Distinguish selectivity of < from <= and > from >=.

Historically, the selectivity functions have simply not distinguished
< from <=, or > from >=, arguing that the fraction of the population that
satisfies the "=" aspect can be considered to be vanishingly small, if the
comparison value isn't any of the most-common-values for the variable.
(If it is, the code path that executes the operator against each MCV will
take care of things properly.)  But that isn't really true unless we're
dealing with a continuum of variable values, and in practice we seldom are.
If "x = const" would estimate a nonzero number of rows for a given const
value, then it follows that we ought to estimate different numbers of rows
for "x < const" and "x <= const", even if the const is not one of the MCVs.
Handling this more honestly makes a significant difference in edge cases,
such as the estimate for a tight range (x BETWEEN y AND z where y and z
are close together).

Hence, split scalarltsel into scalarltsel/scalarlesel, and similarly
split scalargtsel into scalargtsel/scalargesel.  Adjust <= and >=
operator definitions to reference the new selectivity functions.
Improve the core ineq_histogram_selectivity() function to make a
correction for equality.  (Along the way, I learned quite a bit about
exactly why that function gives good answers, which I tried to memorialize
in improved comments.)

The corresponding join selectivity functions were, and remain, just stubs.
But I chose to split them similarly, to avoid confusion and to prevent the
need for doing this exercise again if someone ever makes them less stubby.

In passing, change ineq_histogram_selectivity's clamp for extreme
probability estimates so that it varies depending on the histogram
size, instead of being hardwired at 0.0001.  With the default histogram
size of 100 entries, you still get the old clamp value, but bigger
histograms should allow us to put more faith in edge values.

Tom Lane, reviewed by Aleksander Alekseev and Kuntal Ghosh

Discussion: https://postgr.es/m/12232.1499140410@sss.pgh.pa.us

contrib/citext/Makefile

@@ -3,7 +3,8 @@
 MODULES = citext
 
 EXTENSION = citext
-DATA = citext--1.4.sql citext--1.3--1.4.sql \
+DATA = citext--1.4.sql citext--1.4--1.5.sql \
+	citext--1.3--1.4.sql \
 	citext--1.2--1.3.sql citext--1.1--1.2.sql \
 	citext--1.0--1.1.sql citext--unpackaged--1.0.sql
 PGFILEDESC = "citext - case-insensitive character string data type"

contrib/citext/citext--1.4--1.5.sql

@@ -0,0 +1,14 @@
+/* contrib/citext/citext--1.4--1.5.sql */
+
+-- complain if script is sourced in psql, rather than via ALTER EXTENSION
+\echo Use "ALTER EXTENSION citext UPDATE TO '1.5'" to load this file. \quit
+
+ALTER OPERATOR <= (citext, citext) SET (
+    RESTRICT   = scalarlesel,
+    JOIN       = scalarlejoinsel
+);
+
+ALTER OPERATOR >= (citext, citext) SET (
+    RESTRICT   = scalargesel,
+    JOIN       = scalargejoinsel
+);

contrib/citext/citext.control

@@ -1,5 +1,5 @@
 # citext extension
 comment = 'data type for case-insensitive character strings'
-default_version = '1.4'
+default_version = '1.5'
 module_pathname = '$libdir/citext'
 relocatable = true

contrib/cube/Makefile

@@ -4,7 +4,8 @@ MODULE_big = cube
 OBJS= cube.o cubeparse.o $(WIN32RES)
 
 EXTENSION = cube
-DATA = cube--1.2.sql cube--1.1--1.2.sql cube--1.0--1.1.sql \
+DATA = cube--1.2.sql cube--1.2--1.3.sql \
+	cube--1.1--1.2.sql cube--1.0--1.1.sql \
 	cube--unpackaged--1.0.sql
 PGFILEDESC = "cube - multidimensional cube data type"
 

contrib/cube/cube--1.2--1.3.sql

@@ -0,0 +1,12 @@
+/* contrib/cube/cube--1.2--1.3.sql */
+
+-- complain if script is sourced in psql, rather than via ALTER EXTENSION
+\echo Use "ALTER EXTENSION cube UPDATE TO '1.3'" to load this file. \quit
+
+ALTER OPERATOR <= (cube, cube) SET (
+	RESTRICT = scalarlesel, JOIN = scalarlejoinsel
+);
+
+ALTER OPERATOR >= (cube, cube) SET (
+	RESTRICT = scalargesel, JOIN = scalargejoinsel
+);

contrib/cube/cube.control

@@ -1,5 +1,5 @@
 # cube extension
 comment = 'data type for multidimensional cubes'
-default_version = '1.2'
+default_version = '1.3'
 module_pathname = '$libdir/cube'
 relocatable = true

contrib/hstore/Makefile

@@ -5,7 +5,8 @@ OBJS = hstore_io.o hstore_op.o hstore_gist.o hstore_gin.o hstore_compat.o \
 	$(WIN32RES)
 
 EXTENSION = hstore
-DATA = hstore--1.4.sql hstore--1.3--1.4.sql hstore--1.2--1.3.sql \
+DATA = hstore--1.4.sql hstore--1.4--1.5.sql \
+	hstore--1.3--1.4.sql hstore--1.2--1.3.sql \
 	hstore--1.1--1.2.sql hstore--1.0--1.1.sql \
 	hstore--unpackaged--1.0.sql
 PGFILEDESC = "hstore - key/value pair data type"

contrib/hstore/hstore--1.4--1.5.sql

@@ -0,0 +1,14 @@
+/* contrib/hstore/hstore--1.4--1.5.sql */
+
+-- complain if script is sourced in psql, rather than via ALTER EXTENSION
+\echo Use "ALTER EXTENSION hstore UPDATE TO '1.5'" to load this file. \quit
+
+ALTER OPERATOR #<=# (hstore, hstore) SET (
+       RESTRICT = scalarlesel,
+       JOIN = scalarlejoinsel
+);
+
+ALTER OPERATOR #>=# (hstore, hstore) SET (
+       RESTRICT = scalargesel,
+       JOIN = scalargejoinsel
+);

contrib/hstore/hstore.control

@@ -1,5 +1,5 @@
 # hstore extension
 comment = 'data type for storing sets of (key, value) pairs'
-default_version = '1.4'
+default_version = '1.5'
 module_pathname = '$libdir/hstore'
 relocatable = true

contrib/isn/Makefile

@@ -3,7 +3,8 @@
 MODULES = isn
 
 EXTENSION = isn
-DATA = isn--1.1.sql isn--1.0--1.1.sql isn--unpackaged--1.0.sql
+DATA = isn--1.1.sql isn--1.1--1.2.sql \
+	isn--1.0--1.1.sql isn--unpackaged--1.0.sql
 PGFILEDESC = "isn - data types for international product numbering standards"
 
 REGRESS = isn

contrib/isn/isn--1.1--1.2.sql

@@ -0,0 +1,228 @@
+/* contrib/isn/isn--1.1--1.2.sql */
+
+-- complain if script is sourced in psql, rather than via ALTER EXTENSION
+\echo Use "ALTER EXTENSION isn UPDATE TO '1.2'" to load this file. \quit
+
+ALTER OPERATOR <= (ean13, ean13) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (ean13, ean13) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (ean13, isbn13) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (ean13, isbn13) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (isbn13, ean13) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (isbn13, ean13) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (ean13, ismn13) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (ean13, ismn13) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (ismn13, ean13) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (ismn13, ean13) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (ean13, issn13) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (ean13, issn13) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (ean13, isbn) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (ean13, isbn) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (ean13, ismn) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (ean13, ismn) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (ean13, issn) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (ean13, issn) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (ean13, upc) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (ean13, upc) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (isbn13, isbn13) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (isbn13, isbn13) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (isbn13, isbn) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (isbn13, isbn) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (isbn, isbn) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (isbn, isbn) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (isbn, isbn13) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (isbn, isbn13) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (isbn, ean13) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (isbn, ean13) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (ismn13, ismn13) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (ismn13, ismn13) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (ismn13, ismn) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (ismn13, ismn) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (ismn, ismn) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (ismn, ismn) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (ismn, ismn13) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (ismn, ismn13) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (ismn, ean13) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (ismn, ean13) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (issn13, issn13) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (issn13, issn13) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (issn13, issn) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (issn13, issn) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (issn13, ean13) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (issn13, ean13) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (issn, issn) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (issn, issn) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (issn, issn13) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (issn, issn13) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (issn, ean13) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (issn, ean13) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (upc, upc) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (upc, upc) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);
+
+ALTER OPERATOR <= (upc, ean13) SET (
+	RESTRICT = scalarlesel,
+	JOIN = scalarlejoinsel);
+
+ALTER OPERATOR >= (upc, ean13) SET (
+	RESTRICT = scalargesel,
+	JOIN = scalargejoinsel);

contrib/isn/isn.control

@@ -1,5 +1,5 @@
 # isn extension
 comment = 'data types for international product numbering standards'
-default_version = '1.1'
+default_version = '1.2'
 module_pathname = '$libdir/isn'
 relocatable = true

doc/src/sgml/xindex.sgml

@@ -801,8 +801,7 @@ CREATE OPERATOR < (
    It is important to specify the correct commutator and negator operators,
    as well as suitable restriction and join selectivity
    functions, otherwise the optimizer will be unable to make effective
-   use of the index.  Note that the less-than, equal, and
+   use of the index.
-   greater-than cases should use different selectivity functions.
   </para>
 
   <para>

doc/src/sgml/xoper.sgml

@@ -242,20 +242,11 @@ column OP constant
     <simplelist>
      <member><function>eqsel</> for <literal>=</></member>
      <member><function>neqsel</> for <literal>&lt;&gt;</></member>
-     <member><function>scalarltsel</> for <literal>&lt;</> or <literal>&lt;=</></member>
+     <member><function>scalarltsel</> for <literal>&lt;</></member>
-     <member><function>scalargtsel</> for <literal>&gt;</> or <literal>&gt;=</></member>
+     <member><function>scalarlesel</> for <literal>&lt;=</></member>
-   </simplelist>
+     <member><function>scalargtsel</> for <literal>&gt;</></member>
-    It might seem a little odd that these are the categories, but they
+     <member><function>scalargesel</> for <literal>&gt;=</></member>
-    make sense if you think about it.  <literal>=</> will typically accept only
+    </simplelist>
-    a small fraction of the rows in a table; <literal>&lt;&gt;</> will typically reject
-    only a small fraction.  <literal>&lt;</> will accept a fraction that depends on
-    where the given constant falls in the range of values for that table
-    column (which, it just so happens, is information collected by
-    <command>ANALYZE</command> and made available to the selectivity estimator).
-    <literal>&lt;=</> will accept a slightly larger fraction than <literal>&lt;</> for the same
-    comparison constant, but they're close enough to not be worth
-    distinguishing, especially since we're not likely to do better than a
-    rough guess anyhow.  Similar remarks apply to <literal>&gt;</> and <literal>&gt;=</>.
    </para>
 
