Fix assorted oversights in range selectivity estimation.

calc_rangesel() failed outright when comparing range variables to empty
constant ranges with < or >=, as a result of missing cases in a switch.
It also produced a bogus estimate for > comparison to an empty range.

On top of that, the >= and > cases were mislabeled throughout.  For
nonempty constant ranges, they managed to produce the right answers
anyway as a result of counterbalancing typos.

Also, default_range_selectivity() omitted cases for elem <@ range,
range &< range, and range &> range, so that rather dubious defaults
were applied for these operators.

In passing, rearrange the code in rangesel() so that the elem <@ range
case is handled in a less opaque fashion.

Report and patch by Emre Hasegeli, some additional work by me

src/backend/utils/adt/rangetypes_selfuncs.c

@@ -73,6 +73,7 @@ default_range_selectivity(Oid operator)
 			return 0.005;
 
 		case OID_RANGE_CONTAINS_ELEM_OP:
+		case OID_RANGE_ELEM_CONTAINED_OP:
 
 			/*
 			 * "range @> elem" is more or less identical to a scalar
@@ -86,6 +87,8 @@ default_range_selectivity(Oid operator)
 		case OID_RANGE_GREATER_EQUAL_OP:
 		case OID_RANGE_LEFT_OP:
 		case OID_RANGE_RIGHT_OP:
+		case OID_RANGE_OVERLAPS_LEFT_OP:
+		case OID_RANGE_OVERLAPS_RIGHT_OP:
 			/* these are similar to regular scalar inequalities */
 			return DEFAULT_INEQ_SEL;
 
@@ -109,7 +112,7 @@ rangesel(PG_FUNCTION_ARGS)
 	Node	   *other;
 	bool		varonleft;
 	Selectivity selec;
-	TypeCacheEntry *typcache;
+	TypeCacheEntry *typcache = NULL;
 	RangeType  *constrange = NULL;
 
 	/*
@@ -186,18 +189,27 @@ rangesel(PG_FUNCTION_ARGS)
 			constrange = range_serialize(typcache, &lower, &upper, false);
 		}
 	}
-	else
+	else if (operator == OID_RANGE_ELEM_CONTAINED_OP)
+	{
+		/*
+		 * Here, the Var is the elem, not the range.  For now we just punt and
+		 * return the default estimate.  In future we could disassemble the
+		 * range constant and apply scalarineqsel ...
+		 */
+	}
+	else if (((Const *) other)->consttype == vardata.vartype)
 	{
-		typcache = range_get_typcache(fcinfo, ((Const *) other)->consttype);
+		/* Both sides are the same range type */
+		typcache = range_get_typcache(fcinfo, vardata.vartype);
 
-		if (((Const *) other)->consttype == vardata.vartype)
-			constrange = DatumGetRangeType(((Const *) other)->constvalue);
+		constrange = DatumGetRangeType(((Const *) other)->constvalue);
 	}
 
 	/*
 	 * If we got a valid constant on one side of the operator, proceed to
 	 * estimate using statistics. Otherwise punt and return a default constant
-	 * estimate.
+	 * estimate.  Note that calc_rangesel need not handle
+	 * OID_RANGE_ELEM_CONTAINED_OP.
 	 */
 	if (constrange)
 		selec = calc_rangesel(typcache, &vardata, constrange, operator);
@@ -270,31 +282,37 @@ calc_rangesel(TypeCacheEntry *typcache, VariableStatData *vardata,
 		 */
 		switch (operator)
 		{
+				/* these return false if either argument is empty */
 			case OID_RANGE_OVERLAP_OP:
 			case OID_RANGE_OVERLAPS_LEFT_OP:
 			case OID_RANGE_OVERLAPS_RIGHT_OP:
 			case OID_RANGE_LEFT_OP:
 			case OID_RANGE_RIGHT_OP:
-				/* these return false if either argument is empty */
+				/* nothing is less than an empty range */
+			case OID_RANGE_LESS_OP:
 				selec = 0.0;
 				break;
 
+				/* only empty ranges can be contained by an empty range */
 			case OID_RANGE_CONTAINED_OP:
+				/* only empty ranges are <= an empty range */
 			case OID_RANGE_LESS_EQUAL_OP:
-			case OID_RANGE_GREATER_EQUAL_OP:
-
-				/*
-				 * these return true when both args are empty, false if only
-				 * one is empty
-				 */
 				selec = empty_frac;
 				break;
 
