path: root/src/backend/utils/adt/selfuncs.c

/*-------------------------------------------------------------------------
 *
 * selfuncs.c
 *	  Selectivity functions and index cost estimation functions for
 *	  standard operators and index access methods.
 *
 *	  Selectivity routines are registered in the pg_operator catalog
 *	  in the "oprrest" and "oprjoin" attributes.
 *
 *	  Index cost functions are registered in the pg_am catalog
 *	  in the "amcostestimate" attribute.
 *
 * Portions Copyright (c) 1996-2001, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *	  $Header: /cvsroot/pgsql/src/backend/utils/adt/selfuncs.c,v 1.95 2001/07/16 05:06:59 tgl Exp $
 *
 *-------------------------------------------------------------------------
 */

/*----------
 * Operator selectivity estimation functions are called to estimate the
 * selectivity of WHERE clauses whose top-level operator is their operator.
 * We divide the problem into two cases:
 *		Restriction clause estimation: the clause involves vars of just
 *			one relation.
 *		Join clause estimation: the clause involves vars of multiple rels.
 * Join selectivity estimation is far more difficult and usually less accurate
 * than restriction estimation.
 *
 * When dealing with the inner scan of a nestloop join, we consider the
 * join's joinclauses as restriction clauses for the inner relation, and
 * treat vars of the outer relation as parameters (a/k/a constants of unknown
 * values).  So, restriction estimators need to be able to accept an argument
 * telling which relation is to be treated as the variable.
 *
 * The call convention for a restriction estimator (oprrest function) is
 *
 *		Selectivity oprrest (Query *root,
 *							 Oid operator,
 *							 List *args,
 *							 int varRelid);
 *
 * root: general information about the query (rtable and RelOptInfo lists
 * are particularly important for the estimator).
 * operator: OID of the specific operator in question.
 * args: argument list from the operator clause.
 * varRelid: if not zero, the relid (rtable index) of the relation to
 * be treated as the variable relation.  May be zero if the args list
 * is known to contain vars of only one relation.
 *
 * This is represented at the SQL level (in pg_proc) as
 *
 *		float8 oprrest (opaque, oid, opaque, int4);
 *
 * The call convention for a join estimator (oprjoin function) is similar
 * except that varRelid is not needed:
 *
 *		Selectivity oprjoin (Query *root,
 *							 Oid operator,
 *							 List *args);
 *
 *		float8 oprjoin (opaque, oid, opaque);
 *----------
 */

#include "postgres.h"

#include <ctype.h>
#include <math.h>
#ifdef USE_LOCALE
#include <locale.h>
#endif

#include "access/heapam.h"
#include "catalog/catname.h"
#include "catalog/pg_operator.h"
#include "catalog/pg_proc.h"
#include "catalog/pg_statistic.h"
#include "catalog/pg_type.h"
#include "mb/pg_wchar.h"
#include "nodes/makefuncs.h"
#include "optimizer/clauses.h"
#include "optimizer/cost.h"
#include "optimizer/pathnode.h"
#include "optimizer/plancat.h"
#include "optimizer/prep.h"
#include "parser/parse_func.h"
#include "parser/parse_oper.h"
#include "parser/parsetree.h"
#include "utils/builtins.h"
#include "utils/date.h"
#include "utils/int8.h"
#include "utils/lsyscache.h"
#include "utils/selfuncs.h"
#include "utils/syscache.h"

/*
 * Note: the default selectivity estimates are not chosen entirely at random.
 * We want them to be small enough to ensure that indexscans will be used if
 * available, for typical table densities of ~100 tuples/page.  Thus, for
 * example, 0.01 is not quite small enough, since that makes it appear that
 * nearly all pages will be hit anyway.  Also, since we sometimes estimate
 * eqsel as 1/num_distinct, we probably want DEFAULT_NUM_DISTINCT to equal
 * 1/DEFAULT_EQ_SEL.
 */

/* default selectivity estimate for equalities such as "A = b" */
#define DEFAULT_EQ_SEL	0.005

/* default selectivity estimate for inequalities such as "A < b" */
#define DEFAULT_INEQ_SEL  (1.0 / 3.0)

/* default selectivity estimate for pattern-match operators such as LIKE */
#define DEFAULT_MATCH_SEL	0.005

/* default number of distinct values in a table */
#define DEFAULT_NUM_DISTINCT  200

/* default selectivity estimate for boolean and null test nodes */
#define DEFAULT_UNK_SEL			0.005
#define DEFAULT_NOT_UNK_SEL		(1.0 - DEFAULT_UNK_SEL)
#define DEFAULT_BOOL_SEL		0.5

static bool convert_to_scalar(Datum value, Oid valuetypid, double *scaledvalue,
				  Datum lobound, Datum hibound, Oid boundstypid,
				  double *scaledlobound, double *scaledhibound);
static double convert_numeric_to_scalar(Datum value, Oid typid);
static void convert_string_to_scalar(unsigned char *value,
						 double *scaledvalue,
						 unsigned char *lobound,
						 double *scaledlobound,
						 unsigned char *hibound,
						 double *scaledhibound);
static double convert_one_string_to_scalar(unsigned char *value,
							 int rangelo, int rangehi);
static unsigned char *convert_string_datum(Datum value, Oid typid);
static double convert_timevalue_to_scalar(Datum value, Oid typid);
static double get_att_numdistinct(Query *root, Var *var,
								  Form_pg_statistic stats);
static bool get_restriction_var(List *args, int varRelid,
								Var **var, Node **other,
								bool *varonleft);
static void get_join_vars(List *args, Var **var1, Var **var2);
static Selectivity prefix_selectivity(Query *root, Var *var, char *prefix);
static Selectivity pattern_selectivity(char *patt, Pattern_Type ptype);
static bool string_lessthan(const char *str1, const char *str2,
				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);


/*
 *		eqsel			- Selectivity of "=" for any data types.
 *
 * Note: this routine is also used to estimate selectivity for some
 * operators that are not "=" but have comparable selectivity behavior,
 * such as "~=" (geometric approximate-match).	Even for "=", we must
 * keep in mind that the left and right datatypes may differ.
 */
Datum
eqsel(PG_FUNCTION_ARGS)
{
	Query	   *root = (Query *) PG_GETARG_POINTER(0);
	Oid			operator = PG_GETARG_OID(1);
	List	   *args = (List *) PG_GETARG_POINTER(2);
	int			varRelid = PG_GETARG_INT32(3);
	Var		   *var;
	Node	   *other;
	bool		varonleft;
	Oid			relid;
	HeapTuple	statsTuple;
	Datum	   *values;
	int			nvalues;
	float4	   *numbers;
	int			nnumbers;
	double		selec;

	/*
	 * If expression is not var = something or something = var for
	 * a simple var of a real relation (no subqueries, for now),
	 * then punt and return a default estimate.
	 */
	if (!get_restriction_var(args, varRelid,
							 &var, &other, &varonleft))
		PG_RETURN_FLOAT8(DEFAULT_EQ_SEL);
	relid = getrelid(var->varno, root->rtable);
	if (relid == InvalidOid)
		PG_RETURN_FLOAT8(DEFAULT_EQ_SEL);

	/*
	 * If the something is a NULL constant, assume operator is strict
	 * and return zero, ie, operator will never return TRUE.
	 */
	if (IsA(other, Const) && ((Const *) other)->constisnull)
		PG_RETURN_FLOAT8(0.0);

	/* get stats for the attribute, if available */
	statsTuple = SearchSysCache(STATRELATT,
								ObjectIdGetDatum(relid),
								Int16GetDatum(var->varattno),
								0, 0);
	if (HeapTupleIsValid(statsTuple))
	{
		Form_pg_statistic stats;

		stats = (Form_pg_statistic) GETSTRUCT(statsTuple);

		if (IsA(other, Const))
		{
			/* Var is being compared to a known non-null constant */
			Datum	constval = ((Const *) other)->constvalue;
			bool	match = false;
			int		i;

			/*
			 * Is the constant "=" to any of the column's most common
			 * values?  (Although the given operator may not really be
			 * "=", we will assume that seeing whether it returns TRUE
			 * is an appropriate test.  If you don't like this, maybe you
			 * shouldn't be using eqsel for your operator...)
			 */
			if (get_attstatsslot(statsTuple, var->vartype, var->vartypmod,
								 STATISTIC_KIND_MCV, InvalidOid,
								 &values, &nvalues,
								 &numbers, &nnumbers))
			{
				FmgrInfo	eqproc;

				fmgr_info(get_opcode(operator), &eqproc);

				for (i = 0; i < nvalues; i++)
				{
					/* be careful to apply operator right way 'round */
					if (varonleft)
						match = DatumGetBool(FunctionCall2(&eqproc,
														   values[i],
														   constval));
					else
						match = DatumGetBool(FunctionCall2(&eqproc,
														   constval,
														   values[i]));
					if (match)
						break;
				}
			}
			else
			{
				/* no most-common-value info available */
				values = NULL;
				numbers = NULL;
				i = nvalues = nnumbers = 0;
			}

			if (match)
			{
				/*
				 * Constant is "=" to this common value.  We know
				 * selectivity exactly (or as exactly as VACUUM
				 * could calculate it, anyway).
				 */
				selec = numbers[i];
			}
			else
			{
				/*
				 * Comparison is against a constant that is neither
				 * NULL nor any of the common values.  Its selectivity
				 * cannot be more than this:
				 */
				double	sumcommon = 0.0;
				double	otherdistinct;

				for (i = 0; i < nnumbers; i++)
					sumcommon += numbers[i];
				selec = 1.0 - sumcommon - stats->stanullfrac;
				/*
				 * and in fact it's probably a good deal less.
				 * We approximate that all the not-common values
				 * share this remaining fraction equally, so we
				 * divide by the number of other distinct values.
				 */
				otherdistinct = get_att_numdistinct(root, var, stats)
					- nnumbers;
				if (otherdistinct > 1)
					selec /= otherdistinct;
				/*
				 * Another cross-check: selectivity shouldn't be
				 * estimated as more than the least common
				 * "most common value".
				 */
				if (nnumbers > 0 && selec > numbers[nnumbers-1])
					selec = numbers[nnumbers-1];
			}

			free_attstatsslot(var->vartype, values, nvalues,
							  numbers, nnumbers);
		}
		else
		{
			double		ndistinct;

			/*
			 * Search is for a value that we do not know a priori, but
			 * we will assume it is not NULL.  Estimate the selectivity
			 * as non-null fraction divided by number of distinct values,
			 * so that we get a result averaged over all possible values
			 * whether common or uncommon.  (Essentially, we are assuming
			 * that the not-yet-known comparison value is equally likely
			 * to be any of the possible values, regardless of their
			 * frequency in the table.  Is that a good idea?)
			 */
			selec = 1.0 - stats->stanullfrac;
			ndistinct = get_att_numdistinct(root, var, stats);
			if (ndistinct > 1)
				selec /= ndistinct;
			/*
			 * Cross-check: selectivity should never be
			 * estimated as more than the most common value's.
			 */
			if (get_attstatsslot(statsTuple, var->vartype, var->vartypmod,
								 STATISTIC_KIND_MCV, InvalidOid,
								 NULL, NULL,
								 &numbers, &nnumbers))
			{
				if (nnumbers > 0 && selec > numbers[0])
					selec = numbers[0];
				free_attstatsslot(var->vartype, NULL, 0, numbers, nnumbers);
			}
		}