    <para>
@@ -267,10 +258,12 @@ column OP constant
    </para>
 
    <para>
-    You can use <function>scalarltsel</> and <function>scalargtsel</> for comparisons on data types that
+    You can use <function>scalarltsel</>, <function>scalarlesel</>,
-    have some sensible means of being converted into numeric scalars for
+    <function>scalargtsel</> and <function>scalargesel</> for comparisons on
-    range comparisons.  If possible, add the data type to those understood
+    data types that have some sensible means of being converted into numeric
-    by the function <function>convert_to_scalar()</function> in <filename>src/backend/utils/adt/selfuncs.c</filename>.
+    scalars for range comparisons.  If possible, add the data type to those
+    understood by the function <function>convert_to_scalar()</function> in
+    <filename>src/backend/utils/adt/selfuncs.c</filename>.
     (Eventually, this function should be replaced by per-data-type functions
     identified through a column of the <classname>pg_type</> system catalog; but that hasn't happened
     yet.)  If you do not do this, things will still work, but the optimizer's
@@ -310,8 +303,10 @@ table1.column1 OP table2.column2
      <simplelist>
       <member><function>eqjoinsel</> for <literal>=</></member>
       <member><function>neqjoinsel</> for <literal>&lt;&gt;</></member>
-      <member><function>scalarltjoinsel</> for <literal>&lt;</> or <literal>&lt;=</></member>
+      <member><function>scalarltjoinsel</> for <literal>&lt;</></member>
-      <member><function>scalargtjoinsel</> for <literal>&gt;</> or <literal>&gt;=</></member>
+      <member><function>scalarlejoinsel</> for <literal>&lt;=</></member>
+      <member><function>scalargtjoinsel</> for <literal>&gt;</></member>
+      <member><function>scalargejoinsel</> for <literal>&gt;=</></member>
       <member><function>areajoinsel</> for 2D area-based comparisons</member>
       <member><function>positionjoinsel</> for 2D position-based comparisons</member>
       <member><function>contjoinsel</> for 2D containment-based comparisons</member>

src/backend/optimizer/path/clausesel.c

@@ -71,7 +71,7 @@ static RelOptInfo *find_single_rel_for_clauses(PlannerInfo *root,
  *
  * We also recognize "range queries", such as "x > 34 AND x < 42".  Clauses
  * are recognized as possible range query components if they are restriction
- * opclauses whose operators have scalarltsel() or scalargtsel() as their
+ * opclauses whose operators have scalarltsel or a related function as their
  * restriction selectivity estimator.  We pair up clauses of this form that
  * refer to the same variable.  An unpairable clause of this kind is simply
  * multiplied into the selectivity product in the normal way.  But when we
@@ -92,8 +92,8 @@ static RelOptInfo *find_single_rel_for_clauses(PlannerInfo *root,
  * A free side-effect is that we can recognize redundant inequalities such
  * as "x < 4 AND x < 5"; only the tighter constraint will be counted.
  *
- * Of course this is all very dependent on the behavior of
+ * Of course this is all very dependent on the behavior of the inequality
- * scalarltsel/scalargtsel; perhaps some day we can generalize the approach.
+ * selectivity functions; perhaps some day we can generalize the approach.
  */
 Selectivity
 clauselist_selectivity(PlannerInfo *root,
@@ -218,17 +218,19 @@ clauselist_selectivity(PlannerInfo *root,
 			if (ok)
 			{
 				/*
-				 * If it's not a "<" or ">" operator, just merge the
+				 * If it's not a "<"/"<="/">"/">=" operator, just merge the
 				 * selectivity in generically.  But if it's the right oprrest,
 				 * add the clause to rqlist for later processing.
 				 */
 				switch (get_oprrest(expr->opno))
 				{
 					case F_SCALARLTSEL:
+					case F_SCALARLESEL:
 						addRangeClause(&rqlist, clause,
 									   varonleft, true, s2);
 						break;
 					case F_SCALARGTSEL:
+					case F_SCALARGESEL:
 						addRangeClause(&rqlist, clause,
 									   varonleft, false, s2);
 						break;
@@ -368,7 +370,7 @@ addRangeClause(RangeQueryClause **rqlist, Node *clause,
 
 				/*------
 				 * We have found two similar clauses, such as
-				 * x < y AND x < z.
+				 * x < y AND x <= z.
 				 * Keep only the more restrictive one.
 				 *------
 				 */
@@ -388,7 +390,7 @@ addRangeClause(RangeQueryClause **rqlist, Node *clause,
 
 				/*------
 				 * We have found two similar clauses, such as
-				 * x > y AND x > z.
+				 * x > y AND x >= z.
 				 * Keep only the more restrictive one.
 				 *------
 				 */

src/backend/utils/adt/network.c

@@ -957,8 +957,8 @@ convert_network_to_scalar(Datum value, Oid typid)
 	}
 
 	/*
-	 * Can't get here unless someone tries to use scalarltsel/scalargtsel on
+	 * Can't get here unless someone tries to use scalarineqsel() on an
-	 * an operator with one network and one non-network operand.
+	 * operator with one network and one non-network operand.
 	 */
 	elog(ERROR, "unsupported type: %u", typid);
 	return 0;

src/backend/utils/adt/selfuncs.c

@@ -164,7 +164,7 @@ static double var_eq_non_const(VariableStatData *vardata, Oid operator,
 				 bool varonleft, bool negate);
 static double ineq_histogram_selectivity(PlannerInfo *root,
 						   VariableStatData *vardata,
-						   FmgrInfo *opproc, bool isgt,
+						   FmgrInfo *opproc, bool isgt, bool iseq,
 						   Datum constval, Oid consttype);
 static double eqjoinsel_inner(Oid operator,
 				VariableStatData *vardata1, VariableStatData *vardata2);
@@ -545,18 +545,21 @@ neqsel(PG_FUNCTION_ARGS)
 /*
  *	scalarineqsel		- Selectivity of "<", "<=", ">", ">=" for scalars.
  *
- * This is the guts of both scalarltsel and scalargtsel.  The caller has
+ * This is the guts of scalarltsel/scalarlesel/scalargtsel/scalargesel.
- * commuted the clause, if necessary, so that we can treat the variable as
+ * The isgt and iseq flags distinguish which of the four cases apply.
- * 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
+ * The caller has commuted the clause, if necessary, so that we can treat
- * datatype.
+ * the variable 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 that into
+ * a value and datatype.  (This definition simplifies some callers that
+ * want to estimate against a computed value instead of a Const node.)
  *
  * 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(PlannerInfo *root, Oid operator, bool isgt,
+scalarineqsel(PlannerInfo *root, Oid operator, bool isgt, bool iseq,
 			  VariableStatData *vardata, Datum constval, Oid consttype)
 {
 	Form_pg_statistic stats;
@@ -588,7 +591,8 @@ scalarineqsel(PlannerInfo *root, Oid operator, bool isgt,
 	 * If there is a histogram, determine which bin the constant falls in, and
 	 * compute the resulting contribution to selectivity.
 	 */
-	hist_selec = ineq_histogram_selectivity(root, vardata, &opproc, isgt,
+	hist_selec = ineq_histogram_selectivity(root, vardata,
+											&opproc, isgt, iseq,
 											constval, consttype);
 
 	/*
@@ -758,7 +762,8 @@ histogram_selectivity(VariableStatData *vardata, FmgrInfo *opproc,
  *	ineq_histogram_selectivity	- Examine the histogram for scalarineqsel
  *
  * Determine the fraction of the variable's histogram population that
- * satisfies the inequality condition, ie, VAR < CONST or VAR > CONST.
+ * satisfies the inequality condition, ie, VAR < (or <=, >, >=) CONST.
+ * The isgt and iseq flags distinguish which of the four cases apply.
  *
  * Returns -1 if there is no histogram (valid results will always be >= 0).
  *
@@ -769,7 +774,7 @@ histogram_selectivity(VariableStatData *vardata, FmgrInfo *opproc,
 static double
 ineq_histogram_selectivity(PlannerInfo *root,
 						   VariableStatData *vardata,
-						   FmgrInfo *opproc, bool isgt,
+						   FmgrInfo *opproc, bool isgt, bool iseq,
 						   Datum constval, Oid consttype)
 {
 	double		hist_selec;
@@ -796,11 +801,17 @@ ineq_histogram_selectivity(PlannerInfo *root,
 		if (sslot.nvalues > 1)
 		{
 			/*
-			 * Use binary search to find proper location, ie, the first slot
+			 * Use binary search to find the desired location, namely the
-			 * at which the comparison fails.  (If the given operator isn't
+			 * right end of the histogram bin containing the comparison value,
-			 * actually sort-compatible with the histogram, you'll get garbage
+			 * which is the leftmost entry for which the comparison operator
-			 * results ... but probably not any more garbage-y than you would
+			 * succeeds (if isgt) or fails (if !isgt).  (If the given operator
-			 * from the old linear search.)
+			 * isn't actually sort-compatible with the histogram, you'll get
+			 * garbage results ... but probably not any more garbage-y than
+			 * you would have from the old linear search.)
+			 *
+			 * In this loop, we pay no attention to whether the operator iseq
+			 * or not; that detail will be mopped up below.  (We cannot tell,
+			 * anyway, whether the operator thinks the values are equal.)
 			 *
 			 * If the binary search accesses the first or last histogram
 			 * entry, we try to replace that endpoint with the true column min
@@ -865,25 +876,74 @@ ineq_histogram_selectivity(PlannerInfo *root,
 
 			if (lobound <= 0)
 			{
-				/* Constant is below lower histogram boundary. */
+				/*
+				 * Constant is below lower histogram boundary.  More
+				 * precisely, we have found that no entry in the histogram
+				 * satisfies the inequality clause (if !isgt) or they all do
+				 * (if isgt).  We estimate that that's true of the entire
+				 * table, so set histfrac to 0.0 (which we'll flip to 1.0
+				 * below, if isgt).
+				 */
 				histfrac = 0.0;
 			}
 			else if (lobound >= sslot.nvalues)
 			{
-				/* Constant is above upper histogram boundary. */
+				/*
+				 * Inverse case: constant is above upper histogram boundary.
+				 */
 				histfrac = 1.0;
 			}
 			else
 			{
+				/* We have values[i-1] <= constant <= values[i]. */
 				int			i = lobound;
+				double		eq_selec = 0;
 				double		val,
 							high,
 							low;
 				double		binfrac;
 