-			case OID_RANGE_CONTAINS_OP:
 				/* everything contains an empty range */
+			case OID_RANGE_CONTAINS_OP:
+				/* everything is >= an empty range */
+			case OID_RANGE_GREATER_EQUAL_OP:
 				selec = 1.0;
 				break;
 
+				/* all non-empty ranges are > an empty range */
+			case OID_RANGE_GREATER_OP:
+				selec = 1.0 - empty_frac;
+				break;
+
+				/* an element cannot be empty */
 			case OID_RANGE_CONTAINS_ELEM_OP:
 			default:
 				elog(ERROR, "unexpected operator %u", operator);
@@ -443,13 +461,13 @@ calc_hist_selectivity(TypeCacheEntry *typcache, VariableStatData *vardata,
 		case OID_RANGE_GREATER_OP:
 			hist_selec =
 				1 - calc_hist_selectivity_scalar(typcache, &const_lower,
-												 hist_lower, nhist, true);
+												 hist_lower, nhist, false);
 			break;
 
 		case OID_RANGE_GREATER_EQUAL_OP:
 			hist_selec =
 				1 - calc_hist_selectivity_scalar(typcache, &const_lower,
-												 hist_lower, nhist, false);
+												 hist_lower, nhist, true);
 			break;
 
 		case OID_RANGE_LEFT_OP:

src/include/catalog/pg_operator.h

@@ -1723,10 +1723,10 @@ 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 ));
 DESCR("greater than or equal");
-#define OID_RANGE_GREATER_OP 3886
+#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 ));
 DESCR("greater than");
-#define OID_RANGE_GREATER_EQUAL_OP 3887
+#define OID_RANGE_GREATER_OP 3887
 DATA(insert OID = 3888 (  "&&"	   PGNSP PGUID b f f 3831 3831 16 3888 0 range_overlaps rangesel areajoinsel ));
 DESCR("overlaps");
 #define OID_RANGE_OVERLAP_OP 3888

src/test/regress/expected/rangetypes.out

@@ -260,6 +260,11 @@ select * from numrange_test where nr = '[1.1, 2.2)';
  [1.1,2.2)
 (1 row)
 
+select * from numrange_test where nr < 'empty';
+ nr 
+----
+(0 rows)
+
 select * from numrange_test where nr < numrange(-1000.0, -1000.0,'[]');
   nr   
 -------
@@ -287,6 +292,33 @@ select * from numrange_test where nr < numrange(1000.0, 1001.0,'[]');
  [1.7,1.7]
 (6 rows)
 
+select * from numrange_test where nr <= 'empty';
+  nr   
+-------
+ empty
+(1 row)
+
+select * from numrange_test where nr >= 'empty';
+    nr     
+-----------
+ (,)
+ [3,)
+ (,5)
+ [1.1,2.2)
+ empty
+ [1.7,1.7]
+(6 rows)
+
+select * from numrange_test where nr > 'empty';
+    nr     
+-----------
+ (,)
+ [3,)
+ (,5)
+ [1.1,2.2)
+ [1.7,1.7]
+(5 rows)
+
 select * from numrange_test where nr > numrange(-1001.0, -1000.0,'[]');
     nr     
 -----------

src/test/regress/sql/rangetypes.sql

@@ -67,9 +67,13 @@ SELECT * FROM numrange_test WHERE 1.9 <@ nr;
 select * from numrange_test where nr = 'empty';
 select * from numrange_test where nr = '(1.1, 2.2)';
 select * from numrange_test where nr = '[1.1, 2.2)';
+select * from numrange_test where nr < 'empty';
 select * from numrange_test where nr < numrange(-1000.0, -1000.0,'[]');
 select * from numrange_test where nr < numrange(0.0, 1.0,'[]');
 select * from numrange_test where nr < numrange(1000.0, 1001.0,'[]');
+select * from numrange_test where nr <= 'empty';
+select * from numrange_test where nr >= 'empty';
+select * from numrange_test where nr > 'empty';
 select * from numrange_test where nr > numrange(-1001.0, -1000.0,'[]');
 select * from numrange_test where nr > numrange(0.0, 1.0,'[]');
 select * from numrange_test where nr > numrange(1000.0, 1000.0,'[]');