Introduce SP-GiST operator class over box.

Patch implements quad-tree over boxes, naive approach of 2D quad tree will not
work for any non-point objects because splitting space on node is not
efficient. The idea of pathc is treating 2D boxes as 4D points, so,
object will not overlap (in 4D space).

The performance tests reveal that this technique especially beneficial
with too much overlapping objects, so called "spaghetti data".

Author: Alexander Lebedev with editorization by Emre Hasegeli and me

doc/src/sgml/spgist.sgml

@@ -112,6 +112,24 @@
        <literal>@&gt;</>
       </entry>
      </row>
+     <row>
+      <entry><literal>box_ops</></entry>
+      <entry>box</entry>
+      <entry>
+       <literal>&lt;&lt;</>
+       <literal>&amp;&lt;</>
+       <literal>&amp;&amp;</>
+       <literal>&amp;&gt;</>
+       <literal>&gt;&gt;</>
+       <literal>~=</>
+       <literal>@&gt;</>
+       <literal>&lt;@</>
+       <literal>&amp;&lt;|</>
+       <literal>&lt;&lt;|</>
+       <literal>|&gt;&gt;</literal>
+       <literal>|&amp;&gt;</>
+      </entry>
+     </row>
      <row>
       <entry><literal>text_ops</></entry>
       <entry><type>text</></entry>

src/backend/utils/adt/Makefile

@@ -14,8 +14,8 @@ OBJS = acl.o arrayfuncs.o array_expanded.o array_selfuncs.o \
 	bool.o cash.o char.o date.o datetime.o datum.o dbsize.o domains.o \
 	encode.o enum.o expandeddatum.o \
 	float.o format_type.o formatting.o genfile.o \
-	geo_ops.o geo_selfuncs.o inet_cidr_ntop.o inet_net_pton.o int.o \
-	int8.o json.o jsonb.o jsonb_gin.o jsonb_op.o jsonb_util.o \
+	geo_ops.o geo_selfuncs.o geo_spgist.o inet_cidr_ntop.o inet_net_pton.o \
+	int.o int8.o json.o jsonb.o jsonb_gin.o jsonb_op.o jsonb_util.o \
 	jsonfuncs.o like.o lockfuncs.o mac.o misc.o nabstime.o name.o \
 	network.o network_gist.o network_selfuncs.o \
 	numeric.o numutils.o oid.o oracle_compat.o \

src/include/catalog/pg_amop.h

@@ -832,6 +832,22 @@ DATA(insert (	3474   3831 3831 8 s	3892 4000 0 ));
 DATA(insert (	3474   3831 2283 16 s	3889 4000 0 ));
 DATA(insert (	3474   3831 3831 18 s	3882 4000 0 ));
 
+/*
+ * SP-GiST box_ops
+ */
+DATA(insert (	5000	603  603  1 s	 493	4000 0 ));
+DATA(insert (	5000	603  603  2 s	 494	4000 0 ));
+DATA(insert (	5000	603  603  3 s	 500	4000 0 ));
+DATA(insert (	5000	603  603  4 s	 495	4000 0 ));
+DATA(insert (	5000	603  603  5 s	 496	4000 0 ));
+DATA(insert (	5000	603  603  6 s	 499	4000 0 ));
+DATA(insert (	5000	603  603  7 s	 498	4000 0 ));
+DATA(insert (	5000	603  603  8 s	 497	4000 0 ));
+DATA(insert (	5000	603  603  9 s	2571	4000 0 ));
+DATA(insert (	5000	603  603 10 s	2570	4000 0 ));
+DATA(insert (	5000	603  603 11 s	2573	4000 0 ));
+DATA(insert (	5000	603  603 12 s	2572	4000 0 ));
+
 /*
  * GiST inet_ops
  */

src/include/catalog/pg_amproc.h

@@ -443,6 +443,11 @@ DATA(insert (	4017   25 25 2 4028 ));
 DATA(insert (	4017   25 25 3 4029 ));
 DATA(insert (	4017   25 25 4 4030 ));
 DATA(insert (	4017   25 25 5 4031 ));
+DATA(insert (	5000   603 603 1 5012 ));
+DATA(insert (	5000   603 603 2 5013 ));
+DATA(insert (	5000   603 603 3 5014 ));
+DATA(insert (	5000   603 603 4 5015 ));
+DATA(insert (	5000   603 603 5 5016 ));
 