 				/*
-				 * We have values[i-1] <= constant <= values[i].
+				 * In the cases where we'll need it below, obtain an estimate
+				 * of the selectivity of "x = constval".  We use a calculation
+				 * similar to what var_eq_const() does for a non-MCV constant,
+				 * ie, estimate that all distinct non-MCV values occur equally
+				 * often.  But multiplication by "1.0 - sumcommon - nullfrac"
+				 * will be done by our caller, so we shouldn't do that here.
+				 * Therefore we can't try to clamp the estimate by reference
+				 * to the least common MCV; the result would be too small.
 				 *
+				 * Note: since this is effectively assuming that constval
+				 * isn't an MCV, it's logically dubious if constval in fact is
+				 * one.  But we have to apply *some* correction for equality,
+				 * and anyway we cannot tell if constval is an MCV, since we
+				 * don't have a suitable equality operator at hand.
+				 */
+				if (i == 1 || isgt == iseq)
+				{
+					double		otherdistinct;
+					bool		isdefault;
+					AttStatsSlot mcvslot;
+
+					/* Get estimated number of distinct values */
+					otherdistinct = get_variable_numdistinct(vardata,
+															 &isdefault);
+
+					/* Subtract off the number of known MCVs */
+					if (get_attstatsslot(&mcvslot, vardata->statsTuple,
+										 STATISTIC_KIND_MCV, InvalidOid,
+										 ATTSTATSSLOT_NUMBERS))
+					{
+						otherdistinct -= mcvslot.nnumbers;
+						free_attstatsslot(&mcvslot);
+					}
+
+					/* If result doesn't seem sane, leave eq_selec at 0 */
+					if (otherdistinct > 1)
+						eq_selec = 1.0 / otherdistinct;
+				}
+
+				/*
 				 * Convert the constant and the two nearest bin boundary
 				 * values to a uniform comparison scale, and do a linear
 				 * interpolation within this bin.
@@ -937,13 +997,54 @@ ineq_histogram_selectivity(PlannerInfo *root,
 				 */
 				histfrac = (double) (i - 1) + binfrac;
 				histfrac /= (double) (sslot.nvalues - 1);
+
+				/*
+				 * At this point, histfrac is an estimate of the fraction of
+				 * the population represented by the histogram that satisfies
+				 * "x <= constval".  Somewhat remarkably, this statement is
+				 * true regardless of which operator we were doing the probes
+				 * with, so long as convert_to_scalar() delivers reasonable
+				 * results.  If the probe constant is equal to some histogram
+				 * entry, we would have considered the bin to the left of that
+				 * entry if probing with "<" or ">=", or the bin to the right
+				 * if probing with "<=" or ">"; but binfrac would have come
+				 * out as 1.0 in the first case and 0.0 in the second, leading
+				 * to the same histfrac in either case.  For probe constants
+				 * between histogram entries, we find the same bin and get the
+				 * same estimate with any operator.
+				 *
+				 * The fact that the estimate corresponds to "x <= constval"
+				 * and not "x < constval" is because of the way that ANALYZE
+				 * constructs the histogram: each entry is, effectively, the
+				 * rightmost value in its sample bucket.  So selectivity
+				 * values that are exact multiples of 1/(histogram_size-1)
+				 * should be understood as estimates including a histogram
+				 * entry plus everything to its left.
+				 *
+				 * However, that breaks down for the first histogram entry,
+				 * which necessarily is the leftmost value in its sample
+				 * bucket.  That means the first histogram bin is slightly
+				 * narrower than the rest, by an amount equal to eq_selec.
+				 * Another way to say that is that we want "x <= leftmost" to
+				 * be estimated as eq_selec not zero.  So, if we're dealing
+				 * with the first bin (i==1), rescale to make that true while
+				 * adjusting the rest of that bin linearly.
+				 */
+				if (i == 1)
+					histfrac += eq_selec * (1.0 - binfrac);
+
+				/*
+				 * "x <= constval" is good if we want an estimate for "<=" or
+				 * ">", but if we are estimating for "<" or ">=", we now need
+				 * to decrease the estimate by eq_selec.
+				 */
+				if (isgt == iseq)
+					histfrac -= eq_selec;
 			}
 
 			/*
-			 * Now histfrac = fraction of histogram entries below the
+			 * Now the estimate is finished for "<" and "<=" cases.  If we are
-			 * constant.
+			 * estimating for ">" or ">=", flip it.
-			 *
-			 * Account for "<" vs ">"
 			 */
 			hist_selec = isgt ? (1.0 - histfrac) : histfrac;
 
@@ -951,16 +1052,21 @@ ineq_histogram_selectivity(PlannerInfo *root,
 			 * 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 --- unless we
-			 * got actual current endpoint values from the table.
+			 * got actual current endpoint values from the table, in which
+			 * case just do the usual sanity clamp.  Somewhat arbitrarily, we
+			 * set the cutoff for other cases at a hundredth of the histogram
+			 * resolution.
 			 */
 			if (have_end)
 				CLAMP_PROBABILITY(hist_selec);
 			else
 			{
-				if (hist_selec < 0.0001)
+				double		cutoff = 0.01 / (double) (sslot.nvalues - 1);
-					hist_selec = 0.0001;
+
-				else if (hist_selec > 0.9999)
+				if (hist_selec < cutoff)
-					hist_selec = 0.9999;
+					hist_selec = cutoff;
+				else if (hist_selec > 1.0 - cutoff)
+					hist_selec = 1.0 - cutoff;
 			}
 		}
 
@@ -971,10 +1077,11 @@ ineq_histogram_selectivity(PlannerInfo *root,
 }
 
 /*
- *		scalarltsel		- Selectivity of "<" (also "<=") for scalars.
+ * Common wrapper function for the selectivity estimators that simply
+ * invoke scalarineqsel().
  */
-Datum
+static Datum
-scalarltsel(PG_FUNCTION_ARGS)
+scalarineqsel_wrapper(PG_FUNCTION_ARGS, bool isgt, bool iseq)
 {
 	PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
 	Oid			operator = PG_GETARG_OID(1);
@@ -985,7 +1092,6 @@ scalarltsel(PG_FUNCTION_ARGS)
 	bool		varonleft;
 	Datum		constval;
 	Oid			consttype;
-	bool		isgt;
 	double		selec;
 
 	/*
@@ -1020,14 +1126,8 @@ scalarltsel(PG_FUNCTION_ARGS)
 	/*
 	 * Force the var to be on the left to simplify logic in scalarineqsel.
 	 */
-	if (varonleft)
+	if (!varonleft)
 	{
-		/* we have var < other */
-		isgt = false;
-	}
-	else
-	{
-		/* we have other < var, commute to make var > other */
 		operator = get_commutator(operator);
 		if (!operator)
 		{
@@ -1035,10 +1135,12 @@ scalarltsel(PG_FUNCTION_ARGS)
 			ReleaseVariableStats(vardata);
 			PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
 		}
-		isgt = true;
+		isgt = !isgt;
 	}
 
-	selec = scalarineqsel(root, operator, isgt, &vardata, constval, consttype);
+	/* The rest of the work is done by scalarineqsel(). */
+	selec = scalarineqsel(root, operator, isgt, iseq,
+						  &vardata, constval, consttype);
 
 	ReleaseVariableStats(vardata);
 
@@ -1046,78 +1148,39 @@ scalarltsel(PG_FUNCTION_ARGS)
 }
 
 /*
- *		scalargtsel		- Selectivity of ">" (also ">=") for integers.
+ *		scalarltsel		- Selectivity of "<" for scalars.
  */
 Datum
-scalargtsel(PG_FUNCTION_ARGS)
+scalarltsel(PG_FUNCTION_ARGS)
 {
-	PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
+	return scalarineqsel_wrapper(fcinfo, false, false);
-	Oid			operator = PG_GETARG_OID(1);
+}
-	List	   *args = (List *) PG_GETARG_POINTER(2);
-	int			varRelid = PG_GETARG_INT32(3);
-	VariableStatData vardata;
-	Node	   *other;
-	bool		varonleft;
-	Datum		constval;
-	Oid			consttype;
-	bool		isgt;
-	double		selec;
-
-	/*
-	 * If expression is not variable op something or something op variable,
-	 * then punt and return a default estimate.
-	 */
-	if (!get_restriction_variable(root, args, varRelid,
-								  &vardata, &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))
-	{
-		ReleaseVariableStats(vardata);
-		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)
-	{
-		ReleaseVariableStats(vardata);
-		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?) */
-			ReleaseVariableStats(vardata);
-			PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
-		}
-		isgt = false;
-	}
 
-	selec = scalarineqsel(root, operator, isgt, &vardata, constval, consttype);
+/*
+ *		scalarlesel		- Selectivity of "<=" for scalars.
+ */
+Datum
+scalarlesel(PG_FUNCTION_ARGS)
+{
+	return scalarineqsel_wrapper(fcinfo, false, true);
+}
 
-	ReleaseVariableStats(vardata);
+/*
+ *		scalargtsel		- Selectivity of ">" for scalars.
+ */
+Datum
+scalargtsel(PG_FUNCTION_ARGS)
+{
+	return scalarineqsel_wrapper(fcinfo, true, false);
+}
 
-	PG_RETURN_FLOAT8((float8) selec);
+/*
+ *		scalargesel		- Selectivity of ">=" for scalars.
+ */
+Datum
+scalargesel(PG_FUNCTION_ARGS)
+{
+	return scalarineqsel_wrapper(fcinfo, true, true);
 }
 
 /*
@@ -2722,7 +2785,7 @@ neqjoinsel(PG_FUNCTION_ARGS)
 }
 
 /*
- *		scalarltjoinsel - Join selectivity of "<" and "<=" for scalars
+ *		scalarltjoinsel - Join selectivity of "<" for scalars
  */
 Datum
 scalarltjoinsel(PG_FUNCTION_ARGS)
@@ -2731,7 +2794,16 @@ scalarltjoinsel(PG_FUNCTION_ARGS)
 }
 
 /*
- *		scalargtjoinsel - Join selectivity of ">" and ">=" for scalars
+ *		scalarlejoinsel - Join selectivity of "<=" for scalars
+ */
+Datum
+scalarlejoinsel(PG_FUNCTION_ARGS)
+{
+	PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
+}
+
+/*
+ *		scalargtjoinsel - Join selectivity of ">" for scalars
  */
 Datum
 scalargtjoinsel(PG_FUNCTION_ARGS)
@@ -2739,6 +2811,15 @@ scalargtjoinsel(PG_FUNCTION_ARGS)
 	PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
 }
 
+/*
+ *		scalargejoinsel - Join selectivity of ">=" for scalars
+ */
+Datum
+scalargejoinsel(PG_FUNCTION_ARGS)
+{
+	PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
+}
+
 /*
  * patternjoinsel		- Generic code for pattern-match join selectivity.
  */
@@ -3036,13 +3117,13 @@ mergejoinscansel(PlannerInfo *root, Node *clause,
 	 * fraction that's <= the right-side maximum value.  But only believe
 	 * non-default estimates, else stick with our 1.0.
 	 */
-	selec = scalarineqsel(root, leop, isgt, &leftvar,
+	selec = scalarineqsel(root, leop, isgt, true, &leftvar,
 						  rightmax, op_righttype);
 	if (selec != DEFAULT_INEQ_SEL)
 		*leftend = selec;
 
 	/* And similarly for the right variable. */
-	selec = scalarineqsel(root, revleop, isgt, &rightvar,
+	selec = scalarineqsel(root, revleop, isgt, true, &rightvar,
 						  leftmax, op_lefttype);
 	if (selec != DEFAULT_INEQ_SEL)
 		*rightend = selec;
@@ -3066,13 +3147,13 @@ mergejoinscansel(PlannerInfo *root, Node *clause,
 	 * minimum value.  But only believe non-default estimates, else stick with
 	 * our own default.
 	 */
-	selec = scalarineqsel(root, ltop, isgt, &leftvar,
+	selec = scalarineqsel(root, ltop, isgt, false, &leftvar,
 						  rightmin, op_righttype);
 	if (selec != DEFAULT_INEQ_SEL)
 		*leftstart = selec;
 
 	/* And similarly for the right variable. */
-	selec = scalarineqsel(root, revltop, isgt, &rightvar,
+	selec = scalarineqsel(root, revltop, isgt, false, &rightvar,
 						  leftmin, op_lefttype);
 	if (selec != DEFAULT_INEQ_SEL)
 		*rightstart = selec;
@@ -4029,8 +4110,8 @@ convert_numeric_to_scalar(Datum value, Oid typid)
 	}
 
 	/*
-	 * Can't get here unless someone tries to use scalarltsel/scalargtsel on
+	 * Can't get here unless someone tries to use scalarineqsel() on an
-	 * an operator with one numeric and one non-numeric operand.
+	 * operator with one numeric and one non-numeric operand.
 	 */
 	elog(ERROR, "unsupported type: %u", typid);
 	return 0;
@@ -4211,8 +4292,8 @@ convert_string_datum(Datum value, Oid typid)
 		default:
 
