From bda5281fdc5e41b6f54ff8f47df2ca37df00a19e Mon Sep 17 00:00:00 2001 From: Teodor Sigaev Date: Thu, 11 Jan 2018 14:43:13 +0300 Subject: [PATCH] Fix behavior of ~> (cube, int) operator ~> (cube, int) operator was especially designed for knn-gist search. However, it appears that knn-gist search can't work correctly with current behavior of this operator when dataset contains cubes of variable dimensionality. In this case, the same value of second operator argument can point to different dimension depending on dimensionality of particular cube. Such behavior is incompatible with gist indexing of cubes, and knn-gist doesn't work correctly for it. This patch changes behavior of ~> (cube, int) operator by introducing dimension numbering where value of second argument unambiguously identifies number of dimension. With new behavior, this operator can be correctly supported by knn-gist. Relevant changes to cube operator class are also included. Backpatch to v9.6 where operator was introduced. Since behavior of ~> (cube, int) operator is changed, depending entities must be refreshed after upgrade. Such as, expression indexes using this operator must be reindexed, materialized views must be rebuilt, stored procedures and client code must be revised to correctly use new behavior. That should be mentioned in release notes. Noticed by: Tomas Vondra Author: Alexander Korotkov Reviewed by: Tomas Vondra, Andrey Borodin Discussion: https://www.postgresql.org/message-id/flat/a9657f6a-b497-36ff-e56-482a2c7e3292@2ndquadrant.com --- contrib/cube/cube.c | 118 +++++++++--- contrib/cube/expected/cube.out | 317 +++++++++++++++++++------------ contrib/cube/expected/cube_1.out | 317 +++++++++++++++++++------------ contrib/cube/expected/cube_2.out | 317 +++++++++++++++++++------------ contrib/cube/expected/cube_3.out | 317 +++++++++++++++++++------------ contrib/cube/sql/cube.sql | 33 ++-- doc/src/sgml/cube.sgml | 9 +- 7 files changed, 901 insertions(+), 527 deletions(-) diff --git a/contrib/cube/cube.c b/contrib/cube/cube.c index 3feddef8f3..6c4a5b24c1 100644 --- a/contrib/cube/cube.c +++ b/contrib/cube/cube.c @@ -1368,13 +1368,55 @@ g_cube_distance(PG_FUNCTION_ARGS) if (strategy == CubeKNNDistanceCoord) { + /* + * Handle ordering by ~> operator. See comments of cube_coord_llur() + * for details + */ int coord = PG_GETARG_INT32(1); + bool isLeaf = GistPageIsLeaf(entry->page); - if (IS_POINT(cube)) - retval = cube->x[(coord - 1) % DIM(cube)]; + /* 0 is the only unsupported coordinate value */ + if (coord <= 0) + ereport(ERROR, + (errcode(ERRCODE_ARRAY_ELEMENT_ERROR), + errmsg("cube index %d is out of bounds", coord))); + + if (coord <= 2 * DIM(cube)) + { + /* dimension index */ + int index = (coord - 1) / 2; + /* whether this is upper bound (lower bound otherwise) */ + bool upper = ((coord - 1) % 2 == 1); + + if (IS_POINT(cube)) + { + retval = cube->x[index]; + } + else + { + if (isLeaf) + { + /* For leaf just return required upper/lower bound */ + if (upper) + retval = Max(cube->x[index], cube->x[index + DIM(cube)]); + else + retval = Min(cube->x[index], cube->x[index + DIM(cube)]); + } + else + { + /* + * For non-leaf we should always return lower bound, + * because even upper bound of a child in the subtree can + * be as small as our lower bound. + */ + retval = Min(cube->x[index], cube->x[index + DIM(cube)]); + } + } + } else - retval = Min(cube->x[(coord - 1) % DIM(cube)], - cube->x[(coord - 1) % DIM(cube) + DIM(cube)]); + { + retval = 0.0; + } } else { @@ -1521,43 +1563,73 @@ cube_coord(PG_FUNCTION_ARGS) } -/* - * This function works like cube_coord(), - * but rearranges coordinates of corners to get cube representation - * in the form of (lower left, upper right). - * For historical reasons that extension allows us to create cubes in form - * ((2,1),(1,2)) and instead of normalizing such cube to ((1,1),(2,2)) it - * stores cube in original way. But to get cubes ordered by one of dimensions - * directly from the index without extra sort step we need some - * representation-independent coordinate getter. This function implements it. +/*---- + * This function works like cube_coord(), but rearranges coordinates in the + * way suitable to support coordinate ordering using KNN-GiST. For historical + * reasons this extension allows us to create cubes in form ((2,1),(1,2)) and + * instead of normalizing such cube to ((1,1),(2,2)) it stores cube in original + * way. But in order to get cubes ordered by one of dimensions from the index + * without explicit sort step we need this representation-independent coordinate + * getter. Moreover, indexed dataset may contain cubes of different dimensions + * number. Accordingly, this coordinate getter should be able to return + * lower/upper bound for particular dimension independently on number of cube + * dimensions. + * + * Long story short, this function uses following meaning of coordinates: + * # (2 * N - 1) -- lower bound of Nth dimension, + * # (2 * N) -- upper bound of Nth dimension. + * + * When given coordinate exceeds number of cube dimensions, then 0 returned + * (reproducing logic of GiST indexing of variable-length cubes). */ Datum cube_coord_llur(PG_FUNCTION_ARGS) { NDBOX *cube = PG_GETARG_NDBOX(0); int coord = PG_GETARG_INT32(1); + bool inverse = false; + float8 result; - if (coord <= 0 || coord > 2 * DIM(cube)) + /* 0 is the only unsupported coordinate value */ + if (coord <= 0) ereport(ERROR, (errcode(ERRCODE_ARRAY_ELEMENT_ERROR), errmsg("cube index %d is out of bounds", coord))); - if (coord <= DIM(cube)) + if (coord <= 2 * DIM(cube)) { + /* dimension index */ + int index = (coord - 1) / 2; + /* whether this is upper bound (lower bound otherwise) */ + bool upper = ((coord - 1) % 2 == 1); + if (IS_POINT(cube)) - PG_RETURN_FLOAT8(cube->x[coord - 1]); + { + result = cube->x[index]; + } else - PG_RETURN_FLOAT8(Min(cube->x[coord - 1], - cube->x[coord - 1 + DIM(cube)])); + { + if (upper) + result = Max(cube->x[index], cube->x[index + DIM(cube)]); + else + result = Min(cube->x[index], cube->x[index + DIM(cube)]); + } } else { - if (IS_POINT(cube)) - PG_RETURN_FLOAT8(cube->x[(coord - 1) % DIM(cube)]); - else - PG_RETURN_FLOAT8(Max(cube->x[coord - 1], - cube->x[coord - 1 - DIM(cube)])); + /* + * Return zero if coordinate is out of bound. That reproduces logic of + * how cubes with low dimension number are expanded during GiST + * indexing. + */ + result = 0.0; } + + /* Inverse value if needed */ + if (inverse) + result = -result; + + PG_RETURN_FLOAT8(result); } /* Increase or decrease box size by a radius in at least n dimensions. */ diff --git a/contrib/cube/expected/cube.out b/contrib/cube/expected/cube.out index 9ac2a71295..f537dc8c70 100644 --- a/contrib/cube/expected/cube.out +++ b/contrib/cube/expected/cube.out @@ -1495,25 +1495,25 @@ SELECT cube(array[40,50,60], array[10,20,30])~>1; SELECT cube(array[10,20,30], array[40,50,60])~>2; ?column? ---------- - 20 + 40 (1 row) SELECT cube(array[40,50,60], array[10,20,30])~>2; ?column? ---------- - 20 + 40 (1 row) SELECT cube(array[10,20,30], array[40,50,60])~>3; ?column? ---------- - 30 + 20 (1 row) SELECT cube(array[40,50,60], array[10,20,30])~>3; ?column? ---------- - 30 + 20 (1 row) SELECT cube(array[40,50,60], array[10,20,30])~>0; @@ -1521,7 +1521,7 @@ ERROR: cube index 0 is out of bounds SELECT cube(array[40,50,60], array[10,20,30])~>4; ?column? ---------- - 40 + 50 (1 row) SELECT cube(array[40,50,60], array[10,20,30])~>(-1); @@ -1552,25 +1552,28 @@ SELECT * FROM test_cube WHERE c && '(3000,1000),(0,0)' GROUP BY c ORDER BY c; (2424, 160),(2424, 81) (5 rows) --- kNN with index +-- Test kNN +INSERT INTO test_cube VALUES ('(1,1)'), ('(100000)'), ('(0, 100000)'); -- Some corner cases +SET enable_seqscan = false; +-- Test different metrics SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5; c | dist -------------------------+------------------ (337, 455),(240, 359) | 0 + (1, 1) | 140.007142674936 (759, 187),(662, 163) | 162 (948, 1201),(907, 1156) | 772.000647668122 (1444, 403),(1346, 344) | 846 - (369, 1457),(278, 1409) | 909 (5 rows) SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5; c | dist -------------------------+------ (337, 455),(240, 359) | 0 + (1, 1) | 99 (759, 187),(662, 163) | 162 (948, 1201),(907, 1156) | 656 (1444, 403),(1346, 344) | 846 - (369, 1457),(278, 1409) | 909 (5 rows) SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5; @@ -1578,133 +1581,203 @@ SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c -------------------------+------ (337, 455),(240, 359) | 0 (759, 187),(662, 163) | 162 + (1, 1) | 198 (1444, 403),(1346, 344) | 846 (369, 1457),(278, 1409) | 909 - (948, 1201),(907, 1156) | 1063 (5 rows) --- kNN-based sorting -SELECT * FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by 1st coordinate of lower left corner - c ---------------------------- - (54, 38679),(3, 38602) - (83, 10271),(15, 10265) - (122, 46832),(64, 46762) - (167, 17214),(92, 17184) - (161, 24465),(107, 24374) - (162, 26040),(120, 25963) - (154, 4019),(138, 3990) - (259, 1850),(175, 1820) - (207, 40886),(179, 40879) - (288, 49588),(204, 49571) - (270, 32616),(226, 32607) - (318, 31489),(235, 31404) - (337, 455),(240, 359) - (270, 29508),(264, 29440) - (369, 1457),(278, 1409) +-- Test sorting by coordinates +SELECT c~>1, c FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by left bound + ?column? | c +----------+--------------------------- + 0 | (0, 100000) + 1 | (1, 1) + 3 | (54, 38679),(3, 38602) + 15 | (83, 10271),(15, 10265) + 64 | (122, 46832),(64, 46762) + 92 | (167, 17214),(92, 17184) + 107 | (161, 24465),(107, 24374) + 120 | (162, 26040),(120, 25963) + 138 | (154, 4019),(138, 3990) + 175 | (259, 1850),(175, 1820) + 179 | (207, 40886),(179, 40879) + 204 | (288, 49588),(204, 49571) + 226 | (270, 32616),(226, 32607) + 235 | (318, 31489),(235, 31404) + 240 | (337, 455),(240, 359) (15 rows) -SELECT * FROM test_cube ORDER BY c~>4 LIMIT 15; -- ascending by 2nd coordinate or upper right corner - c ---------------------------- - (30333, 50),(30273, 6) - (43301, 75),(43227, 43) - (19650, 142),(19630, 51) - (2424, 160),(2424, 81) - (3449, 171),(3354, 108) - (18037, 