 /* BRIN opclasses */
 /* minmax bytea */

src/include/catalog/pg_opclass.h

@@ -228,6 +228,7 @@ DATA(insert (	403		range_ops			PGNSP PGUID 3901  3831 t 0 ));
 DATA(insert (	405		range_ops			PGNSP PGUID 3903  3831 t 0 ));
 DATA(insert (	783		range_ops			PGNSP PGUID 3919  3831 t 0 ));
 DATA(insert (	4000	range_ops			PGNSP PGUID 3474  3831 t 0 ));
+DATA(insert (	4000	box_ops			    PGNSP PGUID 5000  603  t 0 ));
 DATA(insert (	4000	quad_point_ops		PGNSP PGUID 4015  600 t 0 ));
 DATA(insert (	4000	kd_point_ops		PGNSP PGUID 4016  600 f 0 ));
 DATA(insert (	4000	text_ops			PGNSP PGUID 4017  25 t 0 ));

src/include/catalog/pg_opfamily.h

@@ -182,5 +182,6 @@ DATA(insert OID = 4081 (	3580	uuid_minmax_ops			PGNSP PGUID ));
 DATA(insert OID = 4103 (	3580	range_inclusion_ops		PGNSP PGUID ));
 DATA(insert OID = 4082 (	3580	pg_lsn_minmax_ops		PGNSP PGUID ));
 DATA(insert OID = 4104 (	3580	box_inclusion_ops		PGNSP PGUID ));
+DATA(insert OID = 5000 (	4000	box_ops		PGNSP PGUID ));
 
 #endif   /* PG_OPFAMILY_H */

src/include/catalog/pg_proc.h

@@ -5097,6 +5097,17 @@ DESCR("SP-GiST support for quad tree over range");
 DATA(insert OID = 3473 (  spg_range_quad_leaf_consistent	PGNSP PGUID 12 1 0 0 0 f f f f t f i s 2 0 16 "2281 2281" _null_ _null_ _null_ _null_  _null_ spg_range_quad_leaf_consistent _null_ _null_ _null_ ));
 DESCR("SP-GiST support for quad tree over range");
 
+DATA(insert OID = 5012 (  spg_box_quad_config PGNSP PGUID 12 1 0 0 0 f f f f t f i s 2 0 2278 "2281 2281" _null_ _null_ _null_ _null_  _null_ spg_box_quad_config _null_ _null_ _null_ ));
+DESCR("SP-GiST support for quad tree over box");
+DATA(insert OID = 5013 (  spg_box_quad_choose PGNSP PGUID 12 1 0 0 0 f f f f t f i s 2 0 2278 "2281 2281" _null_ _null_ _null_ _null_  _null_ spg_box_quad_choose _null_ _null_ _null_ ));
+DESCR("SP-GiST support for quad tree over box");
+DATA(insert OID = 5014 (  spg_box_quad_picksplit	PGNSP PGUID 12 1 0 0 0 f f f f t f i s 2 0 2278 "2281 2281" _null_ _null_ _null_ _null_  _null_ spg_box_quad_picksplit _null_ _null_ _null_ ));
+DESCR("SP-GiST support for quad tree over box");
+DATA(insert OID = 5015 (  spg_box_quad_inner_consistent	PGNSP PGUID 12 1 0 0 0 f f f f t f i s 2 0 2278 "2281 2281" _null_ _null_ _null_ _null_  _null_ spg_box_quad_inner_consistent _null_ _null_ _null_ ));
+DESCR("SP-GiST support for quad tree over box");
+DATA(insert OID = 5016 (  spg_box_quad_leaf_consistent	PGNSP PGUID 12 1 0 0 0 f f f f t f i s 2 0 16 "2281 2281" _null_ _null_ _null_ _null_  _null_ spg_box_quad_leaf_consistent _null_ _null_ _null_ ));
+DESCR("SP-GiST support for quad tree over box");
+
 /* replication slots */
 DATA(insert OID = 3779 (  pg_create_physical_replication_slot PGNSP PGUID 12 1 0 0 0 f f f f t f v u 2 0 2249 "19 16" "{19,16,19,3220}" "{i,i,o,o}" "{slot_name,immediately_reserve,slot_name,xlog_position}" _null_ _null_ pg_create_physical_replication_slot _null_ _null_ _null_ ));
 DESCR("create a physical replication slot");

src/include/utils/geo_decls.h

@@ -426,6 +426,12 @@ extern Datum gist_point_consistent(PG_FUNCTION_ARGS);
 extern Datum gist_point_distance(PG_FUNCTION_ARGS);
 extern Datum gist_point_fetch(PG_FUNCTION_ARGS);
 