 			/*
-			 * Can't get here unless someone tries to use scalarltsel on an
+			 * Can't get here unless someone tries to use scalarineqsel() on
-			 * operator with one string and one non-string operand.
+			 * an operator with one string and one non-string operand.
 			 */
 			elog(ERROR, "unsupported type: %u", typid);
 			return NULL;
@@ -4416,8 +4497,8 @@ convert_timevalue_to_scalar(Datum value, Oid typid)
 	}
 
 	/*
-	 * Can't get here unless someone tries to use scalarltsel/scalargtsel on
+	 * Can't get here unless someone tries to use scalarineqsel() on an
-	 * an operator with one timevalue and one non-timevalue operand.
+	 * operator with one timevalue and one non-timevalue operand.
 	 */
 	elog(ERROR, "unsupported type: %u", typid);
 	return 0;
@@ -5806,7 +5887,8 @@ prefix_selectivity(PlannerInfo *root, VariableStatData *vardata,
 		elog(ERROR, "no >= operator for opfamily %u", opfamily);
 	fmgr_info(get_opcode(cmpopr), &opproc);
 
-	prefixsel = ineq_histogram_selectivity(root, vardata, &opproc, true,
+	prefixsel = ineq_histogram_selectivity(root, vardata,
+										   &opproc, true, true,
 										   prefixcon->constvalue,
 										   prefixcon->consttype);
 
@@ -5832,7 +5914,8 @@ prefix_selectivity(PlannerInfo *root, VariableStatData *vardata,
 	{
 		Selectivity topsel;
 
-		topsel = ineq_histogram_selectivity(root, vardata, &opproc, false,
+		topsel = ineq_histogram_selectivity(root, vardata,
+											&opproc, false, false,
 											greaterstrcon->constvalue,
 											greaterstrcon->consttype);
 

src/include/catalog/catversion.h

@@ -53,6 +53,6 @@
  */
 
 /*							yyyymmddN */
-#define CATALOG_VERSION_NO	201709081
+#define CATALOG_VERSION_NO	201709131
 
 #endif

src/include/catalog/pg_operator.h

@@ -97,9 +97,9 @@ DATA(insert OID =  37 ( "<"		   PGNSP PGUID b f f	23	20	16 419	82 int48lt scalar
 DESCR("less than");
 DATA(insert OID =  76 ( ">"		   PGNSP PGUID b f f	23	20	16 418	80 int48gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID =  80 ( "<="	   PGNSP PGUID b f f	23	20	16 430	76 int48le scalarltsel scalarltjoinsel ));
+DATA(insert OID =  80 ( "<="	   PGNSP PGUID b f f	23	20	16 430	76 int48le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID =  82 ( ">="	   PGNSP PGUID b f f	23	20	16 420	37 int48ge scalargtsel scalargtjoinsel ));
+DATA(insert OID =  82 ( ">="	   PGNSP PGUID b f f	23	20	16 420	37 int48ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 DATA(insert OID =  58 ( "<"		   PGNSP PGUID b f f	16	16	16	59	1695 boollt scalarltsel scalarltjoinsel ));
@@ -112,9 +112,9 @@ DESCR("not equal");
 DATA(insert OID =  91 ( "="		   PGNSP PGUID b t t	16	16	16	91	85 booleq eqsel eqjoinsel ));
 DESCR("equal");
 #define BooleanEqualOperator   91
-DATA(insert OID = 1694 (  "<="	   PGNSP PGUID b f f	16	16	16 1695 59 boolle scalarltsel scalarltjoinsel ));
+DATA(insert OID = 1694 (  "<="	   PGNSP PGUID b f f	16	16	16 1695 59 boolle scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 1695 (  ">="	   PGNSP PGUID b f f	16	16	16 1694 58 boolge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 1695 (  ">="	   PGNSP PGUID b f f	16	16	16 1694 58 boolge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 DATA(insert OID =  92 ( "="		   PGNSP PGUID b t t	18	18	16	92 630 chareq eqsel eqjoinsel ));
@@ -167,9 +167,9 @@ DESCR("less than");
 #define TIDLessOperator    2799
 DATA(insert OID = 2800 (  ">"	   PGNSP PGUID b f f	27	27	16 2799 2801 tidgt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 2801 (  "<="	   PGNSP PGUID b f f	27	27	16 2802 2800 tidle scalarltsel scalarltjoinsel ));
+DATA(insert OID = 2801 (  "<="	   PGNSP PGUID b f f	27	27	16 2802 2800 tidle scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 2802 (  ">="	   PGNSP PGUID b f f	27	27	16 2801 2799 tidge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 2802 (  ">="	   PGNSP PGUID b f f	27	27	16 2801 2799 tidge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 DATA(insert OID = 410 ( "="		   PGNSP PGUID b t t	20	20	16 410 411 int8eq eqsel eqjoinsel ));
@@ -181,9 +181,9 @@ DESCR("less than");
 #define Int8LessOperator	412
 DATA(insert OID = 413 ( ">"		   PGNSP PGUID b f f	20	20	16 412 414 int8gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 414 ( "<="	   PGNSP PGUID b f f	20	20	16 415 413 int8le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 414 ( "<="	   PGNSP PGUID b f f	20	20	16 415 413 int8le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 415 ( ">="	   PGNSP PGUID b f f	20	20	16 414 412 int8ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 415 ( ">="	   PGNSP PGUID b f f	20	20	16 414 412 int8ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 DATA(insert OID = 416 ( "="		   PGNSP PGUID b t t	20	23	16	15 417 int84eq eqsel eqjoinsel ));
@@ -194,9 +194,9 @@ DATA(insert OID = 418 ( "<"		   PGNSP PGUID b f f	20	23	16	76 430 int84lt scalar
 DESCR("less than");
 DATA(insert OID = 419 ( ">"		   PGNSP PGUID b f f	20	23	16	37 420 int84gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 420 ( "<="	   PGNSP PGUID b f f	20	23	16	82 419 int84le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 420 ( "<="	   PGNSP PGUID b f f	20	23	16	82 419 int84le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 430 ( ">="	   PGNSP PGUID b f f	20	23	16	80 418 int84ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 430 ( ">="	   PGNSP PGUID b f f	20	23	16	80 418 int84ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 439 (  "%"	   PGNSP PGUID b f f	20	20	20	 0	 0 int8mod - - ));
 DESCR("modulus");
@@ -277,13 +277,13 @@ DATA(insert OID = 520 (  ">"	   PGNSP PGUID b f f	21	21	16	95 522 int2gt scalarg
 DESCR("greater than");
 DATA(insert OID = 521 (  ">"	   PGNSP PGUID b f f	23	23	16	97 523 int4gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 522 (  "<="	   PGNSP PGUID b f f	21	21	16 524 520 int2le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 522 (  "<="	   PGNSP PGUID b f f	21	21	16 524 520 int2le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 523 (  "<="	   PGNSP PGUID b f f	23	23	16 525 521 int4le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 523 (  "<="	   PGNSP PGUID b f f	23	23	16 525 521 int4le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 524 (  ">="	   PGNSP PGUID b f f	21	21	16 522	95 int2ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 524 (  ">="	   PGNSP PGUID b f f	21	21	16 522	95 int2ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
-DATA(insert OID = 525 (  ">="	   PGNSP PGUID b f f	23	23	16 523	97 int4ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 525 (  ">="	   PGNSP PGUID b f f	23	23	16 523	97 int4ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 526 (  "*"	   PGNSP PGUID b f f	21	21	21 526	 0 int2mul - - ));
 DESCR("multiply");
@@ -313,13 +313,13 @@ DATA(insert OID = 538 (  "<>"	   PGNSP PGUID b f f	21	23	16 539 532 int24ne neqs
 DESCR("not equal");
 DATA(insert OID = 539 (  "<>"	   PGNSP PGUID b f f	23	21	16 538 533 int42ne neqsel neqjoinsel ));
 DESCR("not equal");
-DATA(insert OID = 540 (  "<="	   PGNSP PGUID b f f	21	23	16 543 536 int24le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 540 (  "<="	   PGNSP PGUID b f f	21	23	16 543 536 int24le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 541 (  "<="	   PGNSP PGUID b f f	23	21	16 542 537 int42le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 541 (  "<="	   PGNSP PGUID b f f	23	21	16 542 537 int42le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 542 (  ">="	   PGNSP PGUID b f f	21	23	16 541 534 int24ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 542 (  ">="	   PGNSP PGUID b f f	21	23	16 541 534 int24ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
-DATA(insert OID = 543 (  ">="	   PGNSP PGUID b f f	23	21	16 540 535 int42ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 543 (  ">="	   PGNSP PGUID b f f	23	21	16 540 535 int42ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 544 (  "*"	   PGNSP PGUID b f f	21	23	23 545	 0 int24mul - - ));
 DESCR("multiply");
@@ -357,9 +357,9 @@ DATA(insert OID = 562 (  "<"	   PGNSP PGUID b f f 702 702	16 563 565 abstimelt s
 DESCR("less than");
 DATA(insert OID = 563 (  ">"	   PGNSP PGUID b f f 702 702	16 562 564 abstimegt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 564 (  "<="	   PGNSP PGUID b f f 702 702	16 565 563 abstimele scalarltsel scalarltjoinsel ));
+DATA(insert OID = 564 (  "<="	   PGNSP PGUID b f f 702 702	16 565 563 abstimele scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 565 (  ">="	   PGNSP PGUID b f f 702 702	16 564 562 abstimege scalargtsel scalargtjoinsel ));
+DATA(insert OID = 565 (  ">="	   PGNSP PGUID b f f 702 702	16 564 562 abstimege scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 566 (  "="	   PGNSP PGUID b t t 703 703	16 566 567 reltimeeq eqsel eqjoinsel ));
 DESCR("equal");
@@ -369,9 +369,9 @@ DATA(insert OID = 568 (  "<"	   PGNSP PGUID b f f 703 703	16 569 571 reltimelt s
 DESCR("less than");
 DATA(insert OID = 569 (  ">"	   PGNSP PGUID b f f 703 703	16 568 570 reltimegt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 570 (  "<="	   PGNSP PGUID b f f 703 703	16 571 569 reltimele scalarltsel scalarltjoinsel ));
+DATA(insert OID = 570 (  "<="	   PGNSP PGUID b f f 703 703	16 571 569 reltimele scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 571 (  ">="	   PGNSP PGUID b f f 703 703	16 570 568 reltimege scalargtsel scalargtjoinsel ));
+DATA(insert OID = 571 (  ">="	   PGNSP PGUID b f f 703 703	16 570 568 reltimege scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 572 (  "~="	   PGNSP PGUID b f f 704 704	16 572	 0 tintervalsame eqsel eqjoinsel ));
 DESCR("same as");
@@ -438,9 +438,9 @@ DATA(insert OID = 609 (  "<"	   PGNSP PGUID b f f	26	26	16 610 612 oidlt scalarl
 DESCR("less than");
 DATA(insert OID = 610 (  ">"	   PGNSP PGUID b f f	26	26	16 609 611 oidgt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 611 (  "<="	   PGNSP PGUID b f f	26	26	16 612 610 oidle scalarltsel scalarltjoinsel ));
+DATA(insert OID = 611 (  "<="	   PGNSP PGUID b f f	26	26	16 612 610 oidle scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 612 (  ">="	   PGNSP PGUID b f f	26	26	16 611 609 oidge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 612 (  ">="	   PGNSP PGUID b f f	26	26	16 611 609 oidge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 DATA(insert OID = 644 (  "<>"	   PGNSP PGUID b f f	30	30	16 644 649 oidvectorne neqsel neqjoinsel ));
@@ -449,9 +449,9 @@ DATA(insert OID = 645 (  "<"	   PGNSP PGUID b f f	30	30	16 646 648 oidvectorlt s
 DESCR("less than");
 DATA(insert OID = 646 (  ">"	   PGNSP PGUID b f f	30	30	16 645 647 oidvectorgt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 647 (  "<="	   PGNSP PGUID b f f	30	30	16 648 646 oidvectorle scalarltsel scalarltjoinsel ));
+DATA(insert OID = 647 (  "<="	   PGNSP PGUID b f f	30	30	16 648 646 oidvectorle scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 648 (  ">="	   PGNSP PGUID b f f	30	30	16 647 645 oidvectorge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 648 (  ">="	   PGNSP PGUID b f f	30	30	16 647 645 oidvectorge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 649 (  "="	   PGNSP PGUID b t t	30	30	16 649 644 oidvectoreq eqsel eqjoinsel ));
 DESCR("equal");
@@ -477,20 +477,20 @@ DATA(insert OID = 622 (  "<"	   PGNSP PGUID b f f	700  700	16 623 625 float4lt s
 DESCR("less than");
 DATA(insert OID = 623 (  ">"	   PGNSP PGUID b f f	700  700	16 622 624 float4gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 624 (  "<="	   PGNSP PGUID b f f	700  700	16 625 623 float4le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 624 (  "<="	   PGNSP PGUID b f f	700  700	16 625 623 float4le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 625 (  ">="	   PGNSP PGUID b f f	700  700	16 624 622 float4ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 625 (  ">="	   PGNSP PGUID b f f	700  700	16 624 622 float4ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 630 (  "<>"	   PGNSP PGUID b f f	18	18		16 630	92	charne neqsel neqjoinsel ));
 DESCR("not equal");
 