		ReleaseSysCache(statsTuple);
	}
	else
	{
		/*
		 * No VACUUM ANALYZE stats available, so make a guess using
		 * estimated number of distinct values and assuming they are
		 * equally common.  (The guess is unlikely to be very good,
		 * but we do know a few special cases.)
		 */
		selec = 1.0 / get_att_numdistinct(root, var, NULL);
	}

	/* result should be in range, but make sure... */
	if (selec < 0.0)
		selec = 0.0;
	else if (selec > 1.0)
		selec = 1.0;

	PG_RETURN_FLOAT8((float8) selec);
}

/*
 *		neqsel			- Selectivity of "!=" for any data types.
 *
 * This routine is also used for some operators that are not "!="
 * but have comparable selectivity behavior.  See above comments
 * for eqsel().
 */
Datum
neqsel(PG_FUNCTION_ARGS)
{
	Query	   *root = (Query *) PG_GETARG_POINTER(0);
	Oid			operator = PG_GETARG_OID(1);
	List	   *args = (List *) PG_GETARG_POINTER(2);
	int			varRelid = PG_GETARG_INT32(3);
	Oid			eqop;
	float8		result;

	/*
	 * We want 1 - eqsel() where the equality operator is the one
	 * associated with this != operator, that is, its negator.
	 */
	eqop = get_negator(operator);
	if (eqop)
	{
		result = DatumGetFloat8(DirectFunctionCall4(eqsel,
											 PointerGetDatum(root),
											 ObjectIdGetDatum(eqop),
											 PointerGetDatum(args),
											 Int32GetDatum(varRelid)));
	}
	else
	{
		/* Use default selectivity (should we raise an error instead?) */
		result = DEFAULT_EQ_SEL;
	}
	result = 1.0 - result;
	PG_RETURN_FLOAT8(result);
}

/*
 *	scalarineqsel		- Selectivity of "<", "<=", ">", ">=" for scalars.
 *
 * This is the guts of both scalarltsel and scalargtsel.  The caller has
 * commuted the clause, if necessary, so that we can treat the Var as
 * being on the left.
 *
 * This routine works for any datatype (or pair of datatypes) known to
 * convert_to_scalar().  If it is applied to some other datatype,
 * it will return a default estimate.
 */
static double
scalarineqsel(Query *root, Oid operator, bool isgt,
			  Var *var, Node *other)
{
	Oid			relid;
	Datum		constval;
	Oid			consttype;
	HeapTuple	statsTuple;
	Form_pg_statistic stats;
	FmgrInfo	opproc;
	Datum	   *values;
	int			nvalues;
	float4	   *numbers;
	int			nnumbers;
	double		mcv_selec,
				hist_selec,
				sumcommon;
	double		selec;
	int			i;

	/*
	 * If expression is not var op something or something op var for
	 * a simple var of a real relation (no subqueries, for now),
	 * then punt and return a default estimate.
	 */
	relid = getrelid(var->varno, root->rtable);
	if (relid == InvalidOid)
		return DEFAULT_INEQ_SEL;

	/*
	 * Can't do anything useful if the something is not a constant, either.
	 */
	if (! IsA(other, Const))
		return DEFAULT_INEQ_SEL;

	/*
	 * If the constant is NULL, assume operator is strict
	 * and return zero, ie, operator will never return TRUE.
	 */
	if (((Const *) other)->constisnull)
		return 0.0;
	constval = ((Const *) other)->constvalue;
	consttype = ((Const *) other)->consttype;

	/* get stats for the attribute */
	statsTuple = SearchSysCache(STATRELATT,
								ObjectIdGetDatum(relid),
								Int16GetDatum(var->varattno),
								0, 0);
	if (!HeapTupleIsValid(statsTuple))
	{
		/* no stats available, so default result */
		return DEFAULT_INEQ_SEL;
	}
	stats = (Form_pg_statistic) GETSTRUCT(statsTuple);

	fmgr_info(get_opcode(operator), &opproc);

	/*
	 * If we have most-common-values info, add up the fractions of the
	 * MCV entries that satisfy MCV OP CONST.  These fractions contribute
	 * directly to the result selectivity.  Also add up the total fraction
	 * represented by MCV entries.
	 */
	mcv_selec = 0.0;
	sumcommon = 0.0;

	if (get_attstatsslot(statsTuple, var->vartype, var->vartypmod,
						 STATISTIC_KIND_MCV, InvalidOid,
						 &values, &nvalues,
						 &numbers, &nnumbers))
	{
		for (i = 0; i < nvalues; i++)
		{
			if (DatumGetBool(FunctionCall2(&opproc,
										   values[i],
										   constval)))
				mcv_selec += numbers[i];
			sumcommon += numbers[i];
		}
		free_attstatsslot(var->vartype, values, nvalues, numbers, nnumbers);
	}

	/*
	 * If there is a histogram, determine which bin the constant falls in,
	 * and compute the resulting contribution to selectivity.
	 *
	 * Someday, VACUUM might store more than one histogram per rel/att,
	 * corresponding to more than one possible sort ordering defined for
	 * the column type.  However, to make that work we will need to figure
	 * out which staop to search for --- it's not necessarily the one we
	 * have at hand!  (For example, we might have a '<=' operator rather
	 * than the '<' operator that will appear in staop.)  For now, assume
	 * that whatever appears in pg_statistic is sorted the same way our
	 * operator sorts, or the reverse way if isgt is TRUE.
	 */
	hist_selec = 0.0;

	if (get_attstatsslot(statsTuple, var->vartype, var->vartypmod,
						 STATISTIC_KIND_HISTOGRAM, InvalidOid,
						 &values, &nvalues,
						 NULL, NULL))
	{
		if (nvalues > 1)
		{
			double	histfrac;
			bool	ltcmp;

			ltcmp = DatumGetBool(FunctionCall2(&opproc,
											   values[0],
											   constval));
			if (isgt)
				ltcmp = !ltcmp;
			if (!ltcmp)
			{
				/* Constant is below lower histogram boundary. */
				histfrac = 0.0;
			}
			else
			{
				/*
				 * Scan to find proper location.  This could be made faster
				 * by using a binary-search method, but it's probably not
				 * worth the trouble for typical histogram sizes.
				 */
				for (i = 1; i < nvalues; i++)
				{
					ltcmp = DatumGetBool(FunctionCall2(&opproc,
													   values[i],
													   constval));
					if (isgt)
						ltcmp = !ltcmp;
					if (!ltcmp)
						break;
				}
				if (i >= nvalues)
				{
					/* Constant is above upper histogram boundary. */
					histfrac = 1.0;
				}
				else
				{
					double		val,
								high,
								low;
					double		binfrac;

					/*
					 * We have values[i-1] < constant < values[i].
					 *
					 * Convert the constant and the two nearest bin boundary
					 * values to a uniform comparison scale, and do a linear
					 * interpolation within this bin.
					 */
					if (convert_to_scalar(constval, consttype, &val,
										  values[i-1], values[i],
										  var->vartype,
										  &low, &high))
					{
						if (high <= low)
						{
							/* cope if bin boundaries appear identical */
							binfrac = 0.5;
						}
						else if (val <= low)
							binfrac = 0.0;
						else if (val >= high)
							binfrac = 1.0;
						else
							binfrac = (val - low) / (high - low);
					}
					else
					{
						/*
						 * Ideally we'd produce an error here, on the grounds
						 * that the given operator shouldn't have scalarXXsel
						 * registered as its selectivity func unless we can
						 * deal with its operand types.  But currently, all
						 * manner of stuff is invoking scalarXXsel, so give a
						 * default estimate until that can be fixed.
						 */
						binfrac = 0.5;
					}
					/*
					 * Now, compute the overall selectivity across the values
					 * represented by the histogram.  We have i-1 full bins
					 * and binfrac partial bin below the constant.
					 */
					histfrac = (double) (i-1) + binfrac;
					histfrac /= (double) (nvalues - 1);
				}
			}
			/*
			 * Now histfrac = fraction of histogram entries below the constant.
			 *
			 * Account for "<" vs ">"
			 */
			hist_selec = isgt ? (1.0 - histfrac) : histfrac;
			/*
			 * The histogram boundaries are only approximate to begin
			 * with, and may well be out of date anyway.  Therefore,
			 * don't believe extremely small or large selectivity
			 * estimates.
			 */
			if (hist_selec < 0.0001)
				hist_selec = 0.0001;
			else if (hist_selec > 0.9999)
				hist_selec = 0.9999;
		}

		free_attstatsslot(var->vartype, values, nvalues, NULL, 0);
	}

	/*
	 * Now merge the results from the MCV and histogram calculations,
	 * realizing that the histogram covers only the non-null values that
	 * are not listed in MCV.
	 */
	selec = 1.0 - stats->stanullfrac - sumcommon;

	if (hist_selec > 0.0)
		selec *= hist_selec;
	else
	{
		/*
		 * If no histogram but there are values not accounted for by MCV,
		 * arbitrarily assume half of them will match.
		 */
		selec *= 0.5;
	}

	selec += mcv_selec;

	ReleaseSysCache(statsTuple);

	/* result should be in range, but make sure... */
	if (selec < 0.0)
		selec = 0.0;
	else if (selec > 1.0)
		selec = 1.0;

	return selec;
}

/*
 *		scalarltsel		- Selectivity of "<" (also "<=") for scalars.
 */
Datum
scalarltsel(PG_FUNCTION_ARGS)
{
	Query	   *root = (Query *) PG_GETARG_POINTER(0);
	Oid			operator = PG_GETARG_OID(1);
	List	   *args = (List *) PG_GETARG_POINTER(2);
	int			varRelid = PG_GETARG_INT32(3);
	Var		   *var;
	Node	   *other;
	bool		varonleft;
	bool		isgt;
	double		selec;

	/*
	 * If expression is not var op something or something op var for
	 * a simple var of a real relation (no subqueries, for now),
	 * then punt and return a default estimate.
	 */
	if (!get_restriction_var(args, varRelid,
							 &var, &other, &varonleft))
		PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);

	/*
	 * Force the var to be on the left to simplify logic in scalarineqsel.
	 */
	if (varonleft)
	{
		/* we have var < other */
		isgt = false;
	}
	else
	{
		/* we have other < var, commute to make var > other */
		operator = get_commutator(operator);
		if (!operator)
		{
			/* Use default selectivity (should we raise an error instead?) */
			PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
		}
		isgt = true;
	}

	selec = scalarineqsel(root, operator, isgt, var, other);

	PG_RETURN_FLOAT8((float8) selec);
}

/*
 *		scalargtsel		- Selectivity of ">" (also ">=") for integers.
 */
Datum
scalargtsel(PG_FUNCTION_ARGS)
{
	Query	   *root = (Query *) PG_GETARG_POINTER(0);
	Oid			operator = PG_GETARG_OID(1);
	List	   *args = (List *) PG_GETARG_POINTER(2);
	int			varRelid = PG_GETARG_INT32(3);
	Var		   *var;
	Node	   *other;
	bool		varonleft;
	bool		isgt;
	double		selec;

	/*
	 * If expression is not var op something or something op var for
	 * a simple var of a real relation (no subqueries, for now),
	 * then punt and return a default estimate.
	 */
	if (!get_restriction_var(args, varRelid,
							 &var, &other, &varonleft))
		PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);