+/* utils/adt/geo_spgist.c */
+Datum spg_box_quad_config(PG_FUNCTION_ARGS);
+Datum spg_box_quad_choose(PG_FUNCTION_ARGS);
+Datum spg_box_quad_picksplit(PG_FUNCTION_ARGS);
+Datum spg_box_quad_inner_consistent(PG_FUNCTION_ARGS);
+Datum spg_box_quad_leaf_consistent(PG_FUNCTION_ARGS);
 
 /* geo_selfuncs.c */
 extern Datum areasel(PG_FUNCTION_ARGS);

src/test/regress/expected/box.out

@@ -215,3 +215,243 @@ SELECT '' AS four, height(f1), width(f1) FROM BOX_TBL;
       |      0 |     0
 (4 rows)
 
+--
+-- Test the SP-GiST index
+--
+CREATE TEMPORARY TABLE box_temp (f1 box);
+INSERT INTO box_temp
+	SELECT box(point(i, i), point(i * 2, i * 2))
+	FROM generate_series(1, 50) AS i;
+CREATE INDEX box_spgist ON box_temp USING spgist (f1);
+INSERT INTO box_temp
+	VALUES (NULL),
+		   ('(-0,0)(0,100)'),
+		   ('(-3,4.3333333333)(40,1)'),
+		   ('(0,100)(0,infinity)'),
+		   ('(-infinity,0)(0,infinity)'),
+		   ('(-infinity,-infinity)(infinity,infinity)');
+SET enable_seqscan = false;
+SELECT * FROM box_temp WHERE f1 << '(10,20),(30,40)';
+        f1        
+------------------
+ (2,2),(1,1)
+ (4,4),(2,2)
+ (6,6),(3,3)
+ (8,8),(4,4)
+ (-0,100),(0,0)
+ (0,inf),(0,100)
+ (0,inf),(-inf,0)
+(7 rows)
+
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 << '(10,20),(30,40)';
+                  QUERY PLAN                  
+----------------------------------------------
+ Index Only Scan using box_spgist on box_temp
+   Index Cond: (f1 << '(30,40),(10,20)'::box)
+(2 rows)
+
+SELECT * FROM box_temp WHERE f1 &< '(10,4.333334),(5,100)';
+        f1        
+------------------
+ (2,2),(1,1)
+ (4,4),(2,2)
+ (6,6),(3,3)
+ (8,8),(4,4)
+ (10,10),(5,5)
+ (-0,100),(0,0)
+ (0,inf),(0,100)
+ (0,inf),(-inf,0)
+(8 rows)
+
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 &< '(10,4.333334),(5,100)';
+                     QUERY PLAN                     
+----------------------------------------------------
+ Index Only Scan using box_spgist on box_temp
+   Index Cond: (f1 &< '(10,100),(5,4.333334)'::box)
+(2 rows)
+
+SELECT * FROM box_temp WHERE f1 && '(15,20),(25,30)';
+          f1           
+-----------------------
+ (20,20),(10,10)
+ (22,22),(11,11)
+ (24,24),(12,12)
+ (26,26),(13,13)
+ (28,28),(14,14)
+ (30,30),(15,15)
+ (32,32),(16,16)
+ (34,34),(17,17)
+ (36,36),(18,18)
+ (38,38),(19,19)
+ (40,40),(20,20)
+ (42,42),(21,21)
+ (44,44),(22,22)
+ (46,46),(23,23)
+ (48,48),(24,24)
+ (50,50),(25,25)
+ (inf,inf),(-inf,-inf)
+(17 rows)
+
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 && '(15,20),(25,30)';
+                  QUERY PLAN                  
+----------------------------------------------
+ Index Only Scan using box_spgist on box_temp
+   Index Cond: (f1 && '(25,30),(15,20)'::box)
+(2 rows)
+
+SELECT * FROM box_temp WHERE f1 &> '(40,30),(45,50)';
+        f1         
+-------------------
+ (80,80),(40,40)
+ (82,82),(41,41)
+ (84,84),(42,42)
+ (86,86),(43,43)
+ (88,88),(44,44)
+ (90,90),(45,45)
+ (92,92),(46,46)
+ (94,94),(47,47)
+ (96,96),(48,48)
+ (98,98),(49,49)
+ (100,100),(50,50)
+(11 rows)
+
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 &> '(40,30),(45,50)';
+                  QUERY PLAN                  
+----------------------------------------------
+ Index Only Scan using box_spgist on box_temp
+   Index Cond: (f1 &> '(45,50),(40,30)'::box)
+(2 rows)
+
+SELECT * FROM box_temp WHERE f1 >> '(30,40),(40,30)';
+        f1         
+-------------------
+ (82,82),(41,41)
+ (84,84),(42,42)
+ (86,86),(43,43)
+ (88,88),(44,44)
+ (90,90),(45,45)
+ (92,92),(46,46)
+ (94,94),(47,47)
+ (96,96),(48,48)
+ (98,98),(49,49)
+ (100,100),(50,50)
+(10 rows)
+