155),(17941, 109) - (28511, 208),(28479, 114) - (19946, 217),(19941, 118) - (16906, 191),(16816, 139) - (759, 187),(662, 163) - (22684, 266),(22656, 181) - (24423, 255),(24360, 213) - (45989, 249),(45910, 222) - (11399, 377),(11360, 294) - (12162, 389),(12103, 309) +SELECT c~>2, c FROM test_cube ORDER BY c~>2 LIMIT 15; -- ascending by right bound + ?column? | c +----------+--------------------------- + 0 | (0, 100000) + 1 | (1, 1) + 54 | (54, 38679),(3, 38602) + 83 | (83, 10271),(15, 10265) + 122 | (122, 46832),(64, 46762) + 154 | (154, 4019),(138, 3990) + 161 | (161, 24465),(107, 24374) + 162 | (162, 26040),(120, 25963) + 167 | (167, 17214),(92, 17184) + 207 | (207, 40886),(179, 40879) + 259 | (259, 1850),(175, 1820) + 270 | (270, 29508),(264, 29440) + 270 | (270, 32616),(226, 32607) + 288 | (288, 49588),(204, 49571) + 318 | (318, 31489),(235, 31404) (15 rows) -SELECT * FROM test_cube ORDER BY c~>1 DESC LIMIT 15; -- descending by 1st coordinate of lower left corner - c -------------------------------- - (50027, 49230),(49951, 49214) - (49980, 35004),(49937, 34963) - (49985, 6436),(49927, 6338) - (49999, 27218),(49908, 27176) - (49954, 1340),(49905, 1294) - (49944, 25163),(49902, 25153) - (49981, 34876),(49898, 34786) - (49957, 43390),(49897, 43384) - (49853, 18504),(49848, 18503) - (49902, 41752),(49818, 41746) - (49907, 30225),(49810, 30158) - (49843, 5175),(49808, 5145) - (49887, 24274),(49805, 24184) - (49847, 7128),(49798, 7067) - (49820, 7990),(49771, 7967) +SELECT c~>3, c FROM test_cube ORDER BY c~>3 LIMIT 15; -- ascending by lower bound + ?column? | c +----------+--------------------------- + 0 | (100000) + 1 | (1, 1) + 6 | (30333, 50),(30273, 6) + 43 | (43301, 75),(43227, 43) + 51 | (19650, 142),(19630, 51) + 81 | (2424, 160),(2424, 81) + 108 | (3449, 171),(3354, 108) + 109 | (18037, 155),(17941, 109) + 114 | (28511, 208),(28479, 114) + 118 | (19946, 217),(19941, 118) + 139 | (16906, 191),(16816, 139) + 163 | (759, 187),(662, 163) + 181 | (22684, 266),(22656, 181) + 213 | (24423, 255),(24360, 213) + 222 | (45989, 249),(45910, 222) (15 rows) -SELECT * FROM test_cube ORDER BY c~>4 DESC LIMIT 15; -- descending by 2nd coordinate or upper right corner - c -------------------------------- - (36311, 50073),(36258, 49987) - (30746, 50040),(30727, 49992) - (2168, 50012),(2108, 49914) - (21551, 49983),(21492, 49885) - (17954, 49975),(17865, 49915) - (3531, 49962),(3463, 49934) - (19128, 49932),(19112, 49849) - (31287, 49923),(31236, 49913) - (43925, 49912),(43888, 49878) - (29261, 49910),(29247, 49818) - (14913, 49873),(14849, 49836) - (20007, 49858),(19921, 49778) - (38266, 49852),(38233, 49844) - (37595, 49849),(37581, 49834) - (46151, 49848),(46058, 49830) +SELECT c~>4, c FROM test_cube ORDER BY c~>4 LIMIT 15; -- ascending by upper bound + ?column? | c +----------+--------------------------- + 0 | (100000) + 1 | (1, 1) + 50 | (30333, 50),(30273, 6) + 75 | (43301, 75),(43227, 43) + 142 | (19650, 142),(19630, 51) + 155 | (18037, 155),(17941, 109) + 160 | (2424, 160),(2424, 81) + 171 | (3449, 171),(3354, 108) + 187 | (759, 187),(662, 163) + 191 | (16906, 191),(16816, 139) + 208 | (28511, 208),(28479, 114) + 217 | (19946, 217),(19941, 118) + 249 | (45989, 249),(45910, 222) + 255 | (24423, 255),(24360, 213) + 266 | (22684, 266),(22656, 181) (15 rows) --- same thing for index with points -CREATE TABLE test_point(c