	/*
	 * Force the var to be on the left to simplify logic in scalarineqsel.
	 */
	if (varonleft)
	{
		/* we have var > other */
		isgt = true;
	}
	else
	{
		/* we have other > var, commute to make var < other */
		operator = get_commutator(operator);
		if (!operator)
		{
			/* Use default selectivity (should we raise an error instead?) */
			PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
		}
		isgt = false;
	}

	selec = scalarineqsel(root, operator, isgt, var, other);

	PG_RETURN_FLOAT8((float8) selec);
}

/*
 * patternsel			- Generic code for pattern-match selectivity.
 */
static double
patternsel(PG_FUNCTION_ARGS, Pattern_Type ptype)
{
	Query	   *root = (Query *) PG_GETARG_POINTER(0);
#ifdef NOT_USED
	Oid			operator = PG_GETARG_OID(1);
#endif
	List	   *args = (List *) PG_GETARG_POINTER(2);
	int			varRelid = PG_GETARG_INT32(3);
	Var		   *var;
	Node	   *other;
	bool		varonleft;
	Oid			relid;
	Datum		constval;
	char	   *patt;
	Pattern_Prefix_Status pstatus;
	char	   *prefix;
	char	   *rest;
	double		result;

	/*
	 * If expression is not var op constant for
	 * a simple var of a real relation (no subqueries, for now),
	 * then punt and return a default estimate.
	 */
	if (!get_restriction_var(args, varRelid,
							 &var, &other, &varonleft))
		return DEFAULT_MATCH_SEL;
	if (!varonleft || !IsA(other, Const))
		return DEFAULT_MATCH_SEL;
	relid = getrelid(var->varno, root->rtable);
	if (relid == InvalidOid)
		return DEFAULT_MATCH_SEL;

	/*
	 * If the constant is NULL, assume operator is strict
	 * and return zero, ie, operator will never return TRUE.
	 */
	if (((Const *) other)->constisnull)
		return 0.0;
	constval = ((Const *) other)->constvalue;
	/* the right-hand const is type text for all supported operators */
	Assert(((Const *) other)->consttype == TEXTOID);
	patt = DatumGetCString(DirectFunctionCall1(textout, constval));

	/* divide pattern into fixed prefix and remainder */
	pstatus = pattern_fixed_prefix(patt, ptype, &prefix, &rest);

	if (pstatus == Pattern_Prefix_Exact)
	{
		/*
		 * Pattern specifies an exact match, so pretend operator is '='
		 */
		Oid			eqopr = find_operator("=", var->vartype);
		Const	   *eqcon;
		List	   *eqargs;

		if (eqopr == InvalidOid)
			elog(ERROR, "patternsel: no = operator for type %u",
				 var->vartype);
		eqcon = string_to_const(prefix, var->vartype);
		eqargs = makeList2(var, eqcon);
		result = DatumGetFloat8(DirectFunctionCall4(eqsel,
													PointerGetDatum(root),
													ObjectIdGetDatum(eqopr),
													PointerGetDatum(eqargs),
													Int32GetDatum(varRelid)));
	}
	else
	{
		/*
		 * Not exact-match pattern.  We estimate selectivity of the
		 * fixed prefix and remainder of pattern separately, then
		 * combine the two.
		 */
		Selectivity prefixsel;
		Selectivity restsel;
		Selectivity selec;

		if (pstatus == Pattern_Prefix_Partial)
			prefixsel = prefix_selectivity(root, var, prefix);
		else
			prefixsel = 1.0;
		restsel = pattern_selectivity(rest, ptype);
		selec = prefixsel * restsel;
		/* result should be in range, but make sure... */
		if (selec < 0.0)
			selec = 0.0;
		else if (selec > 1.0)
			selec = 1.0;
		result = selec;
	}

	if (prefix)
		pfree(prefix);
	pfree(patt);

	return result;
}

/*
 *		regexeqsel		- Selectivity of regular-expression pattern match.
 */
Datum
regexeqsel(PG_FUNCTION_ARGS)
{
	PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Regex));
}

/*
 *		icregexeqsel	- Selectivity of case-insensitive regex match.
 */
Datum
icregexeqsel(PG_FUNCTION_ARGS)
{
	PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Regex_IC));
}

/*
 *		likesel			- Selectivity of LIKE pattern match.
 */
Datum
likesel(PG_FUNCTION_ARGS)
{
	PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Like));
}

/*
 *		iclikesel			- Selectivity of ILIKE pattern match.
 */
Datum
iclikesel(PG_FUNCTION_ARGS)
{
	PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Like_IC));
}

/*
 *		regexnesel		- Selectivity of regular-expression pattern non-match.
 */
Datum
regexnesel(PG_FUNCTION_ARGS)
{
	double		result;

	result = patternsel(fcinfo, Pattern_Type_Regex);
	result = 1.0 - result;
	PG_RETURN_FLOAT8(result);
}

/*
 *		icregexnesel	- Selectivity of case-insensitive regex non-match.
 */
Datum
icregexnesel(PG_FUNCTION_ARGS)
{
	double		result;

	result = patternsel(fcinfo, Pattern_Type_Regex_IC);
	result = 1.0 - result;
	PG_RETURN_FLOAT8(result);
}

/*
 *		nlikesel		- Selectivity of LIKE pattern non-match.
 */
Datum
nlikesel(PG_FUNCTION_ARGS)
{
	double		result;

	result = patternsel(fcinfo, Pattern_Type_Like);
	result = 1.0 - result;
	PG_RETURN_FLOAT8(result);
}

/*
 *		icnlikesel		- Selectivity of ILIKE pattern non-match.
 */
Datum
icnlikesel(PG_FUNCTION_ARGS)
{
	double		result;

	result = patternsel(fcinfo, Pattern_Type_Like_IC);
	result = 1.0 - result;
	PG_RETURN_FLOAT8(result);
}

/*
 *		booltestsel		- Selectivity of BooleanTest Node.
 */
Selectivity
booltestsel(Query *root, BooleanTest *clause, int varRelid)
{
	Var			   *var;
	Node		   *arg;
	Oid				relid;
	HeapTuple		statsTuple;
	Datum		   *values;
	int				nvalues;
	float4		   *numbers;
	int				nnumbers;
	double			selec;

	Assert(clause && IsA(clause, BooleanTest));

	arg = (Node *) clause->arg;

	/*
	 * Ignore any binary-compatible relabeling (probably unnecessary,
	 * but can't hurt)
	 */
	if (IsA(arg, RelabelType))
		arg = ((RelabelType *) arg)->arg;

	if (IsA(arg, Var) && (varRelid == 0 || varRelid == ((Var *) arg)->varno))
		var = (Var *) arg;
	else
	{
		/*
		 * If argument is not a Var, we can't get statistics for it, but
		 * perhaps clause_selectivity can do something with it.  We ignore
		 * the possibility of a NULL value when using clause_selectivity,
		 * and just assume the value is either TRUE or FALSE.
		 */
		switch (clause->booltesttype)
	    {
			case IS_UNKNOWN:
				selec = DEFAULT_UNK_SEL;
				break;
			case IS_NOT_UNKNOWN:
				selec = DEFAULT_NOT_UNK_SEL;
				break;
	        case IS_TRUE:
	        case IS_NOT_FALSE:
				selec = (double) clause_selectivity(root, arg, varRelid);
				break;
	        case IS_FALSE:
	        case IS_NOT_TRUE:
				selec = 1.0 - (double) clause_selectivity(root, arg, varRelid);
				break;
	        default:
	            elog(ERROR, "booltestsel: unexpected booltesttype %d",
	                 (int) clause->booltesttype);
				selec = 0.0;	/* Keep compiler quiet */
				break;
		}
		return (Selectivity) selec;
	}

	/* get stats for the attribute, if available */
	relid = getrelid(var->varno, root->rtable);
	if (relid == InvalidOid)
		statsTuple = NULL;
	else
		statsTuple = SearchSysCache(STATRELATT,
									ObjectIdGetDatum(relid),
									Int16GetDatum(var->varattno),
									0, 0);

	if (HeapTupleIsValid(statsTuple))
	{
		Form_pg_statistic stats;
		double			freq_null;

		stats = (Form_pg_statistic) GETSTRUCT(statsTuple);

		freq_null = stats->stanullfrac;

		if (get_attstatsslot(statsTuple, var->vartype, var->vartypmod,
							 STATISTIC_KIND_MCV, InvalidOid,
							 &values, &nvalues,
							 &numbers, &nnumbers)
			&& nnumbers > 0)
		{
			double			freq_true;
			double			freq_false;

			/*
			 * Get first MCV frequency and derive frequency for true.
			 */
			if (DatumGetBool(values[0]))
				freq_true = numbers[0];
			else
				freq_true = 1.0 - numbers[0] - freq_null;

			/*
			 * Next derive freqency for false.
			 * Then use these as appropriate to derive frequency for each case.
			 */
			freq_false = 1.0 - freq_true - freq_null;

			switch (clause->booltesttype)
		    {
		        case IS_UNKNOWN:
					/* select only NULL values */
					selec = freq_null;
					break;
		        case IS_NOT_UNKNOWN:
					/* select non-NULL values */
					selec = 1.0 - freq_null;
					break;
		        case IS_TRUE:
					/* select only TRUE values */
					selec = freq_true;
					break;
		        case IS_NOT_TRUE:
					/* select non-TRUE values */
					selec = 1.0 - freq_true;
					break;
		        case IS_FALSE:
					/* select only FALSE values */
					selec = freq_false;
					break;
		        case IS_NOT_FALSE:
					/* select non-FALSE values */
					selec = 1.0 - freq_false;
					break;
		        default:
		            elog(ERROR, "booltestsel: unexpected booltesttype %d",
		                 (int) clause->booltesttype);
					selec = 0.0; /* Keep compiler quiet */
					break;
			}

			free_attstatsslot(var->vartype, values, nvalues,
							  numbers, nnumbers);
		}
		else
		{
			/*
			 * No most-common-value info available.
			 * Still have null fraction information,
			 * so use it for IS [NOT] UNKNOWN.
			 * Otherwise adjust for null fraction and
			 * assume an even split for boolean tests.
			 */
			switch (clause->booltesttype)
		    {
		        case IS_UNKNOWN:
					/*
					 * Use freq_null directly.
					 */
					selec = freq_null;
					break;
		        case IS_NOT_UNKNOWN:
					/*
					 * Select not unknown (not null) values.
					 * Calculate from freq_null.
					 */
					selec = 1.0 - freq_null;
					break;
		        case IS_TRUE:
		        case IS_NOT_TRUE:
		        case IS_FALSE:
		        case IS_NOT_FALSE:
					selec = (1.0 - freq_null) / 2.0;
					break;
		        default:
		            elog(ERROR, "booltestsel: unexpected booltesttype %d",
		                 (int) clause->booltesttype);
					selec = 0.0; /* Keep compiler quiet */
					break;
			}
		}

		ReleaseSysCache(statsTuple);
	}
	else
	{
		/*
		 * No VACUUM ANALYZE stats available, so use a default value.
		 * (Note: not much point in recursing to clause_selectivity here.)
		 */
		switch (clause->booltesttype)
		{
			case IS_UNKNOWN:
				selec = DEFAULT_UNK_SEL;
				break;
			case IS_NOT_UNKNOWN:
				selec = DEFAULT_NOT_UNK_SEL;
				break;
			case IS_TRUE:
			case IS_NOT_TRUE:
			case IS_FALSE:
			case IS_NOT_FALSE:
				selec = DEFAULT_BOOL_SEL;
				break;
			default:
				elog(ERROR, "booltestsel: unexpected booltesttype %d",
					 (int) clause->booltesttype);
				selec = 0.0; /* Keep compiler quiet */
				break;
		}
	}

