From 05dedace84ef8c93fea5309c3ac55f889011429b Mon Sep 17 00:00:00 2001
From: CVS to git conversion script <webmaster@postgresql.org>
Date: Thu, 20 Jun 2002 20:29:55 +0000
Subject: This commit was manufactured by cvs2git to create branch
 'ecpg_big_bison'.

Sprout from master 2002-06-20 20:29:54 UTC Bruce Momjian <bruce@momjian.us> 'Update copyright to 2002.'
Delete:
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    HISTORY
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    src/test/regress/sql/create_view.sql
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    src/test/regress/sql/foreign_key.sql
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    src/test/regress/sql/numerology.sql
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    src/test/regress/sql/opr_sanity.sql
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    src/test/regress/sql/sql_ascii.sql
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    src/test/regress/sql/transactions.sql
    src/test/regress/sql/triggers.sql
    src/test/regress/sql/type_sanity.sql
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    src/tools/RELEASE_CHANGES
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    src/tutorial/Makefile
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    src/tutorial/beard.c
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---
 src/backend/utils/adt/selfuncs.c | 3583 --------------------------------------
 1 file changed, 3583 deletions(-)
 delete mode 100644 src/backend/utils/adt/selfuncs.c

(limited to 'src/backend/utils/adt/selfuncs.c')

diff --git a/src/backend/utils/adt/selfuncs.c b/src/backend/utils/adt/selfuncs.c
deleted file mode 100644
index 10fc2d29e03..00000000000
--- a/src/backend/utils/adt/selfuncs.c
+++ /dev/null
@@ -1,3583 +0,0 @@
-/*-------------------------------------------------------------------------
- *
- * 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) 1996-2002, 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 1.112 2002/06/20 20:29:38 momjian 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>
-#include <locale.h>
-
-#include "access/heapam.h"
-#include "catalog/catname.h"
-#include "catalog/pg_namespace.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/datum.h"
-#include "utils/int8.h"
-#include "utils/lsyscache.h"
-#include "utils/pg_locale.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
-
-/*
- * Clamp a computed probability estimate (which may suffer from roundoff or
- * estimation errors) to valid range.  Argument must be a float variable.
- */
-#define CLAMP_PROBABILITY(p) \
-	do { \
-		if (p < 0.0) \
-			p = 0.0; \
-		else if (p > 1.0) \
-			p = 1.0; \
-	} while (0)
-
-
-static bool get_var_maximum(Query *root, Var *var, Oid sortop, Datum *max);
-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 void convert_bytea_to_scalar(Datum value,
-						double *scaledvalue,
-						Datum lobound,
-						double *scaledlobound,
-						Datum hibound,
-						double *scaledhibound);
-static double convert_one_string_to_scalar(unsigned char *value,
-							 int rangelo, int rangehi);
-static double convert_one_bytea_to_scalar(unsigned char *value, int valuelen,
-							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;
-				CLAMP_PROBABILITY(selec);
-
-				/*
-				 * 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... */
-	CLAMP_PROBABILITY(selec);
-
-	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.  The caller must also make sure that the other side
- * of the clause is a non-null Const, and dissect same into a value and
- * datatype.
- *
- * 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, Datum constval, Oid consttype)
-{
-	Oid			relid;
-	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;
-
-	/* 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);
-
-							/*
-							 * Watch out for the possibility that we got a
-							 * NaN or Infinity from the division.  This
-							 * can happen despite the previous checks, if
-							 * for example "low" is -Infinity.
-							 */
-							if (isnan(binfrac) ||
-								binfrac < 0.0 || binfrac > 1.0)
-								binfrac = 0.5;
-						}
-					}
-					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... */
-	CLAMP_PROBABILITY(selec);
-
-	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;
-	Datum		constval;
-	Oid			consttype;
-	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);
-
-	/*
-	 * Can't do anything useful if the something is not a constant,
-	 * either.
-	 */
-	if (!IsA(other, Const))
-		PG_RETURN_FLOAT8(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)
-		PG_RETURN_FLOAT8(0.0);
-	constval = ((Const *) other)->constvalue;
-	consttype = ((Const *) other)->consttype;
-
-	/*
-	 * 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, constval, consttype);
-
-	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;
-	Datum		constval;
-	Oid			consttype;
-	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);
-
-	/*
-	 * Can't do anything useful if the something is not a constant,
-	 * either.