 DATA(insert OID = 631 (  "<"	   PGNSP PGUID b f f	18	18	16 633 634 charlt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 632 (  "<="	   PGNSP PGUID b f f	18	18	16 634 633 charle scalarltsel scalarltjoinsel ));
+DATA(insert OID = 632 (  "<="	   PGNSP PGUID b f f	18	18	16 634 633 charle scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 633 (  ">"	   PGNSP PGUID b f f	18	18	16 631 632 chargt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 634 (  ">="	   PGNSP PGUID b f f	18	18	16 632 631 charge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 634 (  ">="	   PGNSP PGUID b f f	18	18	16 632 631 charge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 DATA(insert OID = 639 (  "~"	   PGNSP PGUID b f f	19	25	16 0 640 nameregexeq regexeqsel regexeqjoinsel ));
@@ -510,19 +510,19 @@ DESCR("concatenate");
 
 DATA(insert OID = 660 (  "<"	   PGNSP PGUID b f f	19	19	16 662 663 namelt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 661 (  "<="	   PGNSP PGUID b f f	19	19	16 663 662 namele scalarltsel scalarltjoinsel ));
+DATA(insert OID = 661 (  "<="	   PGNSP PGUID b f f	19	19	16 663 662 namele scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 662 (  ">"	   PGNSP PGUID b f f	19	19	16 660 661 namegt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 663 (  ">="	   PGNSP PGUID b f f	19	19	16 661 660 namege scalargtsel scalargtjoinsel ));
+DATA(insert OID = 663 (  ">="	   PGNSP PGUID b f f	19	19	16 661 660 namege scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 664 (  "<"	   PGNSP PGUID b f f	25	25	16 666 667 text_lt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 665 (  "<="	   PGNSP PGUID b f f	25	25	16 667 666 text_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 665 (  "<="	   PGNSP PGUID b f f	25	25	16 667 666 text_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 666 (  ">"	   PGNSP PGUID b f f	25	25	16 664 665 text_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 667 (  ">="	   PGNSP PGUID b f f	25	25	16 665 664 text_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 667 (  ">="	   PGNSP PGUID b f f	25	25	16 665 664 text_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 DATA(insert OID = 670 (  "="	   PGNSP PGUID b t t	701  701	16 670 671 float8eq eqsel eqjoinsel ));
@@ -532,11 +532,11 @@ DESCR("not equal");
 DATA(insert OID = 672 (  "<"	   PGNSP PGUID b f f	701  701	16 674 675 float8lt scalarltsel scalarltjoinsel ));
 DESCR("less than");
 #define Float8LessOperator	672
-DATA(insert OID = 673 (  "<="	   PGNSP PGUID b f f	701  701	16 675 674 float8le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 673 (  "<="	   PGNSP PGUID b f f	701  701	16 675 674 float8le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 674 (  ">"	   PGNSP PGUID b f f	701  701	16 672 673 float8gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 675 (  ">="	   PGNSP PGUID b f f	701  701	16 673 672 float8ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 675 (  ">="	   PGNSP PGUID b f f	701  701	16 673 672 float8ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 DATA(insert OID = 682 (  "@"	   PGNSP PGUID l f f	 0	21	21	 0	 0 int2abs - - ));
@@ -677,9 +677,9 @@ DATA(insert OID = 813 (  "<"	   PGNSP PGUID b f f 704 704	16 814 816 tintervallt
 DESCR("less than");
 DATA(insert OID = 814 (  ">"	   PGNSP PGUID b f f 704 704	16 813 815 tintervalgt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 815 (  "<="	   PGNSP PGUID b f f 704 704	16 816 814 tintervalle scalarltsel scalarltjoinsel ));
+DATA(insert OID = 815 (  "<="	   PGNSP PGUID b f f 704 704	16 816 814 tintervalle scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 816 (  ">="	   PGNSP PGUID b f f 704 704	16 815 813 tintervalge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 816 (  ">="	   PGNSP PGUID b f f 704 704	16 815 813 tintervalge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 DATA(insert OID = 843 (  "*"	   PGNSP PGUID b f f	790  700	790 845   0 cash_mul_flt4 - - ));
@@ -697,9 +697,9 @@ DATA(insert OID = 902 (  "<"	   PGNSP PGUID b f f	790  790	16 903 905 cash_lt sc
 DESCR("less than");
 DATA(insert OID = 903 (  ">"	   PGNSP PGUID b f f	790  790	16 902 904 cash_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 904 (  "<="	   PGNSP PGUID b f f	790  790	16 905 903 cash_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 904 (  "<="	   PGNSP PGUID b f f	790  790	16 905 903 cash_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 905 (  ">="	   PGNSP PGUID b f f	790  790	16 904 902 cash_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 905 (  ">="	   PGNSP PGUID b f f	790  790	16 904 902 cash_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 906 (  "+"	   PGNSP PGUID b f f	790  790	790 906   0 cash_pl - - ));
 DESCR("add");
@@ -763,11 +763,11 @@ DATA(insert OID = 1057 ( "<>"	   PGNSP PGUID b f f 1042 1042	 16 1057 1054 bpcha
 DESCR("not equal");
 DATA(insert OID = 1058 ( "<"	   PGNSP PGUID b f f 1042 1042	 16 1060 1061 bpcharlt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 1059 ( "<="	   PGNSP PGUID b f f 1042 1042	 16 1061 1060 bpcharle scalarltsel scalarltjoinsel ));
+DATA(insert OID = 1059 ( "<="	   PGNSP PGUID b f f 1042 1042	 16 1061 1060 bpcharle scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 1060 ( ">"	   PGNSP PGUID b f f 1042 1042	 16 1058 1059 bpchargt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 1061 ( ">="	   PGNSP PGUID b f f 1042 1042	 16 1059 1058 bpcharge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 1061 ( ">="	   PGNSP PGUID b f f 1042 1042	 16 1059 1058 bpcharge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 /* generic array comparison operators */
@@ -782,9 +782,9 @@ DESCR("less than");
 DATA(insert OID = 1073 (  ">"	   PGNSP PGUID b f f 2277 2277 16 1072 1074 array_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
 #define ARRAY_GT_OP 1073
-DATA(insert OID = 1074 (  "<="	   PGNSP PGUID b f f 2277 2277 16 1075 1073 array_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 1074 (  "<="	   PGNSP PGUID b f f 2277 2277 16 1075 1073 array_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 1075 (  ">="	   PGNSP PGUID b f f 2277 2277 16 1074 1072 array_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 1075 (  ">="	   PGNSP PGUID b f f 2277 2277 16 1074 1072 array_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 /* date operators */
@@ -798,11 +798,11 @@ DATA(insert OID = 1094 ( "<>"	   PGNSP PGUID b f f	1082	1082   16 1094 1093 date
 DESCR("not equal");
 DATA(insert OID = 1095 ( "<"	   PGNSP PGUID b f f	1082	1082   16 1097 1098 date_lt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 1096 ( "<="	   PGNSP PGUID b f f	1082	1082   16 1098 1097 date_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 1096 ( "<="	   PGNSP PGUID b f f	1082	1082   16 1098 1097 date_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 1097 ( ">"	   PGNSP PGUID b f f	1082	1082   16 1095 1096 date_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 1098 ( ">="	   PGNSP PGUID b f f	1082	1082   16 1096 1095 date_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 1098 ( ">="	   PGNSP PGUID b f f	1082	1082   16 1096 1095 date_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 1099 ( "-"	   PGNSP PGUID b f f	1082	1082   23 0 0 date_mi - - ));
 DESCR("subtract");
@@ -818,11 +818,11 @@ DATA(insert OID = 1109 ( "<>"	   PGNSP PGUID b f f	1083	1083  16 1109 1108 time_
 DESCR("not equal");
 DATA(insert OID = 1110 ( "<"	   PGNSP PGUID b f f	1083	1083  16 1112 1113 time_lt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 1111 ( "<="	   PGNSP PGUID b f f	1083	1083  16 1113 1112 time_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 1111 ( "<="	   PGNSP PGUID b f f	1083	1083  16 1113 1112 time_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 1112 ( ">"	   PGNSP PGUID b f f	1083	1083  16 1110 1111 time_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 1113 ( ">="	   PGNSP PGUID b f f	1083	1083  16 1111 1110 time_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 1113 ( ">="	   PGNSP PGUID b f f	1083	1083  16 1111 1110 time_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 /* timetz operators */
@@ -832,11 +832,11 @@ DATA(insert OID = 1551 ( "<>"	   PGNSP PGUID b f f	1266 1266	16 1551 1550 timetz
 DESCR("not equal");
 DATA(insert OID = 1552 ( "<"	   PGNSP PGUID b f f	1266 1266	16 1554 1555 timetz_lt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 1553 ( "<="	   PGNSP PGUID b f f	1266 1266	16 1555 1554 timetz_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 1553 ( "<="	   PGNSP PGUID b f f	1266 1266	16 1555 1554 timetz_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 1554 ( ">"	   PGNSP PGUID b f f	1266 1266	16 1552 1553 timetz_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 1555 ( ">="	   PGNSP PGUID b f f	1266 1266	16 1553 1552 timetz_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 1555 ( ">="	   PGNSP PGUID b f f	1266 1266	16 1553 1552 timetz_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 /* float48 operators */
@@ -856,9 +856,9 @@ DATA(insert OID = 1122 (  "<"		PGNSP PGUID b f f  700	701  16 1133 1125 float48l
 DESCR("less than");
 DATA(insert OID = 1123 (  ">"		PGNSP PGUID b f f  700	701  16 1132 1124 float48gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 1124 (  "<="		PGNSP PGUID b f f  700	701  16 1135 1123 float48le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 1124 (  "<="		PGNSP PGUID b f f  700	701  16 1135 1123 float48le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 1125 (  ">="		PGNSP PGUID b f f  700	701  16 1134 1122 float48ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 1125 (  ">="		PGNSP PGUID b f f  700	701  16 1134 1122 float48ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 /* float84 operators */
@@ -878,9 +878,9 @@ DATA(insert OID = 1132 (  "<"		PGNSP PGUID b f f  701	700  16 1123 1135 float84l
 DESCR("less than");
 DATA(insert OID = 1133 (  ">"		PGNSP PGUID b f f  701	700  16 1122 1134 float84gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 1134 (  "<="		PGNSP PGUID b f f  701	700  16 1125 1133 float84le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 1134 (  "<="		PGNSP PGUID b f f  701	700  16 1125 1133 float84le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 1135 (  ">="		PGNSP PGUID b f f  701	700  16 1124 1132 float84ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 1135 (  ">="		PGNSP PGUID b f f  701	700  16 1124 1132 float84ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 
@@ -925,11 +925,11 @@ DATA(insert OID = 1321 (  "<>"	   PGNSP PGUID b f f 1184 1184	 16 1321 1320 time
 DESCR("not equal");