	/* result should be in range, but make sure... */
	if (selec < 0.0)
		selec = 0.0;
	else if (selec > 1.0)
		selec = 1.0;

	return (Selectivity) selec;
}

/*
 *		nulltestsel		- Selectivity of NullTest Node.
 */
Selectivity
nulltestsel(Query *root, NullTest *clause, int varRelid)
{
	Var			   *var;
	Node		   *arg;
	Oid				relid;
	HeapTuple		statsTuple;
	double			selec;
	double			defselec;
	double			freq_null;

	Assert(clause && IsA(clause, NullTest));

	switch (clause->nulltesttype)
    {
        case IS_NULL:
			defselec = DEFAULT_UNK_SEL;
			break;
        case IS_NOT_NULL:
			defselec = DEFAULT_NOT_UNK_SEL;
			break;
        default:
            elog(ERROR, "nulltestsel: unexpected nulltesttype %d",
                 (int) clause->nulltesttype);
            return (Selectivity) 0;  /* keep compiler quiet */
	}

	arg = (Node *) clause->arg;

	/*
	 * Ignore any binary-compatible relabeling
	 */
	if (IsA(arg, RelabelType))
		arg = ((RelabelType *) arg)->arg;

	if (IsA(arg, Var) && (varRelid == 0 || varRelid == ((Var *) arg)->varno))
		var = (Var *) arg;
	else
	{
		/*
		 * punt if non-Var argument
		 */
		return (Selectivity) defselec;
	}

	relid = getrelid(var->varno, root->rtable);
	if (relid == InvalidOid)
			return (Selectivity) defselec;

	/* get stats for the attribute, if available */
	statsTuple = SearchSysCache(STATRELATT,
								ObjectIdGetDatum(relid),
								Int16GetDatum(var->varattno),
								0, 0);
	if (HeapTupleIsValid(statsTuple))
	{
		Form_pg_statistic stats;

		stats = (Form_pg_statistic) GETSTRUCT(statsTuple);
		freq_null = stats->stanullfrac;

		switch (clause->nulltesttype)
	    {
	        case IS_NULL:
				/*
				 * Use freq_null directly.
				 */
				selec = freq_null;
				break;
	        case IS_NOT_NULL:
				/*
				 * Select not unknown (not null) values.
				 * Calculate from freq_null.
				 */
				selec = 1.0 - freq_null;
				break;
	        default:
	            elog(ERROR, "nulltestsel: unexpected nulltesttype %d",
	                 (int) clause->nulltesttype);
				return (Selectivity) 0;  /* keep compiler quiet */
		}

		ReleaseSysCache(statsTuple);
	}
	else
	{
		/*
		 * No VACUUM ANALYZE stats available, so make a guess
		 */
		selec = defselec;
	}

	/* result should be in range, but make sure... */
	if (selec < 0.0)
		selec = 0.0;
	else if (selec > 1.0)
		selec = 1.0;

	return (Selectivity) selec;
}

/*
 *		eqjoinsel		- Join selectivity of "="
 */
Datum
eqjoinsel(PG_FUNCTION_ARGS)
{
	Query	   *root = (Query *) PG_GETARG_POINTER(0);
	Oid			operator = PG_GETARG_OID(1);
	List	   *args = (List *) PG_GETARG_POINTER(2);
	Var		   *var1;
	Var		   *var2;
	double		selec;

	get_join_vars(args, &var1, &var2);

	if (var1 == NULL && var2 == NULL)
		selec = DEFAULT_EQ_SEL;
	else
	{
		HeapTuple	statsTuple1 = NULL;
		HeapTuple	statsTuple2 = NULL;
		Form_pg_statistic stats1 = NULL;
		Form_pg_statistic stats2 = NULL;
		double		nd1 = DEFAULT_NUM_DISTINCT;
		double		nd2 = DEFAULT_NUM_DISTINCT;
		bool		have_mcvs1 = false;
		Datum	   *values1 = NULL;
		int			nvalues1 = 0;
		float4	   *numbers1 = NULL;
		int			nnumbers1 = 0;
		bool		have_mcvs2 = false;
		Datum	   *values2 = NULL;
		int			nvalues2 = 0;
		float4	   *numbers2 = NULL;
		int			nnumbers2 = 0;

		if (var1 != NULL)
		{
			/* get stats for the attribute, if available */
			Oid		relid1 = getrelid(var1->varno, root->rtable);

			if (relid1 != InvalidOid)
			{
				statsTuple1 = SearchSysCache(STATRELATT,
											 ObjectIdGetDatum(relid1),
											 Int16GetDatum(var1->varattno),
											 0, 0);
				if (HeapTupleIsValid(statsTuple1))
				{
					stats1 = (Form_pg_statistic) GETSTRUCT(statsTuple1);
					have_mcvs1 = get_attstatsslot(statsTuple1,
												  var1->vartype,
												  var1->vartypmod,
												  STATISTIC_KIND_MCV,
												  InvalidOid,
												  &values1, &nvalues1,
												  &numbers1, &nnumbers1);
				}

				nd1 = get_att_numdistinct(root, var1, stats1);
			}
		}

		if (var2 != NULL)
		{
			/* get stats for the attribute, if available */
			Oid		relid2 = getrelid(var2->varno, root->rtable);

			if (relid2 != InvalidOid)
			{
				statsTuple2 = SearchSysCache(STATRELATT,
											 ObjectIdGetDatum(relid2),
											 Int16GetDatum(var2->varattno),
											 0, 0);
				if (HeapTupleIsValid(statsTuple2))
				{
					stats2 = (Form_pg_statistic) GETSTRUCT(statsTuple2);
					have_mcvs2 = get_attstatsslot(statsTuple2,
												  var2->vartype,
												  var2->vartypmod,
												  STATISTIC_KIND_MCV,
												  InvalidOid,
												  &values2, &nvalues2,
												  &numbers2, &nnumbers2);
				}

				nd2 = get_att_numdistinct(root, var2, stats2);
			}
		}

		if (have_mcvs1 && have_mcvs2)
		{
			/*
			 * We have most-common-value lists for both relations.  Run
			 * through the lists to see which MCVs actually join to each
			 * other with the given operator.  This allows us to determine
			 * the exact join selectivity for the portion of the relations
			 * represented by the MCV lists.  We still have to estimate for
			 * the remaining population, but in a skewed distribution this
			 * gives us a big leg up in accuracy.  For motivation see the
			 * analysis in Y. Ioannidis and S. Christodoulakis, "On the
			 * propagation of errors in the size of join results", Technical
			 * Report 1018, Computer Science Dept., University of Wisconsin,
			 * Madison, March 1991 (available from ftp.cs.wisc.edu).
			 */
			FmgrInfo	eqproc;
			bool	   *hasmatch1;
			bool	   *hasmatch2;
			double		matchprodfreq,
						matchfreq1,
						matchfreq2,
						unmatchfreq1,
						unmatchfreq2,
						otherfreq1,
						otherfreq2,
						totalsel1,
						totalsel2;
			int			i,
						nmatches;

			fmgr_info(get_opcode(operator), &eqproc);
			hasmatch1 = (bool *) palloc(nvalues1 * sizeof(bool));
			memset(hasmatch1, 0, nvalues1 * sizeof(bool));
			hasmatch2 = (bool *) palloc(nvalues2 * sizeof(bool));
			memset(hasmatch2, 0, nvalues2 * sizeof(bool));
			/*
			 * Note we assume that each MCV will match at most one member of
			 * the other MCV list.  If the operator isn't really equality,
			 * there could be multiple matches --- but we don't look for them,
			 * both for speed and because the math wouldn't add up...
			 */
			matchprodfreq = 0.0;
			nmatches = 0;
			for (i = 0; i < nvalues1; i++)
			{
				int		j;

				for (j = 0; j < nvalues2; j++)
				{
					if (hasmatch2[j])
						continue;
					if (DatumGetBool(FunctionCall2(&eqproc,
												   values1[i],
												   values2[j])))
					{
						hasmatch1[i] = hasmatch2[j] = true;
						matchprodfreq += numbers1[i] * numbers2[j];
						nmatches++;
						break;
					}
				}
			}
			/* Sum up frequencies of matched and unmatched MCVs */
			matchfreq1 = unmatchfreq1 = 0.0;
			for (i = 0; i < nvalues1; i++)
			{
				if (hasmatch1[i])
					matchfreq1 += numbers1[i];
				else
					unmatchfreq1 += numbers1[i];
			}
			matchfreq2 = unmatchfreq2 = 0.0;
			for (i = 0; i < nvalues2; i++)
			{
				if (hasmatch2[i])
					matchfreq2 += numbers2[i];
				else
					unmatchfreq2 += numbers2[i];
			}
			pfree(hasmatch1);
			pfree(hasmatch2);
			/*
			 * Compute total frequency of non-null values that are not in
			 * the MCV lists.
			 */
			otherfreq1 = 1.0 - stats1->stanullfrac - matchfreq1 - unmatchfreq1;
			otherfreq2 = 1.0 - stats2->stanullfrac - matchfreq2 - unmatchfreq2;
			/*
			 * We can estimate the total selectivity from the point of view
			 * of relation 1 as: the known selectivity for matched MCVs, plus
			 * unmatched MCVs that are assumed to match against random members
			 * of relation 2's non-MCV population, plus non-MCV values that
			 * are assumed to match against random members of relation 2's
			 * unmatched MCVs plus non-MCV values.
			 */
			totalsel1 = matchprodfreq;
			if (nd2 > nvalues2)
				totalsel1 += unmatchfreq1 * otherfreq2 / (nd2 - nvalues2);
			if (nd2 > nmatches)
				totalsel1 += otherfreq1 * (otherfreq2 + unmatchfreq2) /
					(nd2 - nmatches);
			/* Same estimate from the point of view of relation 2. */
			totalsel2 = matchprodfreq;
			if (nd1 > nvalues1)
				totalsel2 += unmatchfreq2 * otherfreq1 / (nd1 - nvalues1);
			if (nd1 > nmatches)
				totalsel2 += otherfreq2 * (otherfreq1 + unmatchfreq1) /
					(nd1 - nmatches);
			/*
			 * Use the smaller of the two estimates.  This can be justified
			 * in essentially the same terms as given below for the no-stats
			 * case: to a first approximation, we are estimating from the
			 * point of view of the relation with smaller nd.
			 */
			selec = (totalsel1 < totalsel2) ? totalsel1 : totalsel2;
		}
		else
		{
			/*
			 * We do not have MCV lists for both sides.  Estimate the
			 * join selectivity as MIN(1/nd1, 1/nd2).  This is plausible
			 * if we assume that the values are about equally distributed:
			 * a given tuple of rel1 will join to either 0 or N2/nd2 rows
			 * of rel2, so total join rows are at most N1*N2/nd2 giving
			 * a join selectivity of not more than 1/nd2.  By the same logic
			 * it is not more than 1/nd1, so MIN(1/nd1, 1/nd2) is an upper
			 * bound.  Using the MIN() means we estimate from the point of
			 * view of the relation with smaller nd (since the larger nd is
			 * determining the MIN).  It is reasonable to assume that most
			 * tuples in this rel will have join partners, so the bound is
			 * probably reasonably tight and should be taken as-is.
			 *
			 * XXX Can we be smarter if we have an MCV list for just one side?
			 * It seems that if we assume equal distribution for the other
			 * side, we end up with the same answer anyway.
			 */
			if (nd1 > nd2)
				selec = 1.0 / nd1;
			else
				selec = 1.0 / nd2;
		}

		if (have_mcvs1)
			free_attstatsslot(var1->vartype, values1, nvalues1,
							  numbers1, nnumbers1);
		if (have_mcvs2)
			free_attstatsslot(var2->vartype, values2, nvalues2,
							  numbers2, nnumbers2);
		if (HeapTupleIsValid(statsTuple1))
			ReleaseSysCache(statsTuple1);
		if (HeapTupleIsValid(statsTuple2))
			ReleaseSysCache(statsTuple2);
	}
	PG_RETURN_FLOAT8((float8) selec);
}