-	 */
-	if (!IsA(other, Const))
-		PG_RETURN_FLOAT8(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)
-		PG_RETURN_FLOAT8(0.0);
-	constval = ((Const *) other)->constvalue;
-	consttype = ((Const *) other)->consttype;
-
-	/*
-	 * 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, constval, consttype);
-
-	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... */
-		CLAMP_PROBABILITY(selec);
-		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... */
-	CLAMP_PROBABILITY(selec);
-
-	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... */
-	CLAMP_PROBABILITY(selec);
-
-	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;
-					}
-				}
-			}
-			CLAMP_PROBABILITY(matchprodfreq);
-			/* 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];
-			}
-			CLAMP_PROBABILITY(matchfreq1);
-			CLAMP_PROBABILITY(unmatchfreq1);
-			matchfreq2 = unmatchfreq2 = 0.0;
-			for (i = 0; i < nvalues2; i++)
-			{
-				if (hasmatch2[i])
-					matchfreq2 += numbers2[i];
-				else
-					unmatchfreq2 += numbers2[i];
-			}
-			CLAMP_PROBABILITY(matchfreq2);
-			CLAMP_PROBABILITY(unmatchfreq2);
-			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;
-			CLAMP_PROBABILITY(otherfreq1);
-			CLAMP_PROBABILITY(otherfreq2);
-
-			/*
-			 * 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);
-	}
-
-	CLAMP_PROBABILITY(selec);
-
-	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);
-}
-
-/*
- * mergejoinscansel			- Scan selectivity of merge join.
- *
- * A merge join will stop as soon as it exhausts either input stream.
- * Therefore, if we can estimate the ranges of both input variables,
- * we can estimate how much of the input will actually be read.  This
- * can have a considerable impact on the cost when using indexscans.
- *
- * clause should be a clause already known to be mergejoinable.
- *
- * *leftscan is set to the fraction of the left-hand variable expected
- * to be scanned (0 to 1), and similarly *rightscan for the right-hand
- * variable.
- */
-void
-mergejoinscansel(Query *root, Node *clause,
-				 Selectivity *leftscan,
-				 Selectivity *rightscan)
-{
-	Var		   *left,
-			   *right;
-	Oid			opno,
-				lsortop,
-				rsortop,
-				ltop,
-				gtop,
-				revltop;
-	Datum		leftmax,
-				rightmax;
-	double		selec;
-
-	/* Set default results if we can't figure anything out. */
-	*leftscan = *rightscan = 1.0;
-
-	/* Deconstruct the merge clause */
-	if (!is_opclause(clause))
-		return;					/* shouldn't happen */
-	opno = ((Oper *) ((Expr *) clause)->oper)->opno;
-	left = get_leftop((Expr *) clause);
-	right = get_rightop((Expr *) clause);
-	if (!right)
-		return;					/* shouldn't happen */
-
-	/* Can't do anything if inputs are not Vars */
-	if (!IsA(left, Var) ||!IsA(right, Var))
-		return;
-
-	/* Verify mergejoinability and get left and right "<" operators */
-	if (!op_mergejoinable(opno,
-						  left->vartype,
-						  right->vartype,
-						  &lsortop,
-						  &rsortop))
-		return;					/* shouldn't happen */
-
-	/* Try to get maximum values of both vars */
-	if (!get_var_maximum(root, left, lsortop, &leftmax))
-		return;					/* no max available from stats */
-
-	if (!get_var_maximum(root, right, rsortop, &rightmax))
-		return;					/* no max available from stats */
-
-	/* Look up the "left < right" and "left > right" operators */
-	op_mergejoin_crossops(opno, &ltop, &gtop, NULL, NULL);
-
-	/* Look up the "right < left" operator */
-	revltop = get_commutator(gtop);
-	if (!OidIsValid(revltop))
-		return;					/* shouldn't happen */
-
-	/*
-	 * Now, the fraction of the left variable that will be scanned is the
-	 * fraction that's <= the right-side maximum value.  But only believe
-	 * non-default estimates, else stick with our 1.0.