 DATA(insert OID = 1322 (  "<"	   PGNSP PGUID b f f 1184 1184	 16 1324 1325 timestamptz_lt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 1323 (  "<="	   PGNSP PGUID b f f 1184 1184	 16 1325 1324 timestamptz_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 1323 (  "<="	   PGNSP PGUID b f f 1184 1184	 16 1325 1324 timestamptz_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 1324 (  ">"	   PGNSP PGUID b f f 1184 1184	 16 1322 1323 timestamptz_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 1325 (  ">="	   PGNSP PGUID b f f 1184 1184	 16 1323 1322 timestamptz_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 1325 (  ">="	   PGNSP PGUID b f f 1184 1184	 16 1323 1322 timestamptz_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 1327 (  "+"	   PGNSP PGUID b f f 1184 1186 1184  2554 0 timestamptz_pl_interval - - ));
 DESCR("add");
@@ -945,11 +945,11 @@ DATA(insert OID = 1331 (  "<>"	   PGNSP PGUID b f f 1186 1186	 16 1331 1330 inte
 DESCR("not equal");
 DATA(insert OID = 1332 (  "<"	   PGNSP PGUID b f f 1186 1186	 16 1334 1335 interval_lt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 1333 (  "<="	   PGNSP PGUID b f f 1186 1186	 16 1335 1334 interval_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 1333 (  "<="	   PGNSP PGUID b f f 1186 1186	 16 1335 1334 interval_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 1334 (  ">"	   PGNSP PGUID b f f 1186 1186	 16 1332 1333 interval_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 1335 (  ">="	   PGNSP PGUID b f f 1186 1186	 16 1333 1332 interval_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 1335 (  ">="	   PGNSP PGUID b f f 1186 1186	 16 1333 1332 interval_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 DATA(insert OID = 1336 (  "-"	   PGNSP PGUID l f f	0 1186 1186    0	0 interval_um - - ));
@@ -1126,11 +1126,11 @@ DATA(insert OID = 1221 (  "<>"	   PGNSP PGUID b f f 829 829	 16 1221 1220 macadd
 DESCR("not equal");
 DATA(insert OID = 1222 (  "<"	   PGNSP PGUID b f f 829 829	 16 1224 1225 macaddr_lt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 1223 (  "<="	   PGNSP PGUID b f f 829 829	 16 1225 1224 macaddr_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 1223 (  "<="	   PGNSP PGUID b f f 829 829	 16 1225 1224 macaddr_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 1224 (  ">"	   PGNSP PGUID b f f 829 829	 16 1222 1223 macaddr_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 1225 (  ">="	   PGNSP PGUID b f f 829 829	 16 1223 1222 macaddr_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 1225 (  ">="	   PGNSP PGUID b f f 829 829	 16 1223 1222 macaddr_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 DATA(insert OID = 3147 (  "~"	   PGNSP PGUID l f f	  0 829 829 0 0 macaddr_not - - ));
@@ -1147,11 +1147,11 @@ DATA(insert OID = 3363 (  "<>"	   PGNSP PGUID b f f 774 774	 16 3363 3362 macadd
 DESCR("not equal");
 DATA(insert OID = 3364 (  "<"	   PGNSP PGUID b f f 774 774	 16 3366 3367 macaddr8_lt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 3365 (  "<="	   PGNSP PGUID b f f 774 774	 16 3367 3366 macaddr8_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 3365 (  "<="	   PGNSP PGUID b f f 774 774	 16 3367 3366 macaddr8_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 3366 (  ">"	   PGNSP PGUID b f f 774 774	 16 3364 3365 macaddr8_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 3367 (  ">="	   PGNSP PGUID b f f 774 774	 16 3365 3364 macaddr8_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 3367 (  ">="	   PGNSP PGUID b f f 774 774	 16 3365 3364 macaddr8_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 DATA(insert OID = 3368 (  "~"	   PGNSP PGUID l f f	  0 774 774 0 0 macaddr8_not - - ));
@@ -1168,11 +1168,11 @@ DATA(insert OID = 1202 (  "<>"	   PGNSP PGUID b f f 869 869	 16 1202 1201 networ
 DESCR("not equal");
 DATA(insert OID = 1203 (  "<"	   PGNSP PGUID b f f 869 869	 16 1205 1206 network_lt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 1204 (  "<="	   PGNSP PGUID b f f 869 869	 16 1206 1205 network_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 1204 (  "<="	   PGNSP PGUID b f f 869 869	 16 1206 1205 network_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 1205 (  ">"	   PGNSP PGUID b f f 869 869	 16 1203 1204 network_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 1206 (  ">="	   PGNSP PGUID b f f 869 869	 16 1204 1203 network_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 1206 (  ">="	   PGNSP PGUID b f f 869 869	 16 1204 1203 network_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 931  (  "<<"	   PGNSP PGUID b f f 869 869	 16 933		0 network_sub networksel networkjoinsel ));
 DESCR("is subnet");
@@ -1231,11 +1231,11 @@ DATA(insert OID = 1753 (  "<>"	   PGNSP PGUID b f f 1700 1700	 16 1753 1752 nume
 DESCR("not equal");
 DATA(insert OID = 1754 (  "<"	   PGNSP PGUID b f f 1700 1700	 16 1756 1757 numeric_lt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 1755 (  "<="	   PGNSP PGUID b f f 1700 1700	 16 1757 1756 numeric_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 1755 (  "<="	   PGNSP PGUID b f f 1700 1700	 16 1757 1756 numeric_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 1756 (  ">"	   PGNSP PGUID b f f 1700 1700	 16 1754 1755 numeric_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 1757 (  ">="	   PGNSP PGUID b f f 1700 1700	 16 1755 1754 numeric_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 1757 (  ">="	   PGNSP PGUID b f f 1700 1700	 16 1755 1754 numeric_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 1758 (  "+"	   PGNSP PGUID b f f 1700 1700 1700 1758	0 numeric_add - - ));
 DESCR("add");
@@ -1260,9 +1260,9 @@ DATA(insert OID = 1786 (  "<"	  PGNSP PGUID b f f 1560 1560 16 1787 1789 bitlt s
 DESCR("less than");
 DATA(insert OID = 1787 (  ">"	  PGNSP PGUID b f f 1560 1560 16 1786 1788 bitgt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 1788 (  "<="	  PGNSP PGUID b f f 1560 1560 16 1789 1787 bitle scalarltsel scalarltjoinsel ));
+DATA(insert OID = 1788 (  "<="	  PGNSP PGUID b f f 1560 1560 16 1789 1787 bitle scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 1789 (  ">="	  PGNSP PGUID b f f 1560 1560 16 1788 1786 bitge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 1789 (  ">="	  PGNSP PGUID b f f 1560 1560 16 1788 1786 bitge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 1791 (  "&"	  PGNSP PGUID b f f 1560 1560 1560 1791  0 bitand - - ));
 DESCR("bitwise and");
@@ -1296,9 +1296,9 @@ DATA(insert OID = 1806 (  "<"	  PGNSP PGUID b f f 1562 1562 16 1807 1809 varbitl
 DESCR("less than");
 DATA(insert OID = 1807 (  ">"	  PGNSP PGUID b f f 1562 1562 16 1806 1808 varbitgt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 1808 (  "<="	  PGNSP PGUID b f f 1562 1562 16 1809 1807 varbitle scalarltsel scalarltjoinsel ));
+DATA(insert OID = 1808 (  "<="	  PGNSP PGUID b f f 1562 1562 16 1809 1807 varbitle scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 1809 (  ">="	  PGNSP PGUID b f f 1562 1562 16 1808 1806 varbitge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 1809 (  ">="	  PGNSP PGUID b f f 1562 1562 16 1808 1806 varbitge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 DATA(insert OID = 1849 (  "+"	   PGNSP PGUID b f f 1186 1083 1083  1800 0 interval_pl_time - - ));
@@ -1312,9 +1312,9 @@ DATA(insert OID = 1864 ( "<"	   PGNSP PGUID b f f	21	20	16 1871  1867 int28lt sc
 DESCR("less than");
 DATA(insert OID = 1865 ( ">"	   PGNSP PGUID b f f	21	20	16 1870  1866 int28gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 1866 ( "<="	   PGNSP PGUID b f f	21	20	16 1873  1865 int28le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 1866 ( "<="	   PGNSP PGUID b f f	21	20	16 1873  1865 int28le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 1867 ( ">="	   PGNSP PGUID b f f	21	20	16 1872  1864 int28ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 1867 ( ">="	   PGNSP PGUID b f f	21	20	16 1872  1864 int28ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 DATA(insert OID = 1868 ( "="	   PGNSP PGUID b t t	20	21	16	1862 1869 int82eq eqsel eqjoinsel ));
@@ -1325,9 +1325,9 @@ DATA(insert OID = 1870 ( "<"	   PGNSP PGUID b f f	20	21	16	1865 1873 int82lt sca
 DESCR("less than");
 DATA(insert OID = 1871 ( ">"	   PGNSP PGUID b f f	20	21	16	1864 1872 int82gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 1872 ( "<="	   PGNSP PGUID b f f	20	21	16	1867 1871 int82le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 1872 ( "<="	   PGNSP PGUID b f f	20	21	16	1867 1871 int82le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 1873 ( ">="	   PGNSP PGUID b f f	20	21	16	1866 1870 int82ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 1873 ( ">="	   PGNSP PGUID b f f	20	21	16	1866 1870 int82ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 DATA(insert OID = 1874 ( "&"	   PGNSP PGUID b f f	21	21	21	1874  0 int2and - - ));
@@ -1389,11 +1389,11 @@ DATA(insert OID = 1956 ( "<>"	   PGNSP PGUID b f f 17 17	16 1956 1955 byteane ne
 DESCR("not equal");
 DATA(insert OID = 1957 ( "<"	   PGNSP PGUID b f f 17 17	16 1959 1960 bytealt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 1958 ( "<="	   PGNSP PGUID b f f 17 17	16 1960 1959 byteale scalarltsel scalarltjoinsel ));
+DATA(insert OID = 1958 ( "<="	   PGNSP PGUID b f f 17 17	16 1960 1959 byteale scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 1959 ( ">"	   PGNSP PGUID b f f 17 17	16 1957 1958 byteagt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 1960 ( ">="	   PGNSP PGUID b f f 17 17	16 1958 1957 byteage scalargtsel scalargtjoinsel ));
+DATA(insert OID = 1960 ( ">="	   PGNSP PGUID b f f 17 17	16 1958 1957 byteage scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 DATA(insert OID = 2016 (  "~~"	   PGNSP PGUID b f f 17 17	16 0	2017 bytealike likesel likejoinsel ));
@@ -1411,11 +1411,11 @@ DATA(insert OID = 2061 (  "<>"	   PGNSP PGUID b f f 1114 1114	 16 2061 2060 time
 DESCR("not equal");
 DATA(insert OID = 2062 (  "<"	   PGNSP PGUID b f f 1114 1114	 16 2064 2065 timestamp_lt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 2063 (  "<="	   PGNSP PGUID b f f 1114 1114	 16 2065 2064 timestamp_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 2063 (  "<="	   PGNSP PGUID b f f 1114 1114	 16 2065 2064 timestamp_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 2064 (  ">"	   PGNSP PGUID b f f 1114 1114	 16 2062 2063 timestamp_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 2065 (  ">="	   PGNSP PGUID b f f 1114 1114	 16 2063 2062 timestamp_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 2065 (  ">="	   PGNSP PGUID b f f 1114 1114	 16 2063 2062 timestamp_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 2066 (  "+"	   PGNSP PGUID b f f 1114 1186 1114  2553 0 timestamp_pl_interval - - ));
 DESCR("add");
@@ -1428,18 +1428,18 @@ DESCR("subtract");
 