cube); -INSERT INTO test_point(SELECT cube(array[c->1,c->2,c->3,c->4]) FROM test_cube); -CREATE INDEX ON test_point USING gist(c); -SELECT * FROM test_point ORDER BY c~>1, c~>2 LIMIT 15; -- ascending by 1st then by 2nd coordinate - c --------------------------- - (54, 38679, 3, 38602) - (83, 10271, 15, 10265) - (122, 46832, 64, 46762) - (154, 4019, 138, 3990) - (161, 24465, 107, 24374) - (162, 26040, 120, 25963) - (167, 17214, 92, 17184) - (207, 40886, 179, 40879) - (259, 1850, 175, 1820) - (270, 29508, 264, 29440) - (270, 32616, 226, 32607) - (288, 49588, 204, 49571) - (318, 31489, 235, 31404) - (326, 18837, 285, 18817) - (337, 455, 240, 359) +-- Same queries with sequential scan (should give the same results as above) +RESET enable_seqscan; +SET enable_indexscan = OFF; +SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5; + c | dist +-------------------------+------------------ + (337, 455),(240, 359) | 0 + (1, 1) | 140.007142674936 + (759, 187),(662, 163) | 162 + (948, 1201),(907, 1156) | 772.000647668122 + (1444, 403),(1346, 344) | 846 +(5 rows) + +SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5; + c | dist +-------------------------+------ + (337, 455),(240, 359) | 0 + (1, 1) | 99 + (759, 187),(662, 163) | 162 + (948, 1201),(907, 1156) | 656 + (1444, 403),(1346, 344) | 846 +(5 rows) + +SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5; + c | dist +-------------------------+------ + (337, 455),(240, 359) | 0 + (759, 187),(662, 163) | 162 + (1, 1) | 198 + (1444, 403),(1346, 344) | 846 + (369, 1457),(278, 1409) | 909 +(5 rows) + +SELECT c~>1, c FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by left bound + ?column? | c +----------+--------------------------- + 0 | (0, 100000) + 1 | (1, 1) + 3 | (54, 38679),(3, 38602) + 15 | (83, 10271),(15, 10265) + 64 | (122, 46832),(64, 46762) + 92 | (167, 17214),(92, 17184) + 107 | (161, 24465),(107, 24374) + 120 | (162, 26040),(120, 25963) + 138 | (154, 4019),(138, 3990) + 175 | (259, 1850),(175, 1820) + 179 | (207, 40886),(179, 40879) + 204 | (288, 49588),(204, 49571) + 226 | (270, 32616),(226, 32607) + 235 | (318, 31489),(235, 31404) + 240 | (337, 455),(240, 359) (15 rows) -SELECT * FROM test_point ORDER BY c~>4 DESC LIMIT 15; -- descending by 1st coordinate - c ------------------------------- - (30746, 50040, 30727, 49992) - (36311, 50073, 36258, 49987) - (3531, 49962, 3463, 49934) - (17954, 49975, 17865, 49915) - (2168, 50012, 2108, 49914) - (31287, 49923, 31236, 49913) - (21551, 49983, 21492, 49885) - (43925, 49912, 43888, 49878) - (19128, 49932, 19112, 49849) - (38266, 49852, 38233, 49844) - (14913, 49873, 14849, 49836) - (37595, 49849, 37581, 49834) - (46151, 49848, 46058, 49830) - (29261, 49910, 29247, 49818) - (19233, 49824, 19185, 49794) +SELECT c~>2, c FROM test_cube ORDER BY c~>2 LIMIT 15; -- ascending by right bound + ?column? | c +----------+--------------------------- + 0 | (0, 100000) + 1 | (1, 1) + 54 | (54, 38679),(3, 38602) + 83 | (83, 10271),(15, 10265) + 122 | (122, 46832),(64, 46762) + 154 | (154, 4019),(138, 3990) + 161 | (161, 24465),(107, 24374) + 162 | (162, 26040),(120, 25963) + 167 | (167, 17214),(92, 17184) + 207 | (207, 40886),(179, 40879) + 259 | (259, 1850),(175, 1820) + 270 | (270, 29508),(264, 29440) + 270 | (270, 32616),(226, 32607) + 288 | (288, 49588),(204, 49571) + 318 | (318, 31489),(235, 31404) (15 rows) +SELECT c~>3, c