-	 */
-	selec = scalarineqsel(root, ltop, false, left,
-						  rightmax, right->vartype);
-	if (selec != DEFAULT_INEQ_SEL)
-		*leftscan = selec;
-
-	/* And similarly for the right variable. */
-	selec = scalarineqsel(root, revltop, false, right,
-						  leftmax, left->vartype);
-	if (selec != DEFAULT_INEQ_SEL)
-		*rightscan = selec;
-
-	/*
-	 * Only one of the two fractions can really be less than 1.0; believe
-	 * the smaller estimate and reset the other one to exactly 1.0.
-	 */
-	if (*leftscan > *rightscan)
-		*leftscan = 1.0;
-	else
-		*rightscan = 1.0;
-}
-
-/*
- * get_var_maximum
- *		Estimate the maximum value of the specified variable.
- *		If successful, store value in *max and return TRUE.
- *		If no data available, return FALSE.
- *
- * sortop is the "<" comparison operator to use.  (To extract the
- * minimum instead of the maximum, just pass the ">" operator instead.)
- */
-static bool
-get_var_maximum(Query *root, Var *var, Oid sortop, Datum *max)
-{
-	Datum		tmax = 0;
-	bool		have_max = false;
-	Oid			relid;
-	HeapTuple	statsTuple;
-	Form_pg_statistic stats;
-	int16		typLen;
-	bool		typByVal;
-	Datum	   *values;
-	int			nvalues;
-	int			i;
-
-	relid = getrelid(var->varno, root->rtable);
-	if (relid == InvalidOid)
-		return false;
-
-	/* 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 false;
-	}
-	stats = (Form_pg_statistic) GETSTRUCT(statsTuple);
-
-	get_typlenbyval(var->vartype, &typLen, &typByVal);
-
-	/*
-	 * If there is a histogram, grab the last or first value as appropriate.
-	 *
-	 * If there is a histogram that is sorted with some other operator
-	 * than the one we want, fail --- this suggests that there is data
-	 * we can't use.
-	 */
-	if (get_attstatsslot(statsTuple, var->vartype, var->vartypmod,
-						 STATISTIC_KIND_HISTOGRAM, sortop,
-						 &values, &nvalues,
-						 NULL, NULL))
-	{
-		if (nvalues > 0)
-		{
-			tmax = datumCopy(values[nvalues-1], typByVal, typLen);
-			have_max = true;
-		}
-		free_attstatsslot(var->vartype, values, nvalues, NULL, 0);
-	}
-	else
-	{
-		Oid		rsortop = get_commutator(sortop);
-
-		if (OidIsValid(rsortop) &&
-			get_attstatsslot(statsTuple, var->vartype, var->vartypmod,
-							 STATISTIC_KIND_HISTOGRAM, rsortop,
-							 &values, &nvalues,
-							 NULL, NULL))
-		{
-			if (nvalues > 0)
-			{
-				tmax = datumCopy(values[0], typByVal, typLen);
-				have_max = true;
-			}
-			free_attstatsslot(var->vartype, values, nvalues, NULL, 0);
-		}
-		else if (get_attstatsslot(statsTuple, var->vartype, var->vartypmod,
-								  STATISTIC_KIND_HISTOGRAM, InvalidOid,
-								  &values, &nvalues,
-								  NULL, NULL))
-		{
-			free_attstatsslot(var->vartype, values, nvalues, NULL, 0);
-			ReleaseSysCache(statsTuple);
-			return false;
-		}
-	}
-
-	/*
-	 * If we have most-common-values info, look for a large MCV.  This
-	 * is needed even if we also have a histogram, since the histogram
-	 * excludes the MCVs.  However, usually the MCVs will not be the
-	 * extreme values, so avoid unnecessary data copying.