/*
 *		neqjoinsel		- Join selectivity of "!="
 */
Datum
neqjoinsel(PG_FUNCTION_ARGS)
{
	Query	   *root = (Query *) PG_GETARG_POINTER(0);
	Oid			operator = PG_GETARG_OID(1);
	List	   *args = (List *) PG_GETARG_POINTER(2);
	Oid			eqop;
	float8		result;

	/*
	 * We want 1 - eqjoinsel() where the equality operator is the one
	 * associated with this != operator, that is, its negator.
	 */
	eqop = get_negator(operator);
	if (eqop)
	{
		result = DatumGetFloat8(DirectFunctionCall3(eqjoinsel,
											 PointerGetDatum(root),
											 ObjectIdGetDatum(eqop),
											 PointerGetDatum(args)));

	}
	else
	{
		/* Use default selectivity (should we raise an error instead?) */
		result = DEFAULT_EQ_SEL;
	}
	result = 1.0 - result;
	PG_RETURN_FLOAT8(result);
}

/*
 *		scalarltjoinsel - Join selectivity of "<" and "<=" for scalars
 */
Datum
scalarltjoinsel(PG_FUNCTION_ARGS)
{
	PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
}

/*
 *		scalargtjoinsel - Join selectivity of ">" and ">=" for scalars
 */
Datum
scalargtjoinsel(PG_FUNCTION_ARGS)
{
	PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
}

/*
 *		regexeqjoinsel	- Join selectivity of regular-expression pattern match.
 */
Datum
regexeqjoinsel(PG_FUNCTION_ARGS)
{
	PG_RETURN_FLOAT8(DEFAULT_MATCH_SEL);
}

/*
 *		icregexeqjoinsel	- Join selectivity of case-insensitive regex match.
 */
Datum
icregexeqjoinsel(PG_FUNCTION_ARGS)
{
	PG_RETURN_FLOAT8(DEFAULT_MATCH_SEL);
}

/*
 *		likejoinsel			- Join selectivity of LIKE pattern match.
 */
Datum
likejoinsel(PG_FUNCTION_ARGS)
{
	PG_RETURN_FLOAT8(DEFAULT_MATCH_SEL);
}

/*
 *		iclikejoinsel			- Join selectivity of ILIKE pattern match.
 */
Datum
iclikejoinsel(PG_FUNCTION_ARGS)
{
	PG_RETURN_FLOAT8(DEFAULT_MATCH_SEL);
}

/*
 *		regexnejoinsel	- Join selectivity of regex non-match.
 */
Datum
regexnejoinsel(PG_FUNCTION_ARGS)
{
	float8		result;

	result = DatumGetFloat8(regexeqjoinsel(fcinfo));
	result = 1.0 - result;
	PG_RETURN_FLOAT8(result);
}

/*
 *		icregexnejoinsel	- Join selectivity of case-insensitive regex non-match.
 */
Datum
icregexnejoinsel(PG_FUNCTION_ARGS)
{
	float8		result;

	result = DatumGetFloat8(icregexeqjoinsel(fcinfo));
	result = 1.0 - result;
	PG_RETURN_FLOAT8(result);
}

/*
 *		nlikejoinsel		- Join selectivity of LIKE pattern non-match.
 */
Datum
nlikejoinsel(PG_FUNCTION_ARGS)
{
	float8		result;

	result = DatumGetFloat8(likejoinsel(fcinfo));
	result = 1.0 - result;
	PG_RETURN_FLOAT8(result);
}

/*
 *		icnlikejoinsel		- Join selectivity of ILIKE pattern non-match.
 */
Datum
icnlikejoinsel(PG_FUNCTION_ARGS)
{
	float8		result;

	result = DatumGetFloat8(iclikejoinsel(fcinfo));
	result = 1.0 - result;
	PG_RETURN_FLOAT8(result);
}


/*
 * convert_to_scalar
 *	  Convert non-NULL values of the indicated types to the comparison
 *	  scale needed by scalarltsel()/scalargtsel().
 *	  Returns "true" if successful.
 *
 * XXX this routine is a hack: ideally we should look up the conversion
 * subroutines in pg_type.
 *
 * All numeric datatypes are simply converted to their equivalent
 * "double" values.  XXX what about NUMERIC values that are outside
 * the range of "double"?
 *
 * String datatypes are converted by convert_string_to_scalar(),
 * which is explained below.  The reason why this routine deals with
 * three values at a time, not just one, is that we need it for strings.
 *
 * The several datatypes representing absolute times are all converted
 * to Timestamp, which is actually a double, and then we just use that
 * double value.  Note this will give bad results for the various "special"
 * values of Timestamp --- what can we do with those?
 *
 * The several datatypes representing relative times (intervals) are all
 * converted to measurements expressed in seconds.
 */
static bool
convert_to_scalar(Datum value, Oid valuetypid, double *scaledvalue,
				  Datum lobound, Datum hibound, Oid boundstypid,
				  double *scaledlobound, double *scaledhibound)
{
	switch (valuetypid)
	{
		/*
		 * Built-in numeric types
		 */
		case BOOLOID:
		case INT2OID:
		case INT4OID:
		case INT8OID:
		case FLOAT4OID:
		case FLOAT8OID:
		case NUMERICOID:
		case OIDOID:
		case REGPROCOID:
			*scaledvalue = convert_numeric_to_scalar(value, valuetypid);
			*scaledlobound = convert_numeric_to_scalar(lobound, boundstypid);
			*scaledhibound = convert_numeric_to_scalar(hibound, boundstypid);
			return true;

		/*
		 * Built-in string types
		 */
		case CHAROID:
		case BPCHAROID:
		case VARCHAROID:
		case TEXTOID:
		case NAMEOID:
			{
				unsigned char *valstr = convert_string_datum(value, valuetypid);
				unsigned char *lostr = convert_string_datum(lobound, boundstypid);
				unsigned char *histr = convert_string_datum(hibound, boundstypid);

				convert_string_to_scalar(valstr, scaledvalue,
										 lostr, scaledlobound,
										 histr, scaledhibound);
				pfree(valstr);
				pfree(lostr);
				pfree(histr);
				return true;
			}

		/*
		 * Built-in time types
		 */
		case TIMESTAMPOID:
		case ABSTIMEOID:
		case DATEOID:
		case INTERVALOID:
		case RELTIMEOID:
		case TINTERVALOID:
		case TIMEOID:
		case TIMETZOID:
			*scaledvalue = convert_timevalue_to_scalar(value, valuetypid);
			*scaledlobound = convert_timevalue_to_scalar(lobound, boundstypid);
			*scaledhibound = convert_timevalue_to_scalar(hibound, boundstypid);
			return true;

		/*
		 * Built-in network types
		 */
		case INETOID:
		case CIDROID:
		case MACADDROID:
			*scaledvalue = convert_network_to_scalar(value, valuetypid);
			*scaledlobound = convert_network_to_scalar(lobound, boundstypid);
			*scaledhibound = convert_network_to_scalar(hibound, boundstypid);
			return true;
	}
	/* Don't know how to convert */
	return false;
}

/*
 * Do convert_to_scalar()'s work for any numeric data type.
 */
static double
convert_numeric_to_scalar(Datum value, Oid typid)
{
	switch (typid)
	{
		case BOOLOID:
			return (double) DatumGetBool(value);
		case INT2OID:
			return (double) DatumGetInt16(value);
		case INT4OID:
			return (double) DatumGetInt32(value);
		case INT8OID:
			return (double) DatumGetInt64(value);
		case FLOAT4OID:
			return (double) DatumGetFloat4(value);
		case FLOAT8OID:
			return (double) DatumGetFloat8(value);
		case NUMERICOID:
			return (double) DatumGetFloat8(DirectFunctionCall1(numeric_float8,
															   value));
		case OIDOID:
		case REGPROCOID:
			/* we can treat OIDs as integers... */
			return (double) DatumGetObjectId(value);
	}

	/*
	 * Can't get here unless someone tries to use scalarltsel/scalargtsel
	 * on an operator with one numeric and one non-numeric operand.
	 */
	elog(ERROR, "convert_numeric_to_scalar: unsupported type %u", typid);
	return 0;
}

/*
 * Do convert_to_scalar()'s work for any character-string data type.
 *
 * String datatypes are converted to a scale that ranges from 0 to 1,
 * where we visualize the bytes of the string as fractional digits.
 *
 * We do not want the base to be 256, however, since that tends to
 * generate inflated selectivity estimates; few databases will have
 * occurrences of all 256 possible byte values at each position.
 * Instead, use the smallest and largest byte values seen in the bounds
 * as the estimated range for each byte, after some fudging to deal with
 * the fact that we probably aren't going to see the full range that way.
 *
 * An additional refinement is that we discard any common prefix of the
 * three strings before computing the scaled values.  This allows us to
 * "zoom in" when we encounter a narrow data range.  An example is a phone
 * number database where all the values begin with the same area code.
 * (Actually, the bounds will be adjacent histogram-bin-boundary values,
 * so this is more likely to happen than you might think.)
 */
static void
convert_string_to_scalar(unsigned char *value,
						 double *scaledvalue,
						 unsigned char *lobound,
						 double *scaledlobound,
						 unsigned char *hibound,
						 double *scaledhibound)
{
	int			rangelo,
				rangehi;
	unsigned char *sptr;

	rangelo = rangehi = hibound[0];
	for (sptr = lobound; *sptr; sptr++)
	{
		if (rangelo > *sptr)
			rangelo = *sptr;
		if (rangehi < *sptr)
			rangehi = *sptr;
	}
	for (sptr = hibound; *sptr; sptr++)
	{
		if (rangelo > *sptr)
			rangelo = *sptr;
		if (rangehi < *sptr)
			rangehi = *sptr;
	}
	/* If range includes any upper-case ASCII chars, make it include all */
	if (rangelo <= 'Z' && rangehi >= 'A')
	{
		if (rangelo > 'A')
			rangelo = 'A';
		if (rangehi < 'Z')
			rangehi = 'Z';
	}
	/* Ditto lower-case */
	if (rangelo <= 'z' && rangehi >= 'a')
	{
		if (rangelo > 'a')
			rangelo = 'a';
		if (rangehi < 'z')
			rangehi = 'z';
	}
	/* Ditto digits */
	if (rangelo <= '9' && rangehi >= '0')
	{
		if (rangelo > '0')
			rangelo = '0';
		if (rangehi < '9')
			rangehi = '9';
	}

	/*
	 * If range includes less than 10 chars, assume we have not got enough
	 * data, and make it include regular ASCII set.
	 */
	if (rangehi - rangelo < 9)
	{
		rangelo = ' ';
		rangehi = 127;
	}