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 >> '(30,40),(40,30)';
+                  QUERY PLAN                  
+----------------------------------------------
+ Index Only Scan using box_spgist on box_temp
+   Index Cond: (f1 >> '(40,40),(30,30)'::box)
+(2 rows)
+
+SELECT * FROM box_temp WHERE f1 <<| '(10,4.33334),(5,100)';
+            f1            
+--------------------------
+ (2,2),(1,1)
+ (4,4),(2,2)
+ (40,4.3333333333),(-3,1)
+(3 rows)
+
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 <<| '(10,4.33334),(5,100)';
+                     QUERY PLAN                     
+----------------------------------------------------
+ Index Only Scan using box_spgist on box_temp
+   Index Cond: (f1 <<| '(10,100),(5,4.33334)'::box)
+(2 rows)
+
+SELECT * FROM box_temp WHERE f1 &<| '(10,4.3333334),(5,1)';
+            f1            
+--------------------------
+ (2,2),(1,1)
+ (4,4),(2,2)
+ (40,4.3333333333),(-3,1)
+(3 rows)
+
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 &<| '(10,4.3333334),(5,1)';
+                     QUERY PLAN                     
+----------------------------------------------------
+ Index Only Scan using box_spgist on box_temp
+   Index Cond: (f1 &<| '(10,4.3333334),(5,1)'::box)
+(2 rows)
+
+SELECT * FROM box_temp WHERE f1 |&> '(49.99,49.99),(49.99,49.99)';
+        f1         
+-------------------
+ (100,100),(50,50)
+ (0,inf),(0,100)
+(2 rows)
+
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 |&> '(49.99,49.99),(49.99,49.99)';
+                        QUERY PLAN                         
+-----------------------------------------------------------
+ Index Only Scan using box_spgist on box_temp
+   Index Cond: (f1 |&> '(49.99,49.99),(49.99,49.99)'::box)
+(2 rows)
+
+SELECT * FROM box_temp WHERE f1 |>> '(37,38),(39,40)';
+        f1         
+-------------------
+ (82,82),(41,41)
+ (84,84),(42,42)
+ (86,86),(43,43)
+ (88,88),(44,44)
+ (90,90),(45,45)
+ (92,92),(46,46)
+ (94,94),(47,47)
+ (96,96),(48,48)
+ (98,98),(49,49)
+ (100,100),(50,50)
+ (0,inf),(0,100)
+(11 rows)
+
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 |>> '(37,38),(39,40)';
+                  QUERY PLAN                   
+-----------------------------------------------
+ Index Only Scan using box_spgist on box_temp
+   Index Cond: (f1 |>> '(39,40),(37,38)'::box)
+(2 rows)
+
+SELECT * FROM box_temp WHERE f1 @> '(10,11),(15,16)';
+          f1           
+-----------------------
+ (16,16),(8,8)
+ (18,18),(9,9)
+ (20,20),(10,10)
+ (inf,inf),(-inf,-inf)
+(4 rows)
+
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 @> '(10,11),(15,15)';
+                  QUERY PLAN                  
+----------------------------------------------
+ Index Only Scan using box_spgist on box_temp
+   Index Cond: (f1 @> '(15,15),(10,11)'::box)
+(2 rows)
+
+SELECT * FROM box_temp WHERE f1 <@ '(10,15),(30,35)';
+       f1        
+-----------------
+ (30,30),(15,15)
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 <@ '(10,15),(30,35)';
+                  QUERY PLAN                  
+----------------------------------------------
+ Index Only Scan using box_spgist on box_temp
+   Index Cond: (f1 <@ '(30,35),(10,15)'::box)
+(2 rows)
+
+SELECT * FROM box_temp WHERE f1 ~= '(20,20),(40,40)';
+       f1        
+-----------------
+ (40,40),(20,20)
+(1 row)
+
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 ~= '(20,20),(40,40)';
+                  QUERY PLAN                  
+----------------------------------------------
+ Index Only Scan using box_spgist on box_temp
+   Index Cond: (f1 ~= '(40,40),(20,20)'::box)
+(2 rows)
+
+RESET enable_seqscan;
+DROP INDEX box_spgist;