 DATA(insert OID = 2314 ( "~<~"	PGNSP PGUID b f f 25 25 16 2318 2317 text_pattern_lt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 2315 ( "~<=~" PGNSP PGUID b f f 25 25 16 2317 2318 text_pattern_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 2315 ( "~<=~" PGNSP PGUID b f f 25 25 16 2317 2318 text_pattern_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 2317 ( "~>=~" PGNSP PGUID b f f 25 25 16 2315 2314 text_pattern_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 2317 ( "~>=~" PGNSP PGUID b f f 25 25 16 2315 2314 text_pattern_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 2318 ( "~>~"	PGNSP PGUID b f f 25 25 16 2314 2315 text_pattern_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
 
 DATA(insert OID = 2326 ( "~<~"	PGNSP PGUID b f f 1042 1042 16 2330 2329 bpchar_pattern_lt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 2327 ( "~<=~" PGNSP PGUID b f f 1042 1042 16 2329 2330 bpchar_pattern_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 2327 ( "~<=~" PGNSP PGUID b f f 1042 1042 16 2329 2330 bpchar_pattern_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 2329 ( "~>=~" PGNSP PGUID b f f 1042 1042 16 2327 2326 bpchar_pattern_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 2329 ( "~>=~" PGNSP PGUID b f f 1042 1042 16 2327 2326 bpchar_pattern_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 2330 ( "~>~"	PGNSP PGUID b f f 1042 1042 16 2326 2327 bpchar_pattern_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
@@ -1448,11 +1448,11 @@ DESCR("greater than");
 
 DATA(insert OID = 2345 ( "<"	   PGNSP PGUID b f f	1082	1114   16 2375 2348 date_lt_timestamp scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 2346 ( "<="	   PGNSP PGUID b f f	1082	1114   16 2374 2349 date_le_timestamp scalarltsel scalarltjoinsel ));
+DATA(insert OID = 2346 ( "<="	   PGNSP PGUID b f f	1082	1114   16 2374 2349 date_le_timestamp scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 2347 ( "="	   PGNSP PGUID b t f	1082	1114   16 2373 2350 date_eq_timestamp eqsel eqjoinsel ));
 DESCR("equal");
-DATA(insert OID = 2348 ( ">="	   PGNSP PGUID b f f	1082	1114   16 2372 2345 date_ge_timestamp scalargtsel scalargtjoinsel ));
+DATA(insert OID = 2348 ( ">="	   PGNSP PGUID b f f	1082	1114   16 2372 2345 date_ge_timestamp scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 2349 ( ">"	   PGNSP PGUID b f f	1082	1114   16 2371 2346 date_gt_timestamp scalargtsel scalargtjoinsel ));
 DESCR("greater than");
@@ -1461,11 +1461,11 @@ DESCR("not equal");
 
 DATA(insert OID = 2358 ( "<"	   PGNSP PGUID b f f	1082	1184   16 2388 2361 date_lt_timestamptz scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 2359 ( "<="	   PGNSP PGUID b f f	1082	1184   16 2387 2362 date_le_timestamptz scalarltsel scalarltjoinsel ));
+DATA(insert OID = 2359 ( "<="	   PGNSP PGUID b f f	1082	1184   16 2387 2362 date_le_timestamptz scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 2360 ( "="	   PGNSP PGUID b t f	1082	1184   16 2386 2363 date_eq_timestamptz eqsel eqjoinsel ));
 DESCR("equal");
-DATA(insert OID = 2361 ( ">="	   PGNSP PGUID b f f	1082	1184   16 2385 2358 date_ge_timestamptz scalargtsel scalargtjoinsel ));
+DATA(insert OID = 2361 ( ">="	   PGNSP PGUID b f f	1082	1184   16 2385 2358 date_ge_timestamptz scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 2362 ( ">"	   PGNSP PGUID b f f	1082	1184   16 2384 2359 date_gt_timestamptz scalargtsel scalargtjoinsel ));
 DESCR("greater than");
@@ -1474,11 +1474,11 @@ DESCR("not equal");
 
 DATA(insert OID = 2371 ( "<"	   PGNSP PGUID b f f	1114	1082   16 2349 2374 timestamp_lt_date scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 2372 ( "<="	   PGNSP PGUID b f f	1114	1082   16 2348 2375 timestamp_le_date scalarltsel scalarltjoinsel ));
+DATA(insert OID = 2372 ( "<="	   PGNSP PGUID b f f	1114	1082   16 2348 2375 timestamp_le_date scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 2373 ( "="	   PGNSP PGUID b t f	1114	1082   16 2347 2376 timestamp_eq_date eqsel eqjoinsel ));
 DESCR("equal");
-DATA(insert OID = 2374 ( ">="	   PGNSP PGUID b f f	1114	1082   16 2346 2371 timestamp_ge_date scalargtsel scalargtjoinsel ));
+DATA(insert OID = 2374 ( ">="	   PGNSP PGUID b f f	1114	1082   16 2346 2371 timestamp_ge_date scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 2375 ( ">"	   PGNSP PGUID b f f	1114	1082   16 2345 2372 timestamp_gt_date scalargtsel scalargtjoinsel ));
 DESCR("greater than");
@@ -1487,11 +1487,11 @@ DESCR("not equal");
 
 DATA(insert OID = 2384 ( "<"	   PGNSP PGUID b f f	1184	1082   16 2362 2387 timestamptz_lt_date scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 2385 ( "<="	   PGNSP PGUID b f f	1184	1082   16 2361 2388 timestamptz_le_date scalarltsel scalarltjoinsel ));
+DATA(insert OID = 2385 ( "<="	   PGNSP PGUID b f f	1184	1082   16 2361 2388 timestamptz_le_date scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 2386 ( "="	   PGNSP PGUID b t f	1184	1082   16 2360 2389 timestamptz_eq_date eqsel eqjoinsel ));
 DESCR("equal");
-DATA(insert OID = 2387 ( ">="	   PGNSP PGUID b f f	1184	1082   16 2359 2384 timestamptz_ge_date scalargtsel scalargtjoinsel ));
+DATA(insert OID = 2387 ( ">="	   PGNSP PGUID b f f	1184	1082   16 2359 2384 timestamptz_ge_date scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 2388 ( ">"	   PGNSP PGUID b f f	1184	1082   16 2358 2385 timestamptz_gt_date scalargtsel scalargtjoinsel ));
 DESCR("greater than");
@@ -1502,11 +1502,11 @@ DESCR("not equal");
 
 DATA(insert OID = 2534 ( "<"	   PGNSP PGUID b f f	1114	1184   16 2544 2537 timestamp_lt_timestamptz scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 2535 ( "<="	   PGNSP PGUID b f f	1114	1184   16 2543 2538 timestamp_le_timestamptz scalarltsel scalarltjoinsel ));
+DATA(insert OID = 2535 ( "<="	   PGNSP PGUID b f f	1114	1184   16 2543 2538 timestamp_le_timestamptz scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 2536 ( "="	   PGNSP PGUID b t f	1114	1184   16 2542 2539 timestamp_eq_timestamptz eqsel eqjoinsel ));
 DESCR("equal");
-DATA(insert OID = 2537 ( ">="	   PGNSP PGUID b f f	1114	1184   16 2541 2534 timestamp_ge_timestamptz scalargtsel scalargtjoinsel ));
+DATA(insert OID = 2537 ( ">="	   PGNSP PGUID b f f	1114	1184   16 2541 2534 timestamp_ge_timestamptz scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 2538 ( ">"	   PGNSP PGUID b f f	1114	1184   16 2540 2535 timestamp_gt_timestamptz scalargtsel scalargtjoinsel ));
 DESCR("greater than");
@@ -1515,11 +1515,11 @@ DESCR("not equal");
 