FROM test_cube ORDER BY c~>3 LIMIT 15; -- ascending by lower bound + ?column? | c +----------+--------------------------- + 0 | (100000) + 1 | (1, 1) + 6 | (30333, 50),(30273, 6) + 43 | (43301, 75),(43227, 43) + 51 | (19650, 142),(19630, 51) + 81 | (2424, 160),(2424, 81) + 108 | (3449, 171),(3354, 108) + 109 | (18037, 155),(17941, 109) + 114 | (28511, 208),(28479, 114) + 118 | (19946, 217),(19941, 118) + 139 | (16906, 191),(16816, 139) + 163 | (759, 187),(662, 163) + 181 | (22684, 266),(22656, 181) + 213 | (24423, 255),(24360, 213) + 222 | (45989, 249),(45910, 222) +(15 rows) + +SELECT c~>4, c FROM test_cube ORDER BY c~>4 LIMIT 15; -- ascending by upper bound + ?column? | c +----------+--------------------------- + 0 | (100000) + 1 | (1, 1) + 50 | (30333, 50),(30273, 6) + 75 | (43301, 75),(43227, 43) + 142 | (19650, 142),(19630, 51) + 155 | (18037, 155),(17941, 109) + 160 | (2424, 160),(2424, 81) + 171 | (3449, 171),(3354, 108) + 187 | (759, 187),(662, 163) + 191 | (16906, 191),(16816, 139) + 208 | (28511, 208),(28479, 114) + 217 | (19946, 217),(19941, 118) + 249 | (45989, 249),(45910, 222) + 255 | (24423, 255),(24360, 213) + 266 | (22684, 266),(22656, 181) +(15 rows) + +RESET enable_indexscan; diff --git a/contrib/cube/expected/cube_1.out b/contrib/cube/expected/cube_1.out index 194c3e693f..db43406fd0 100644 --- a/contrib/cube/expected/cube_1.out +++ b/contrib/cube/expected/cube_1.out @@ -1495,25 +1495,25 @@ SELECT cube(array[40,50,60], array[10,20,30])~>1; SELECT cube(array[10,20,30], array[40,50,60])~>2; ?column? ---------- - 20 + 40 (1 row) SELECT cube(array[40,50,60], array[10,20,30])~>2; ?column? ---------- - 20 + 40 (1 row) SELECT cube(array[10,20,30], array[40,50,60])~>3; ?column? ---------- - 30 + 20 (1 row) SELECT cube(array[40,50,60], array[10,20,30])~>3; ?column? ---------- - 30 + 20 (1 row) SELECT cube(array[40,50,60], array[10,20,30])~>0; @@ -1521,7 +1521,7 @@ ERROR: cube index 0 is out of bounds SELECT cube(array[40,50,60], array[10,20,30])~>4; ?column? ---------- - 40 + 50 (1 row) SELECT cube(array[40,50,60], array[10,20,30])~>(-1); @@ -1552,25 +1552,28 @@ SELECT * FROM test_cube WHERE c && '(3000,1000),(0,0)' GROUP BY c ORDER BY c; (2424, 160),(2424, 81) (5 rows) --- kNN with index +-- Test kNN +INSERT INTO test_cube VALUES ('(1,1)'), ('(100000)'), ('(0, 100000)'); -- Some corner cases +SET enable_seqscan = false; +-- Test different metrics SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5; c | dist -------------------------+------------------ (337, 455),(240, 359) | 0 + (1, 1) | 140.007142674936 (759, 187),(662, 163) | 162 (948, 1201),(907, 1156) | 772.000647668122 (1444, 403),(1346, 344) | 846 - (369, 1457),(278, 1409) | 909 (5 rows) SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5; c | dist -------------------------+------ (337, 455),(240, 359) | 0 + (1, 1) | 99 (759, 187),(662, 163) | 162 (948, 1201),(907, 1156) | 656 (1444, 403),(1346, 344) | 846 - (369, 1457),(278, 1409) | 909 (5 rows) SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5; @@ -1578,133 +1581,203 @@ SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c -------------------------+------ (337, 455),(240, 359) | 0 (759, 187),(662, 163) | 162 + (1, 1) | 198 (1444, 403),(1346, 344) | 846 (369, 1457),(278, 1409) | 909 - (948, 1201),(907, 1156) | 1063 (5 rows) --- kNN-based sorting -SELECT * FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by 