src/test/regress/expected/opr_sanity.out

@@ -1728,15 +1728,19 @@ ORDER BY 1, 2, 3;
        4000 |            6 | ~=
        4000 |            7 | @>
        4000 |            8 | <@
+       4000 |            9 | &<|
+       4000 |           10 | <<|
        4000 |           10 | <^
        4000 |           11 | <
        4000 |           11 | >^
+       4000 |           11 | |>>
        4000 |           12 | <=
+       4000 |           12 | |&>
        4000 |           14 | >=
        4000 |           15 | >
        4000 |           16 | @>
        4000 |           18 | =
-(108 rows)
+(112 rows)
 
 -- Check that all opclass search operators have selectivity estimators.
 -- This is not absolutely required, but it seems a reasonable thing

src/test/regress/sql/box.sql

@@ -117,3 +117,65 @@ SELECT '' AS one, b1.*, b2.*
    WHERE b1.f1 @> b2.f1 and not b1.f1 ~= b2.f1;
 
 SELECT '' AS four, height(f1), width(f1) FROM BOX_TBL;
+
+--
+-- Test the SP-GiST index
+--
+
+CREATE TEMPORARY TABLE box_temp (f1 box);
+
+INSERT INTO box_temp
+	SELECT box(point(i, i), point(i * 2, i * 2))
+	FROM generate_series(1, 50) AS i;
+
+CREATE INDEX box_spgist ON box_temp USING spgist (f1);
+
+INSERT INTO box_temp
+	VALUES (NULL),
+		   ('(-0,0)(0,100)'),
+		   ('(-3,4.3333333333)(40,1)'),
+		   ('(0,100)(0,infinity)'),
+		   ('(-infinity,0)(0,infinity)'),
+		   ('(-infinity,-infinity)(infinity,infinity)');
+
+SET enable_seqscan = false;
+
+SELECT * FROM box_temp WHERE f1 << '(10,20),(30,40)';
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 << '(10,20),(30,40)';
+
+SELECT * FROM box_temp WHERE f1 &< '(10,4.333334),(5,100)';
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 &< '(10,4.333334),(5,100)';
+
+SELECT * FROM box_temp WHERE f1 && '(15,20),(25,30)';
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 && '(15,20),(25,30)';
+
+SELECT * FROM box_temp WHERE f1 &> '(40,30),(45,50)';
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 &> '(40,30),(45,50)';
+
+SELECT * FROM box_temp WHERE f1 >> '(30,40),(40,30)';
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 >> '(30,40),(40,30)';
+
+SELECT * FROM box_temp WHERE f1 <<| '(10,4.33334),(5,100)';
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 <<| '(10,4.33334),(5,100)';
+
+SELECT * FROM box_temp WHERE f1 &<| '(10,4.3333334),(5,1)';
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 &<| '(10,4.3333334),(5,1)';
+
+SELECT * FROM box_temp WHERE f1 |&> '(49.99,49.99),(49.99,49.99)';
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 |&> '(49.99,49.99),(49.99,49.99)';
+
+SELECT * FROM box_temp WHERE f1 |>> '(37,38),(39,40)';
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 |>> '(37,38),(39,40)';
+
+SELECT * FROM box_temp WHERE f1 @> '(10,11),(15,16)';
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 @> '(10,11),(15,15)';
+
+SELECT * FROM box_temp WHERE f1 <@ '(10,15),(30,35)';
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 <@ '(10,15),(30,35)';
+
+SELECT * FROM box_temp WHERE f1 ~= '(20,20),(40,40)';
+EXPLAIN (COSTS OFF) SELECT * FROM box_temp WHERE f1 ~= '(20,20),(40,40)';
+
+RESET enable_seqscan;
+
+DROP INDEX box_spgist;