 DATA(insert OID = 2540 ( "<"	   PGNSP PGUID b f f	1184	1114   16 2538 2543 timestamptz_lt_timestamp scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 2541 ( "<="	   PGNSP PGUID b f f	1184	1114   16 2537 2544 timestamptz_le_timestamp scalarltsel scalarltjoinsel ));
+DATA(insert OID = 2541 ( "<="	   PGNSP PGUID b f f	1184	1114   16 2537 2544 timestamptz_le_timestamp scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 2542 ( "="	   PGNSP PGUID b t f	1184	1114   16 2536 2545 timestamptz_eq_timestamp eqsel eqjoinsel ));
 DESCR("equal");
-DATA(insert OID = 2543 ( ">="	   PGNSP PGUID b f f	1184	1114   16 2535 2540 timestamptz_ge_timestamp scalargtsel scalargtjoinsel ));
+DATA(insert OID = 2543 ( ">="	   PGNSP PGUID b f f	1184	1114   16 2535 2540 timestamptz_ge_timestamp scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 2544 ( ">"	   PGNSP PGUID b f f	1184	1114   16 2534 2541 timestamptz_gt_timestamp scalargtsel scalargtjoinsel ));
 DESCR("greater than");
@@ -1624,9 +1624,9 @@ DATA(insert OID = 2974 (  "<"	   PGNSP PGUID b f f 2950 2950 16 2975 2977 uuid_l
 DESCR("less than");
 DATA(insert OID = 2975 (  ">"	   PGNSP PGUID b f f 2950 2950 16 2974 2976 uuid_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 2976 (  "<="	   PGNSP PGUID b f f 2950 2950 16 2977 2975 uuid_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 2976 (  "<="	   PGNSP PGUID b f f 2950 2950 16 2977 2975 uuid_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 2977 (  ">="	   PGNSP PGUID b f f 2950 2950 16 2976 2974 uuid_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 2977 (  ">="	   PGNSP PGUID b f f 2950 2950 16 2976 2974 uuid_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 /* pg_lsn operators */
@@ -1638,9 +1638,9 @@ DATA(insert OID = 3224 (  "<"	   PGNSP PGUID b f f 3220 3220 16 3225 3227 pg_lsn
 DESCR("less than");
 DATA(insert OID = 3225 (  ">"	   PGNSP PGUID b f f 3220 3220 16 3224 3226 pg_lsn_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 3226 (  "<="	   PGNSP PGUID b f f 3220 3220 16 3227 3225 pg_lsn_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 3226 (  "<="	   PGNSP PGUID b f f 3220 3220 16 3227 3225 pg_lsn_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 3227 (  ">="	   PGNSP PGUID b f f 3220 3220 16 3226 3224 pg_lsn_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 3227 (  ">="	   PGNSP PGUID b f f 3220 3220 16 3226 3224 pg_lsn_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 3228 (  "-"	   PGNSP PGUID b f f 3220 3220 1700    0	0 pg_lsn_mi - - ));
 DESCR("minus");
@@ -1654,9 +1654,9 @@ DATA(insert OID = 3518 (  "<"	   PGNSP PGUID b f f 3500 3500 16 3519 3521 enum_l
 DESCR("less than");
 DATA(insert OID = 3519 (  ">"	   PGNSP PGUID b f f 3500 3500 16 3518 3520 enum_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 3520 (  "<="	   PGNSP PGUID b f f 3500 3500 16 3521 3519 enum_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 3520 (  "<="	   PGNSP PGUID b f f 3500 3500 16 3521 3519 enum_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 3521 (  ">="	   PGNSP PGUID b f f 3500 3500 16 3520 3518 enum_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 3521 (  ">="	   PGNSP PGUID b f f 3500 3500 16 3520 3518 enum_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 /*
@@ -1664,13 +1664,13 @@ DESCR("greater than or equal");
  */
 DATA(insert OID = 3627 (  "<"	   PGNSP PGUID b f f 3614	 3614	 16 3632 3631	 tsvector_lt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 3628 (  "<="	   PGNSP PGUID b f f 3614	 3614	 16 3631 3632	 tsvector_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 3628 (  "<="	   PGNSP PGUID b f f 3614	 3614	 16 3631 3632	 tsvector_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 3629 (  "="	   PGNSP PGUID b t f 3614	 3614	 16 3629 3630	 tsvector_eq eqsel eqjoinsel ));
 DESCR("equal");
 DATA(insert OID = 3630 (  "<>"	   PGNSP PGUID b f f 3614	 3614	 16 3630 3629	 tsvector_ne neqsel neqjoinsel ));
 DESCR("not equal");
-DATA(insert OID = 3631 (  ">="	   PGNSP PGUID b f f 3614	 3614	 16 3628 3627	 tsvector_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 3631 (  ">="	   PGNSP PGUID b f f 3614	 3614	 16 3628 3627	 tsvector_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 3632 (  ">"	   PGNSP PGUID b f f 3614	 3614	 16 3627 3628	 tsvector_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
@@ -1686,13 +1686,13 @@ DATA(insert OID = 3661 (  "@@@"    PGNSP PGUID b f f 3615	 3614	 16 3660	0	 ts_m
 DESCR("deprecated, use @@ instead");
 DATA(insert OID = 3674 (  "<"	   PGNSP PGUID b f f 3615	 3615	 16 3679 3678	 tsquery_lt scalarltsel scalarltjoinsel ));
 DESCR("less than");
-DATA(insert OID = 3675 (  "<="	   PGNSP PGUID b f f 3615	 3615	 16 3678 3679	 tsquery_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 3675 (  "<="	   PGNSP PGUID b f f 3615	 3615	 16 3678 3679	 tsquery_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
 DATA(insert OID = 3676 (  "="	   PGNSP PGUID b t f 3615	 3615	 16 3676 3677	 tsquery_eq eqsel eqjoinsel ));
 DESCR("equal");
 DATA(insert OID = 3677 (  "<>"	   PGNSP PGUID b f f 3615	 3615	 16 3677 3676	 tsquery_ne neqsel neqjoinsel ));
 DESCR("not equal");
-DATA(insert OID = 3678 (  ">="	   PGNSP PGUID b f f 3615	 3615	 16 3675 3674	 tsquery_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 3678 (  ">="	   PGNSP PGUID b f f 3615	 3615	 16 3675 3674	 tsquery_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 3679 (  ">"	   PGNSP PGUID b f f 3615	 3615	 16 3674 3675	 tsquery_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
@@ -1726,9 +1726,9 @@ DESCR("less than");
 DATA(insert OID = 2991 (  ">"	   PGNSP PGUID b f f 2249 2249 16 2990 2992 record_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
 #define RECORD_GT_OP 2991
-DATA(insert OID = 2992 (  "<="	   PGNSP PGUID b f f 2249 2249 16 2993 2991 record_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 2992 (  "<="	   PGNSP PGUID b f f 2249 2249 16 2993 2991 record_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 2993 (  ">="	   PGNSP PGUID b f f 2249 2249 16 2992 2990 record_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 2993 (  ">="	   PGNSP PGUID b f f 2249 2249 16 2992 2990 record_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 /* byte-oriented tests for identical rows and fast sorting */
@@ -1740,9 +1740,9 @@ DATA(insert OID = 3190 (  "*<"	   PGNSP PGUID b f f 2249 2249 16 3191 3193 recor
 DESCR("less than");
 DATA(insert OID = 3191 (  "*>"	   PGNSP PGUID b f f 2249 2249 16 3190 3192 record_image_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 3192 (  "*<="   PGNSP PGUID b f f 2249 2249 16 3193 3191 record_image_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 3192 (  "*<="   PGNSP PGUID b f f 2249 2249 16 3193 3191 record_image_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 3193 (  "*>="   PGNSP PGUID b f f 2249 2249 16 3192 3190 record_image_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 3193 (  "*>="   PGNSP PGUID b f f 2249 2249 16 3192 3190 record_image_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 
 /* generic range type operators */
@@ -1753,10 +1753,10 @@ DESCR("not equal");
 DATA(insert OID = 3884 (  "<"	   PGNSP PGUID b f f 3831 3831 16 3887 3886 range_lt rangesel scalarltjoinsel ));
 DESCR("less than");
 #define OID_RANGE_LESS_OP 3884
-DATA(insert OID = 3885 (  "<="	   PGNSP PGUID b f f 3831 3831 16 3886 3887 range_le rangesel scalarltjoinsel ));
+DATA(insert OID = 3885 (  "<="	   PGNSP PGUID b f f 3831 3831 16 3886 3887 range_le rangesel scalarlejoinsel ));
 DESCR("less than or equal");
 #define OID_RANGE_LESS_EQUAL_OP 3885
-DATA(insert OID = 3886 (  ">="	   PGNSP PGUID b f f 3831 3831 16 3885 3884 range_ge rangesel scalargtjoinsel ));
+DATA(insert OID = 3886 (  ">="	   PGNSP PGUID b f f 3831 3831 16 3885 3884 range_ge rangesel scalargejoinsel ));
 DESCR("greater than or equal");
 #define OID_RANGE_GREATER_EQUAL_OP 3886
 DATA(insert OID = 3887 (  ">"	   PGNSP PGUID b f f 3831 3831 16 3884 3885 range_gt rangesel scalargtjoinsel ));
@@ -1829,9 +1829,9 @@ DATA(insert OID = 3242 (  "<"		PGNSP PGUID b f f 3802 3802 16 3243 3245 jsonb_lt
 DESCR("less than");
 DATA(insert OID = 3243 (  ">"		PGNSP PGUID b f f 3802 3802 16 3242 3244 jsonb_gt scalargtsel scalargtjoinsel ));
 DESCR("greater than");
-DATA(insert OID = 3244 (  "<="	PGNSP PGUID b f f 3802 3802 16 3245 3243 jsonb_le scalarltsel scalarltjoinsel ));
+DATA(insert OID = 3244 (  "<="	PGNSP PGUID b f f 3802 3802 16 3245 3243 jsonb_le scalarlesel scalarlejoinsel ));
 DESCR("less than or equal");
-DATA(insert OID = 3245 (  ">="	PGNSP PGUID b f f 3802 3802 16 3244 3242 jsonb_ge scalargtsel scalargtjoinsel ));
+DATA(insert OID = 3245 (  ">="	PGNSP PGUID b f f 3802 3802 16 3244 3242 jsonb_ge scalargesel scalargejoinsel ));
 DESCR("greater than or equal");
 DATA(insert OID = 3246 (  "@>"	   PGNSP PGUID b f f 3802 3802 16 3250 0 jsonb_contains contsel contjoinsel ));
 DESCR("contains");

src/include/catalog/pg_proc.h

@@ -264,6 +264,15 @@ DESCR("join selectivity of < and related operators on scalar datatypes");
 DATA(insert OID = 108 (  scalargtjoinsel   PGNSP PGUID 12 1 0 0 0 f f f f t f s s 5 0 701 "2281 26 2281 21 2281" _null_ _null_ _null_ _null_ _null_ scalargtjoinsel _null_ _null_ _null_ ));
 DESCR("join selectivity of > and related operators on scalar datatypes");
 
+DATA(insert OID = 336 (  scalarlesel	   PGNSP PGUID 12 1 0 0 0 f f f f t f s s 4 0 701 "2281 26 2281 23" _null_ _null_ _null_ _null_ _null_	scalarlesel _null_ _null_ _null_ ));
+DESCR("restriction selectivity of <= and related operators on scalar datatypes");
+DATA(insert OID = 337 (  scalargesel	   PGNSP PGUID 12 1 0 0 0 f f f f t f s s 4 0 701 "2281 26 2281 23" _null_ _null_ _null_ _null_ _null_	scalargesel _null_ _null_ _null_ ));
+DESCR("restriction selectivity of >= and related operators on scalar datatypes");
+DATA(insert OID = 386 (  scalarlejoinsel   PGNSP PGUID 12 1 0 0 0 f f f f t f s s 5 0 701 "2281 26 2281 21 2281" _null_ _null_ _null_ _null_ _null_ scalarlejoinsel _null_ _null_ _null_ ));
+DESCR("join selectivity of <= and related operators on scalar datatypes");
+DATA(insert OID = 398 (  scalargejoinsel   PGNSP PGUID 12 1 0 0 0 f f f f t f s s 5 0 701 "2281 26 2281 21 2281" _null_ _null_ _null_ _null_ _null_ scalargejoinsel _null_ _null_ _null_ ));
+DESCR("join selectivity of >= and related operators on scalar datatypes");
+
 DATA(insert OID =  109 (  unknownin		   PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 705 "2275" _null_ _null_ _null_ _null_ _null_ unknownin _null_ _null_ _null_ ));
 DESCR("I/O");
 DATA(insert OID =  110 (  unknownout	   PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 2275 "705" _null_ _null_ _null_ _null_ _null_ unknownout _null_ _null_ _null_ ));

src/tutorial/complex.source

@@ -174,7 +174,7 @@ CREATE OPERATOR < (
 CREATE OPERATOR <= (
    leftarg = complex, rightarg = complex, procedure = complex_abs_le,
    commutator = >= , negator = > ,
-   restrict = scalarltsel, join = scalarltjoinsel
+   restrict = scalarlesel, join = scalarlejoinsel
 );
 CREATE OPERATOR = (
    leftarg = complex, rightarg = complex, procedure = complex_abs_eq,
@@ -186,7 +186,7 @@ CREATE OPERATOR = (
 CREATE OPERATOR >= (
    leftarg = complex, rightarg = complex, procedure = complex_abs_ge,
    commutator = <= , negator = < ,
-   restrict = scalargtsel, join = scalargtjoinsel
+   restrict = scalargesel, join = scalargejoinsel
 );
 CREATE OPERATOR > (
    leftarg = complex, rightarg = complex, procedure = complex_abs_gt,