-	 */
-	if (get_attstatsslot(statsTuple, var->vartype, var->vartypmod,
-						 STATISTIC_KIND_MCV, InvalidOid,
-						 &values, &nvalues,
-						 NULL, NULL))
-	{
-		bool	large_mcv = false;
-		FmgrInfo	opproc;
-
-		fmgr_info(get_opcode(sortop), &opproc);
-
-		for (i = 0; i < nvalues; i++)
-		{
-			if (!have_max)
-			{
-				tmax = values[i];
-				large_mcv = have_max = true;
-			}
-			else if (DatumGetBool(FunctionCall2(&opproc, tmax, values[i])))
-			{
-				tmax = values[i];
-				large_mcv = true;
-			}
-		}
-		if (large_mcv)
-			tmax = datumCopy(tmax, typByVal, typLen);
-		free_attstatsslot(var->vartype, values, nvalues, NULL, 0);
-	}
-
-	ReleaseSysCache(statsTuple);
-
-	*max = tmax;
-	return have_max;
-}
-
-/*
- * 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.  (NUMERIC values that are outside the range of "double"
- * are clamped to +/- HUGE_VAL.)
- *
- * 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 bytea datatype is just enough different from strings that it has
- * to be treated separately.
- *
- * 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 correct results even for the "special"
- * values of Timestamp, since those are chosen to compare correctly;
- * see timestamp_cmp.
- *
- * 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:
-		case REGPROCEDUREOID:
-		case REGOPEROID:
-		case REGOPERATOROID:
-		case REGCLASSOID:
-		case REGTYPEOID:
-			*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 bytea type
-			 */
-		case BYTEAOID:
-			{
-				convert_bytea_to_scalar(value, scaledvalue,
-										lobound, scaledlobound,
-										hibound, scaledhibound);
-				return true;
-			}
-
-			/*
-			 * Built-in time types
-			 */
-		case TIMESTAMPOID:
-		case TIMESTAMPTZOID:
-		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:
-			/* Note: out-of-range values will be clamped to +-HUGE_VAL */
-			return (double)
-				DatumGetFloat8(DirectFunctionCall1(numeric_float8_no_overflow,
-												   value));
-		case OIDOID:
-		case REGPROCOID:
-		case REGPROCEDUREOID:
-		case REGOPEROID:
-		case REGOPERATOROID:
-		case REGCLASSOID:
-		case REGTYPEOID:
-			/* 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.
- *
- * When using a non-C locale, 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;
-	char	   *xfrmstr;
-	size_t		xfrmsize;
-	size_t		xfrmlen;
-
-	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;
-	}
-
-	if (!lc_collate_is_c())
-	{
-		/* 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;
-	}
-
-	return (unsigned char *) val;
-}
-
-/*
- * Do convert_to_scalar()'s work for any bytea data type.
- *
- * Very similar to convert_string_to_scalar except we can't assume
- * null-termination and therefore pass explicit lengths around.
- *
- * Also, assumptions about likely "normal" ranges of characters have been
- * removed - a data range of 0..255 is always used, for now.  (Perhaps
- * someday we will add information about actual byte data range to
- * pg_statistic.)
- */
-static void
-convert_bytea_to_scalar(Datum value,
-						double *scaledvalue,
-						Datum lobound,
-						double *scaledlobound,
-						Datum hibound,
-						double *scaledhibound)
-{
-	int			rangelo,
-				rangehi,
-				valuelen = VARSIZE(DatumGetPointer(value)) - VARHDRSZ,
-				loboundlen = VARSIZE(DatumGetPointer(lobound)) - VARHDRSZ,
-				hiboundlen = VARSIZE(DatumGetPointer(hibound)) - VARHDRSZ,
-				i,
-				minlen;
-	unsigned char *valstr = (unsigned char *) VARDATA(DatumGetPointer(value)),
-			   *lostr = (unsigned char *) VARDATA(DatumGetPointer(lobound)),
-			   *histr = (unsigned char *) VARDATA(DatumGetPointer(hibound));
-
-	/*
-	 * Assume bytea data is uniformly distributed across all byte values.
-	 */
-	rangelo = 0;
-	rangehi = 255;
-
-	/*
-	 * Now strip any common prefix of the three strings.
-	 */
-	minlen = Min(Min(valuelen, loboundlen), hiboundlen);
-	for (i = 0; i < minlen; i++)
-	{
-		if (*lostr != *histr || *lostr != *valstr)
-			break;
-		lostr++, histr++, valstr++;
-		loboundlen--, hiboundlen--, valuelen--;
-	}
-
-	/*
-	 * Now we can do the conversions.