	/*
	 * Now strip any common prefix of the three strings.
	 */
	while (*lobound)
	{
		if (*lobound != *hibound || *lobound != *value)
			break;
		lobound++, hibound++, value++;
	}

	/*
	 * Now we can do the conversions.
	 */
	*scaledvalue = convert_one_string_to_scalar(value, rangelo, rangehi);
	*scaledlobound = convert_one_string_to_scalar(lobound, rangelo, rangehi);
	*scaledhibound = convert_one_string_to_scalar(hibound, rangelo, rangehi);
}

static double
convert_one_string_to_scalar(unsigned char *value, int rangelo, int rangehi)
{
	int			slen = strlen((char *) value);
	double		num,
				denom,
				base;

	if (slen <= 0)
		return 0.0;				/* empty string has scalar value 0 */

	/*
	 * Since base is at least 10, need not consider more than about 20
	 * chars
	 */
	if (slen > 20)
		slen = 20;

	/* Convert initial characters to fraction */
	base = rangehi - rangelo + 1;
	num = 0.0;
	denom = base;
	while (slen-- > 0)
	{
		int			ch = *value++;

		if (ch < rangelo)
			ch = rangelo - 1;
		else if (ch > rangehi)
			ch = rangehi + 1;
		num += ((double) (ch - rangelo)) / denom;
		denom *= base;
	}

	return num;
}

/*
 * Convert a string-type Datum into a palloc'd, null-terminated string.
 *
 * If USE_LOCALE is defined, we must pass the string through strxfrm()
 * before continuing, so as to generate correct locale-specific results.
 */
static unsigned char *
convert_string_datum(Datum value, Oid typid)
{
	char	   *val;

#ifdef USE_LOCALE
	char	   *xfrmstr;
	size_t		xfrmsize;
	size_t		xfrmlen;

#endif

	switch (typid)
	{
		case CHAROID:
			val = (char *) palloc(2);
			val[0] = DatumGetChar(value);
			val[1] = '\0';
			break;
		case BPCHAROID:
		case VARCHAROID:
		case TEXTOID:
			{
				char	   *str = (char *) VARDATA(DatumGetPointer(value));
				int			strlength = VARSIZE(DatumGetPointer(value)) - VARHDRSZ;

				val = (char *) palloc(strlength + 1);
				memcpy(val, str, strlength);
				val[strlength] = '\0';
				break;
			}
		case NAMEOID:
			{
				NameData   *nm = (NameData *) DatumGetPointer(value);

				val = pstrdup(NameStr(*nm));
				break;
			}
		default:

			/*
			 * Can't get here unless someone tries to use scalarltsel on
			 * an operator with one string and one non-string operand.
			 */
			elog(ERROR, "convert_string_datum: unsupported type %u", typid);
			return NULL;
	}

#ifdef USE_LOCALE
	/* Guess that transformed string is not much bigger than original */
	xfrmsize = strlen(val) + 32;/* arbitrary pad value here... */
	xfrmstr = (char *) palloc(xfrmsize);
	xfrmlen = strxfrm(xfrmstr, val, xfrmsize);
	if (xfrmlen >= xfrmsize)
	{
		/* Oops, didn't make it */
		pfree(xfrmstr);
		xfrmstr = (char *) palloc(xfrmlen + 1);
		xfrmlen = strxfrm(xfrmstr, val, xfrmlen + 1);
	}
	pfree(val);
	val = xfrmstr;
#endif

	return (unsigned char *) val;
}

/*
 * Do convert_to_scalar()'s work for any timevalue data type.
 */
static double
convert_timevalue_to_scalar(Datum value, Oid typid)
{
	switch (typid)
	{
		case TIMESTAMPOID:
			return DatumGetTimestamp(value);
		case ABSTIMEOID:
			return DatumGetTimestamp(DirectFunctionCall1(abstime_timestamp,
														 value));
		case DATEOID:
			return DatumGetTimestamp(DirectFunctionCall1(date_timestamp,
														 value));
		case INTERVALOID:
			{
				Interval   *interval = DatumGetIntervalP(value);

				/*
				 * Convert the month part of Interval to days using
				 * assumed average month length of 365.25/12.0 days.  Not
				 * too accurate, but plenty good enough for our purposes.
				 */
				return interval->time +
					interval->month * (365.25 / 12.0 * 24.0 * 60.0 * 60.0);
			}
		case RELTIMEOID:
			return DatumGetRelativeTime(value);
		case TINTERVALOID:
			{
				TimeInterval interval = DatumGetTimeInterval(value);

				if (interval->status != 0)
					return interval->data[1] - interval->data[0];
				return 0;		/* for lack of a better idea */
			}
		case TIMEOID:
			return DatumGetTimeADT(value);
		case TIMETZOID:
			{
				TimeTzADT  *timetz = DatumGetTimeTzADTP(value);

				/* use GMT-equivalent time */
				return (double) (timetz->time + timetz->zone);
			}
	}

	/*
	 * Can't get here unless someone tries to use scalarltsel/scalargtsel
	 * on an operator with one timevalue and one non-timevalue operand.
	 */
	elog(ERROR, "convert_timevalue_to_scalar: unsupported type %u", typid);
	return 0;
}


/*
 * get_att_numdistinct
 *	  Estimate the number of distinct values of an attribute.
 *
 * var: identifies the attribute to examine.
 * stats: pg_statistic tuple for attribute, or NULL if not available.
 */
static double
get_att_numdistinct(Query *root, Var *var, Form_pg_statistic stats)
{
	RelOptInfo *rel;
	double		ntuples;

	/*
	 * Special-case boolean columns: presumably, two distinct values.
	 *
	 * Are there any other cases we should wire in special estimates for?
	 */
	if (var->vartype == BOOLOID)
		return 2.0;

	/*
	 * Otherwise we need to get the relation size.
	 */
	rel = find_base_rel(root, var->varno);
	ntuples = rel->tuples;

	if (ntuples <= 0.0)
		return DEFAULT_NUM_DISTINCT; /* no data available; return a default */

	/*
	 * Look to see if there is a unique index on the attribute.
	 * If so, we assume it's distinct, ignoring pg_statistic info
	 * which could be out of date.
	 */
	if (has_unique_index(rel, var->varattno))
		return ntuples;

	/*
	 * If ANALYZE determined a fixed or scaled estimate, use it.
	 */
	if (stats)
	{
		if (stats->stadistinct > 0.0)
			return stats->stadistinct;
		if (stats->stadistinct < 0.0)
			return - stats->stadistinct * ntuples;
	}

	/*
	 * ANALYZE does not compute stats for system attributes,
	 * but some of them can reasonably be assumed unique anyway.
	 */
	switch (var->varattno)
	{
		case ObjectIdAttributeNumber:
		case SelfItemPointerAttributeNumber:
			return ntuples;
		case TableOidAttributeNumber:
			return 1.0;
	}

	/*
	 * Estimate ndistinct = ntuples if the table is small, else use default.
	 */
	if (ntuples < DEFAULT_NUM_DISTINCT)
		return ntuples;

	return DEFAULT_NUM_DISTINCT;
}

/*
 * get_restriction_var
 *		Examine the args of a restriction clause to see if it's of the
 *		form (var op something) or (something op var).  If so, extract
 *		and return the var and the other argument.
 *
 * Inputs:
 *	args: clause argument list
 *	varRelid: see specs for restriction selectivity functions
 *
 * Outputs: (these are set only if TRUE is returned)
 *	*var: gets Var node
 *	*other: gets other clause argument
 *	*varonleft: set TRUE if var is on the left, FALSE if on the right
 *
 * Returns TRUE if a Var is identified, otherwise FALSE.
 */
static bool
get_restriction_var(List *args,
					int varRelid,
					Var **var,
					Node **other,
					bool *varonleft)
{
	Node	   *left,
			   *right;

	if (length(args) != 2)
		return false;

	left = (Node *) lfirst(args);
	right = (Node *) lsecond(args);

	/* Ignore any binary-compatible relabeling */

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

	/* Look for the var */

	if (IsA(left, Var) &&
		(varRelid == 0 || varRelid == ((Var *) left)->varno))
	{
		*var = (Var *) left;
		*other = right;
		*varonleft = true;
	}
	else if (IsA(right, Var) &&
			 (varRelid == 0 || varRelid == ((Var *) right)->varno))
	{
		*var = (Var *) right;
		*other = left;
		*varonleft = false;
	}
	else
	{
		/* Duh, it's too complicated for me... */
		return false;
	}

	return true;
}

/*
 * get_join_vars
 *
 * Extract the two Vars from a join clause's argument list.  Returns
 * NULL for arguments that are not simple vars.
 */
static void
get_join_vars(List *args, Var **var1, Var **var2)
{
	Node	   *left,
			   *right;

	if (length(args) != 2)
	{
		*var1 = NULL;
		*var2 = NULL;
		return;
	}

	left = (Node *) lfirst(args);
	right = (Node *) lsecond(args);

	/* Ignore any binary-compatible relabeling */
	if (IsA(left, RelabelType))
		left = ((RelabelType *) left)->arg;
	if (IsA(right, RelabelType))
		right = ((RelabelType *) right)->arg;

	if (IsA(left, Var))
		*var1 = (Var *) left;
	else
		*var1 = NULL;

	if (IsA(right, Var))
		*var2 = (Var *) right;
	else
		*var2 = NULL;
}

/*-------------------------------------------------------------------------
 *
 * Pattern analysis functions
 *
 * These routines support analysis of LIKE and regular-expression patterns
 * by the planner/optimizer.  It's important that they agree with the
 * regular-expression code in backend/regex/ and the LIKE code in
 * backend/utils/adt/like.c.
 *
 * Note that the prefix-analysis functions are called from
 * backend/optimizer/path/indxpath.c as well as from routines in this file.
 *
 *-------------------------------------------------------------------------
 */

/*
 * Extract the fixed prefix, if any, for a pattern.
 * *prefix is set to a palloc'd prefix string,
 * or to NULL if no fixed prefix exists for the pattern.
 * *rest is set to point to the remainder of the pattern after the
 * portion describing the fixed prefix.
 * The return value distinguishes no fixed prefix, a partial prefix,
 * or an exact-match-only pattern.
 */

static Pattern_Prefix_Status
like_fixed_prefix(char *patt, bool case_insensitive,
				  char **prefix, char **rest)
{
	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;
		}

		/*
		 * XXX I suspect isalpha() is not an adequately locale-sensitive
		 * test for characters that can vary under case folding?
		 */
		if (case_insensitive && isalpha((unsigned char) patt[pos]))
			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';
	*rest = &patt[pos];

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

	if (match_pos > 0)
		return Pattern_Prefix_Partial;

	pfree(match);
	*prefix = NULL;
	return Pattern_Prefix_None;
}

static Pattern_Prefix_Status
regex_fixed_prefix(char *patt, bool case_insensitive,
				   char **prefix, char **rest)
{
	char	   *match;
	int			pos,
				match_pos,
				paren_depth;

	/* Pattern must be anchored left */
	if (patt[0] != '^')
	{
		*prefix = NULL;
		*rest = patt;
		return Pattern_Prefix_None;
	}

	/*
	 * If unquoted | is present at paren level 0 in pattern, then there
	 * are multiple alternatives for the start of the string.
	 */
	paren_depth = 0;
	for (pos = 1; patt[pos]; pos++)
	{
		if (patt[pos] == '|' && paren_depth == 0)
		{
			*prefix = NULL;
			*rest = patt;
			return Pattern_Prefix_None;
		}
		else if (patt[pos] == '(')
			paren_depth++;
		else if (patt[pos] == ')' && paren_depth > 0)
			paren_depth--;
		else if (patt[pos] == '\\')
		{
			/* backslash quotes the next character */
			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++)
	{

