAROID:
			result = varcharlt((char *) datum1, (char *) datum2);
			break;

		case NAMEOID:
			result = namelt((NameData *) datum1, (NameData *) datum2);
			break;

		default:
			elog(ERROR, "string_lessthan: unexpected datatype %u", datatype);
			result = false;
			break;
	}

	pfree(DatumGetPointer(datum1));
	pfree(DatumGetPointer(datum2));

	return result;
}