-	 */
-	*scaledvalue = convert_one_bytea_to_scalar(valstr, valuelen, rangelo, rangehi);
-	*scaledlobound = convert_one_bytea_to_scalar(lostr, loboundlen, rangelo, rangehi);
-	*scaledhibound = convert_one_bytea_to_scalar(histr, hiboundlen, rangelo, rangehi);
-}
-
-static double
-convert_one_bytea_to_scalar(unsigned char *value, int valuelen,
-							int rangelo, int rangehi)
-{
-	double		num,
-				denom,
-				base;
-
-	if (valuelen <= 0)
-		return 0.0;				/* empty string has scalar value 0 */
-
-	/*
-	 * Since base is 256, need not consider more than about 10 chars (even
-	 * this many seems like overkill)
-	 */
-	if (valuelen > 10)
-		valuelen = 10;
-
-	/* Convert initial characters to fraction */
-	base = rangehi - rangelo + 1;
-	num = 0.0;
-	denom = base;
-	while (valuelen-- > 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;
-}
-
-/*
- * 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 TIMESTAMPTZOID:
-			return DatumGetTimestampTz(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.
-				 */
-#ifdef HAVE_INT64_TIMESTAMP
-				return (interval->time + (interval->month * ((365.25 / 12.0) * 86400000000.0)));
-#else
-				return interval->time +
-					interval->month * (365.25 / 12.0 * 24.0 * 60.0 * 60.0);
-#endif
-			}
-		case RELTIMEOID:
-#ifdef HAVE_INT64_TIMESTAMP
-			return (DatumGetRelativeTime(value) * 1000000.0);
-#else
-			return DatumGetRelativeTime(value);
-#endif
-		case TINTERVALOID:
-			{
-				TimeInterval interval = DatumGetTimeInterval(value);
-
-#ifdef HAVE_INT64_TIMESTAMP
-				if (interval->status != 0)
-					return ((interval->data[1] - interval->data[0]) * 1000000.0);
-#else
-				if (interval->status != 0)
-					return interval->data[1] - interval->data[0];
-#endif
-				return 0;		/* for lack of a better idea */
-			}
-		case TIMEOID:
-			return DatumGetTimeADT(value);
-		case TIMETZOID:
-			{
-				TimeTzADT  *timetz = DatumGetTimeTzADTP(value);
-
-				/* use GMT-equivalent time */
-#ifdef HAVE_INT64_TIMESTAMP
-				return (double) (timetz->time + (timetz->zone * 1000000.0));
-#else
-				return (double) (timetz->time + timetz->zone);
-#endif
-			}
-	}
-
-	/*
-	 * 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.
- *
- * NB: be careful to produce an integral result, since callers may compare
- * the result to exact integer counts.
- */
-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 floor((-stats->stadistinct * ntuples) + 0.5);
-	}
-
-	/*
-	 * 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	0.20	/* about 1/5 */
-#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;
-}
-
-
-/*
- * We want test whether the database's LC_COLLATE 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, a
- * non-C locale may have arbitrary 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, the optimization is disabled in all non-C locales.
- *
- * (In theory, locales other than C may be LIKE-safe so this function
- * could be different from lc_collate_is_c(), but in a different
- * theory, non-C locales are completely unpredicable so it's unlikely
- * to happen.)
- *
- * Be sure to maintain the correspondence with the code in initdb.
- */
-bool
-locale_is_like_safe(void)
-{
-	return lc_collate_is_c();
-}
-
-/*
- * 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;
-
-		case BYTEAOID:
-			result = DatumGetBool(DirectFunctionCall2(bytealt,
-													  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 */
-/* NB: we assume that only built-in system operators are searched for */
-static Oid
-find_operator(const char *opname, Oid datatype)
-{
-	return GetSysCacheOid(OPERNAMENSP,
-						  PointerGetDatum(opname),
-						  ObjectIdGetDatum(datatype),
-						  ObjectIdGetDatum(datatype),
-						  ObjectIdGetDatum(PG_CATALOG_NAMESPACE));
-}
-
-/*
- * 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();
-}
-- 
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