		/*
		 * Check for characters that indicate multiple possible matches
		 * here. XXX I suspect isalpha() is not an adequately
		 * locale-sensitive test for characters that can vary under case
		 * folding?
		 */
		if (patt[pos] == '.' ||
			patt[pos] == '(' ||
			patt[pos] == '[' ||
			patt[pos] == '$' ||
			(case_insensitive && isalpha((unsigned char) patt[pos])))
			break;

		/*
		 * Check for quantifiers.  Except for +, this means the preceding
		 * character is optional, so we must remove it from the prefix
		 * too!
		 */
		if (patt[pos] == '*' ||
			patt[pos] == '?' ||
			patt[pos] == '{')
		{
			if (match_pos > 0)
				match_pos--;
			pos--;
			break;
		}
		if (patt[pos] == '+')
		{
			pos--;
			break;
		}
		if (patt[pos] == '\\')
		{
			/* backslash quotes the next character */
			pos++;
			if (patt[pos] == '\0')
				break;
		}
		match[match_pos++] = patt[pos];
	}

	match[match_pos] = '\0';
	*rest = &patt[pos];

	if (patt[pos] == '$' && patt[pos + 1] == '\0')
	{
		*rest = &patt[pos + 1];
		return Pattern_Prefix_Exact;	/* pattern specifies exact match */
	}

	if (match_pos > 0)
		return Pattern_Prefix_Partial;

	pfree(match);
	*prefix = NULL;
	return Pattern_Prefix_None;
}

Pattern_Prefix_Status
pattern_fixed_prefix(char *patt, Pattern_Type ptype,
					 char **prefix, char **rest)
{
	Pattern_Prefix_Status result;

	switch (ptype)
	{
		case Pattern_Type_Like:
			result = like_fixed_prefix(patt, false, prefix, rest);
			break;
		case Pattern_Type_Like_IC:
			result = like_fixed_prefix(patt, true, prefix, rest);
			break;
		case Pattern_Type_Regex:
			result = regex_fixed_prefix(patt, false, prefix, rest);
			break;
		case Pattern_Type_Regex_IC:
			result = regex_fixed_prefix(patt, true, prefix, rest);
			break;
		default:
			elog(ERROR, "pattern_fixed_prefix: bogus ptype");
			result = Pattern_Prefix_None;		/* keep compiler quiet */
			break;
	}
	return result;
}

/*
 * Estimate the selectivity of a fixed prefix for a pattern match.
 *
 * A fixed prefix "foo" is estimated as the selectivity of the expression
 * "var >= 'foo' AND var < 'fop'" (see also indxqual.c).
 *
 * XXX Note: we make use of the upper bound to estimate operator selectivity
 * even if the locale is such that we cannot rely on the upper-bound string.
 * The selectivity only needs to be approximately right anyway, so it seems
 * more useful to use the upper-bound code than not.
 */
static Selectivity
prefix_selectivity(Query *root, Var *var, char *prefix)
{
	Selectivity prefixsel;
	Oid			cmpopr;
	Const	   *prefixcon;
	List	   *cmpargs;
	char	   *greaterstr;

	cmpopr = find_operator(">=", var->vartype);
	if (cmpopr == InvalidOid)
		elog(ERROR, "prefix_selectivity: no >= operator for type %u",
			 var->vartype);
	prefixcon = string_to_const(prefix, var->vartype);
	cmpargs = makeList2(var, prefixcon);
	/* Assume scalargtsel is appropriate for all supported types */
	prefixsel = DatumGetFloat8(DirectFunctionCall4(scalargtsel,
												   PointerGetDatum(root),
												   ObjectIdGetDatum(cmpopr),
												   PointerGetDatum(cmpargs),
												   Int32GetDatum(0)));

	/*-------
	 * If we can create a string larger than the prefix, say
	 *	"x < greaterstr".
	 *-------
	 */
	greaterstr = make_greater_string(prefix, var->vartype);
	if (greaterstr)
	{
		Selectivity topsel;

		cmpopr = find_operator("<", var->vartype);
		if (cmpopr == InvalidOid)
			elog(ERROR, "prefix_selectivity: no < operator for type %u",
				 var->vartype);
		prefixcon = string_to_const(greaterstr, var->vartype);
		cmpargs = makeList2(var, prefixcon);
		/* Assume scalarltsel is appropriate for all supported types */
		topsel = DatumGetFloat8(DirectFunctionCall4(scalarltsel,
													PointerGetDatum(root),
													ObjectIdGetDatum(cmpopr),
													PointerGetDatum(cmpargs),
													Int32GetDatum(0)));

		/*
		 * Merge the two selectivities in the same way as for a range
		 * query (see clauselist_selectivity()).
		 */
		prefixsel = topsel + prefixsel - 1.0;

		/*
		 * A zero or slightly negative prefixsel should be converted into
		 * a small positive value; we probably are dealing with a very
		 * tight range and got a bogus result due to roundoff errors.
		 * However, if prefixsel is very negative, then we probably have
		 * default selectivity estimates on one or both sides of the
		 * range.  In that case, insert a not-so-wildly-optimistic default
		 * estimate.
		 */
		if (prefixsel <= 0.0)
		{
			if (prefixsel < -0.01)
			{

				/*
				 * No data available --- use a default estimate that is
				 * small, but not real small.
				 */
				prefixsel = 0.005;
			}
			else
			{

				/*
				 * It's just roundoff error; use a small positive value
				 */
				prefixsel = 1.0e-10;
			}
		}
	}

	return prefixsel;
}


/*
 * Estimate the selectivity of a pattern of the specified type.
 * Note that any fixed prefix of the pattern will have been removed already.
 *
 * For now, we use a very simplistic approach: fixed characters reduce the
 * selectivity a good deal, character ranges reduce it a little,
 * wildcards (such as % for LIKE or .* for regex) increase it.
 */

#define FIXED_CHAR_SEL	0.04	/* about 1/25 */
#define CHAR_RANGE_SEL	0.25
#define ANY_CHAR_SEL	0.9		/* not 1, since it won't match
								 * end-of-string */
#define FULL_WILDCARD_SEL 5.0
#define PARTIAL_WILDCARD_SEL 2.0

static Selectivity
like_selectivity(char *patt, bool case_insensitive)
{
	Selectivity sel = 1.0;
	int			pos;

	/* Skip any leading %; it's already factored into initial sel */
	pos = (*patt == '%') ? 1 : 0;
	for (; patt[pos]; pos++)
	{
		/* % and _ are wildcard characters in LIKE */
		if (patt[pos] == '%')
			sel *= FULL_WILDCARD_SEL;
		else if (patt[pos] == '_')
			sel *= ANY_CHAR_SEL;
		else if (patt[pos] == '\\')
		{
			/* Backslash quotes the next character */
			pos++;
			if (patt[pos] == '\0')
				break;
			sel *= FIXED_CHAR_SEL;
		}
		else
			sel *= FIXED_CHAR_SEL;
	}
	/* Could get sel > 1 if multiple wildcards */
	if (sel > 1.0)
		sel = 1.0;
	return sel;
}

static Selectivity
regex_selectivity_sub(char *patt, int pattlen, bool case_insensitive)
{
	Selectivity sel = 1.0;
	int			paren_depth = 0;
	int			paren_pos = 0;	/* dummy init to keep compiler quiet */
	int			pos;

	for (pos = 0; pos < pattlen; pos++)
	{
		if (patt[pos] == '(')
		{
			if (paren_depth == 0)
				paren_pos = pos;/* remember start of parenthesized item */
			paren_depth++;
		}
		else if (patt[pos] == ')' && paren_depth > 0)
		{
			paren_depth--;
			if (paren_depth == 0)
				sel *= regex_selectivity_sub(patt + (paren_pos + 1),
											 pos - (paren_pos + 1),
											 case_insensitive);
		}
		else if (patt[pos] == '|' && paren_depth == 0)
		{

			/*
			 * If unquoted | is present at paren level 0 in pattern, we
			 * have multiple alternatives; sum their probabilities.
			 */
			sel += regex_selectivity_sub(patt + (pos + 1),
										 pattlen - (pos + 1),
										 case_insensitive);
			break;				/* rest of pattern is now processed */
		}
		else if (patt[pos] == '[')
		{
			bool		negclass = false;

			if (patt[++pos] == '^')
			{
				negclass = true;
				pos++;
			}
			if (patt[pos] == ']')		/* ']' at start of class is not
										 * special */
				pos++;
			while (pos < pattlen && patt[pos] != ']')
				pos++;
			if (paren_depth == 0)
				sel *= (negclass ? (1.0 - CHAR_RANGE_SEL) : CHAR_RANGE_SEL);
		}
		else if (patt[pos] == '.')
		{
			if (paren_depth == 0)
				sel *= ANY_CHAR_SEL;
		}
		else if (patt[pos] == '*' ||
				 patt[pos] == '?' ||
				 patt[pos] == '+')
		{
			/* Ought to be smarter about quantifiers... */
			if (paren_depth == 0)
				sel *= PARTIAL_WILDCARD_SEL;
		}
		else if (patt[pos] == '{')
		{
			while (pos < pattlen && patt[pos] != '}')
				pos++;
			if (paren_depth == 0)
				sel *= PARTIAL_WILDCARD_SEL;
		}
		else if (patt[pos] == '\\')
		{
			/* backslash quotes the next character */
			pos++;
			if (pos >= pattlen)
				break;
			if (paren_depth == 0)
				sel *= FIXED_CHAR_SEL;
		}
		else
		{
			if (paren_depth == 0)
				sel *= FIXED_CHAR_SEL;
		}
	}
	/* Could get sel > 1 if multiple wildcards */
	if (sel > 1.0)
		sel = 1.0;
	return sel;
}

static Selectivity
regex_selectivity(char *patt, bool case_insensitive)
{
	Selectivity sel;
	int			pattlen = strlen(patt);

	/* If patt doesn't end with $, consider it to have a trailing wildcard */
	if (pattlen > 0 && patt[pattlen - 1] == '$' &&
		(pattlen == 1 || patt[pattlen - 2] != '\\'))
	{
		/* has trailing $ */
		sel = regex_selectivity_sub(patt, pattlen - 1, case_insensitive);
	}
	else
	{
		/* no trailing $ */
		sel = regex_selectivity_sub(patt, pattlen, case_insensitive);
		sel *= FULL_WILDCARD_SEL;
		if (sel > 1.0)
			sel = 1.0;
	}
	return sel;
}

static Selectivity
pattern_selectivity(char *patt, Pattern_Type ptype)
{
	Selectivity result;

	switch (ptype)
	{
		case Pattern_Type_Like:
			result = like_selectivity(patt, false);
			break;
		case Pattern_Type_Like_IC:
			result = like_selectivity(patt, true);
			break;
		case Pattern_Type_Regex:
			result = regex_selectivity(patt, false);
			break;
		case Pattern_Type_Regex_IC:
			result = regex_selectivity(patt, true);
			break;
		default:
			elog(ERROR, "pattern_selectivity: bogus ptype");
			result = 1.0;		/* keep compiler quiet */
			break;
	}
	return result;
}

/*
 * Test whether the database's LOCALE setting is safe for LIKE/regexp index
 * optimization.  The key requirement here is that given a prefix string,
 * say "foo", we must be able to generate another string "fop" that is
 * greater than all strings "foobar" starting with "foo".  Unfortunately,
 * many non-C locales have bizarre collation rules in which "fop" > "foo"
 * is not sufficient to ensure "fop" > "foobar".  Until we can come up
 * with a more bulletproof way of generating the upper-bound string,
 * disable the optimization in locales where it is not known to be safe.
 */
bool
locale_is_like_safe(void)
{
#ifdef USE_LOCALE
	/* Cache result so we only have to compute it once */
	static int	result = -1;
	char	   *localeptr;

	if (result >= 0)
		return (bool) result;
	localeptr = setlocale(LC_COLLATE, NULL);
	if (!localeptr)
		elog(STOP, "Invalid LC_COLLATE setting");

	/*
	 * Currently we accept only "C" and "POSIX" (do any systems still
	 * return "POSIX"?).  Which other locales allow safe optimization?
	 */
	if (strcmp(localeptr, "C") == 0)
		result = true;
	else if (strcmp(localeptr, "POSIX") == 0)
		result = true;
	else
		result = false;
	return (bool) result;
#else							/* not USE_LOCALE */
	return true;				/* We must be in C locale, which is OK */
#endif	 /* USE_LOCALE */
}

/*
 * 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 this is actually not sufficient, since it only copes with the case
 * where individual characters collate in an order different from their
 * numeric code assignments.  It does not handle cases where there are
 * cross-character effects, such as specially sorted digraphs, multiple
 * sort passes, etc.  For now, we just shut down the whole thing in locales
 * that do such things :-(
 */
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;
}

/*
 * 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 = DatumGetBool(DirectFunctionCall2(text_lt,
													  datum1, datum2));
			break;

		case BPCHAROID:
			result = DatumGetBool(DirectFunctionCall2(bpcharlt,
													  datum1, datum2));
			break;

		case VARCHAROID:
			result = DatumGetBool(DirectFunctionCall2(varcharlt,
													  datum1, datum2));
			break;

		case NAMEOID:
			result = DatumGetBool(DirectFunctionCall2(namelt,
													  datum1, datum2));
			break;

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

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

	return result;
}

/* See if there is a binary op of the given name for the given datatype */
static Oid
find_operator(const char *opname, Oid datatype)
{
	return GetSysCacheOid(OPERNAME,
						  PointerGetDatum(opname),
						  ObjectIdGetDatum(datatype),
						  ObjectIdGetDatum(datatype),
						  CharGetDatum('b'));
}

/*
 * 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 DirectFunctionCall1(namein, CStringGetDatum(str));
	else
		return DirectFunctionCall1(textin, CStringGetDatum(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);
}

/*-------------------------------------------------------------------------
 *
 * Index cost estimation functions
 *
 * genericcostestimate is a general-purpose estimator for use when we
 * don't have any better idea about how to estimate.  Index-type-specific
 * knowledge can be incorporated in the type-specific routines.
 *
 *-------------------------------------------------------------------------
 */

static void
genericcostestimate(Query *root, RelOptInfo *rel,
					IndexOptInfo *index, List *indexQuals,
					Cost *indexStartupCost,
					Cost *indexTotalCost,
					Selectivity *indexSelectivity,
					double *indexCorrelation)
{
	double		numIndexTuples;
	double		numIndexPages;
	List	   *selectivityQuals = indexQuals;

	/*
	 * If the index is partial, AND the index predicate with the explicitly
	 * given indexquals to produce a more accurate idea of the index
	 * restriction.  This may produce redundant clauses, which we hope that
	 * cnfify and clauselist_selectivity will deal with intelligently.
	 *
	 * Note that index->indpred and indexQuals are both in implicit-AND
	 * form to start with, which we have to make explicit to hand to
	 * canonicalize_qual, and then we get back implicit-AND form again.
	 */
	if (index->indpred != NIL)
	{
		Expr   *andedQuals;

		andedQuals = make_ands_explicit(nconc(listCopy(index->indpred),
											  indexQuals));
		selectivityQuals = canonicalize_qual(andedQuals, true);
	}

  	/* Estimate the fraction of main-table tuples that will be visited */
 	*indexSelectivity = clauselist_selectivity(root, selectivityQuals,
  											   lfirsti(rel->relids));

	/*
	 * Estimate the number of tuples that will be visited.  We do it in
	 * this rather peculiar-looking way in order to get the right answer
	 * for partial indexes.  We can bound the number of tuples by the
	 * index size, in any case.
	 */
	numIndexTuples = *indexSelectivity * rel->tuples;

	if (numIndexTuples > index->tuples)
		numIndexTuples = index->tuples;

  	/*
	 * Always estimate at least one tuple is touched, even when
	 * indexSelectivity estimate is tiny.
	 */
	if (numIndexTuples < 1.0)
		numIndexTuples = 1.0;

  	/*
	 * Estimate the number of index pages that will be retrieved.
	 *
	 * For all currently-supported index types, the first page of the index
	 * is a metadata page, and we should figure on fetching that plus a
	 * pro-rated fraction of the remaining pages.
	 */
	if (index->pages > 1 && index->tuples > 0)
	{
		numIndexPages = (numIndexTuples / index->tuples) * (index->pages - 1);
		numIndexPages += 1;		/* count the metapage too */
		numIndexPages = ceil(numIndexPages);
	}
	else
		numIndexPages = 1.0;

	/*
	 * Compute the index access cost.
	 *
	 * Our generic assumption is that the index pages will be read
	 * sequentially, so they have cost 1.0 each, not random_page_cost.
	 * Also, we charge for evaluation of the indexquals at each index
	 * tuple. All the costs are assumed to be paid incrementally during
	 * the scan.
	 */
	*indexStartupCost = 0;
	*indexTotalCost = numIndexPages +
		(cpu_index_tuple_cost + cost_qual_eval(indexQuals)) * numIndexTuples;

	/*
	 * Generic assumption about index correlation: there isn't any.
	 */
	*indexCorrelation = 0.0;
}


Datum
btcostestimate(PG_FUNCTION_ARGS)
{
	Query	   *root = (Query *) PG_GETARG_POINTER(0);
	RelOptInfo *rel = (RelOptInfo *) PG_GETARG_POINTER(1);
	IndexOptInfo *index = (IndexOptInfo *) PG_GETARG_POINTER(2);
	List	   *indexQuals = (List *) PG_GETARG_POINTER(3);
	Cost	   *indexStartupCost = (Cost *) PG_GETARG_POINTER(4);
	Cost	   *indexTotalCost = (Cost *) PG_GETARG_POINTER(5);
	Selectivity *indexSelectivity = (Selectivity *) PG_GETARG_POINTER(6);
	double	   *indexCorrelation = (double *) PG_GETARG_POINTER(7);

	genericcostestimate(root, rel, index, indexQuals,
						indexStartupCost, indexTotalCost,
						indexSelectivity, indexCorrelation);

	/*
	 * If it's a functional index, leave the default zero-correlation
	 * estimate in place.  If not, and if we can get an estimate for
	 * the first variable's ordering correlation C from pg_statistic,
	 * estimate the index correlation as C / number-of-columns.
	 * (The idea here is that multiple columns dilute the importance
	 * of the first column's ordering, but don't negate it entirely.)
	 */
	if (index->indproc == InvalidOid)
	{
		Oid			relid;
		HeapTuple	tuple;

		relid = getrelid(lfirsti(rel->relids), root->rtable);
		Assert(relid != InvalidOid);
		tuple = SearchSysCache(STATRELATT,
							   ObjectIdGetDatum(relid),
							   Int16GetDatum(index->indexkeys[0]),
							   0, 0);
		if (HeapTupleIsValid(tuple))
		{
			Oid		typid;
			int32	typmod;
			float4 *numbers;
			int		nnumbers;

			get_atttypetypmod(relid, index->indexkeys[0],
							  &typid, &typmod);
			if (get_attstatsslot(tuple, typid, typmod,
								 STATISTIC_KIND_CORRELATION,
								 index->ordering[0],
								 NULL, NULL, &numbers, &nnumbers))
			{
				double	varCorrelation;
				int		nKeys;

				Assert(nnumbers == 1);
				varCorrelation = numbers[0];
				for (nKeys = 1; index->indexkeys[nKeys] != 0; nKeys++)
					/*skip*/;

				*indexCorrelation = varCorrelation / nKeys;

				free_attstatsslot(typid, NULL, 0, numbers, nnumbers);
			}
			ReleaseSysCache(tuple);
		}
	}

	PG_RETURN_VOID();
}

Datum
rtcostestimate(PG_FUNCTION_ARGS)
{
	Query	   *root = (Query *) PG_GETARG_POINTER(0);
	RelOptInfo *rel = (RelOptInfo *) PG_GETARG_POINTER(1);
	IndexOptInfo *index = (IndexOptInfo *) PG_GETARG_POINTER(2);
	List	   *indexQuals = (List *) PG_GETARG_POINTER(3);
	Cost	   *indexStartupCost = (Cost *) PG_GETARG_POINTER(4);
	Cost	   *indexTotalCost = (Cost *) PG_GETARG_POINTER(5);
	Selectivity *indexSelectivity = (Selectivity *) PG_GETARG_POINTER(6);
	double	   *indexCorrelation = (double *) PG_GETARG_POINTER(7);

	genericcostestimate(root, rel, index, indexQuals,
						indexStartupCost, indexTotalCost,
						indexSelectivity, indexCorrelation);

	PG_RETURN_VOID();
}

Datum
hashcostestimate(PG_FUNCTION_ARGS)
{
	Query	   *root = (Query *) PG_GETARG_POINTER(0);
	RelOptInfo *rel = (RelOptInfo *) PG_GETARG_POINTER(1);
	IndexOptInfo *index = (IndexOptInfo *) PG_GETARG_POINTER(2);
	List	   *indexQuals = (List *) PG_GETARG_POINTER(3);
	Cost	   *indexStartupCost = (Cost *) PG_GETARG_POINTER(4);
	Cost	   *indexTotalCost = (Cost *) PG_GETARG_POINTER(5);
	Selectivity *indexSelectivity = (Selectivity *) PG_GETARG_POINTER(6);
	double	   *indexCorrelation = (double *) PG_GETARG_POINTER(7);

	genericcostestimate(root, rel, index, indexQuals,
						indexStartupCost, indexTotalCost,
						indexSelectivity, indexCorrelation);

	PG_RETURN_VOID();
}

Datum
gistcostestimate(PG_FUNCTION_ARGS)
{
	Query	   *root = (Query *) PG_GETARG_POINTER(0);
	RelOptInfo *rel = (RelOptInfo *) PG_GETARG_POINTER(1);
	IndexOptInfo *index = (IndexOptInfo *) PG_GETARG_POINTER(2);
	List	   *indexQuals = (List *) PG_GETARG_POINTER(3);
	Cost	   *indexStartupCost = (Cost *) PG_GETARG_POINTER(4);
	Cost	   *indexTotalCost = (Cost *) PG_GETARG_POINTER(5);
	Selectivity *indexSelectivity = (Selectivity *) PG_GETARG_POINTER(6);
	double	   *indexCorrelation = (double *) PG_GETARG_POINTER(7);

	genericcostestimate(root, rel, index, indexQuals,
						indexStartupCost, indexTotalCost,
						indexSelectivity, indexCorrelation);

	PG_RETURN_VOID();
}