1st coordinate of lower left corner - c ---------------------------- - (54, 38679),(3, 38602) - (83, 10271),(15, 10265) - (122, 46832),(64, 46762) - (167, 17214),(92, 17184) - (161, 24465),(107, 24374) - (162, 26040),(120, 25963) - (154, 4019),(138, 3990) - (259, 1850),(175, 1820) - (207, 40886),(179, 40879) - (288, 49588),(204, 49571) - (270, 32616),(226, 32607) - (318, 31489),(235, 31404) - (337, 455),(240, 359) - (270, 29508),(264, 29440) - (369, 1457),(278, 1409) +-- Test sorting by coordinates +SELECT c~>1, c FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by left bound + ?column? | c +----------+--------------------------- + 0 | (0, 100000) + 1 | (1, 1) + 3 | (54, 38679),(3, 38602) + 15 | (83, 10271),(15, 10265) + 64 | (122, 46832),(64, 46762) + 92 | (167, 17214),(92, 17184) + 107 | (161, 24465),(107, 24374) + 120 | (162, 26040),(120, 25963) + 138 | (154, 4019),(138, 3990) + 175 | (259, 1850),(175, 1820) + 179 | (207, 40886),(179, 40879) + 204 | (288, 49588),(204, 49571) + 226 | (270, 32616),(226, 32607) + 235 | (318, 31489),(235, 31404) + 240 | (337, 455),(240, 359) (15 rows) -SELECT * FROM test_cube ORDER BY c~>4 LIMIT 15; -- ascending by 2nd coordinate or upper right corner - c ---------------------------- - (30333, 50),(30273, 6) - (43301, 75),(43227, 43) - (19650, 142),(19630, 51) - (2424, 160),(2424, 81) - (3449, 171),(3354, 108) - (18037, 155),(17941, 109) - (28511, 208),(28479, 114) - (19946, 217),(19941, 118) - (16906, 191),(16816, 139) - (759, 187),(662, 163) - (22684, 266),(22656, 181) - (24423, 255),(24360, 213) - (45989, 249),(45910, 222) - (11399, 377),(11360, 294) - (12162, 389),(12103, 309) +SELECT c~>2, c FROM test_cube ORDER BY c~>2 LIMIT 15; -- ascending by right bound + ?column? | c +----------+--------------------------- + 0 | (0, 100000) + 1 | (1, 1) + 54 | (54, 38679),(3, 38602) + 83 | (83, 10271),(15, 10265) + 122 | (122, 46832),(64, 46762) + 154 | (154, 4019),(138, 3990) + 161 | (161, 24465),(107, 24374) + 162 | (162, 26040),(120, 25963) + 167 | (167, 17214),(92, 17184) + 207 | (207, 40886),(179, 40879) + 259 | (259, 1850),(175, 1820) + 270 | (270, 29508),(264, 29440) + 270 | (270, 32616),(226, 32607) + 288 | (288, 49588),(204, 49571) + 318 | (318, 31489),(235, 31404) (15 rows) -SELECT * FROM test_cube ORDER BY c~>1 DESC LIMIT 15; -- descending by 1st coordinate of lower left corner - c -------------------------------- - (50027, 49230),(49951, 49214) - (49980, 35004),(49937, 34963) - (49985, 6436),(49927, 6338) - (49999, 27218),(49908, 27176) - (49954, 1340),(49905, 1294) - (49944, 25163),(49902, 25153) - (49981, 34876),(49898, 34786) - (49957, 43390),(49897, 43384) - (49853, 18504),(49848, 18503) - (49902, 41752),(49818, 41746) - (49907, 30225),(49810, 30158) - (49843, 5175),(49808, 5145) - (49887, 24274),(49805, 24184) - (49847, 7128),(49798, 7067) - (49820, 7990),(49771, 7967) +SELECT c~>3, c FROM test_cube ORDER BY c~>3 LIMIT 15; -- ascending by lower bound + ?column? | c +----------+--------------------------- + 0 | (100000) + 1 | (1, 1) + 6 | (30333, 50),(30273, 6) + 43 | (43301, 75),(43227, 43) + 51 | (19650, 142),(19630, 51) + 81 | (2424, 160),(2424, 81) + 108 | (3449, 171),(3354, 108) + 109 | (18037, 155),(17941, 109) + 114 | (28511, 208),(28479, 114) + 118 | (19946, 217),(19941, 118) + 139 | (16906, 191),(16816, 139) + 163 | (759, 187),(662, 163) + 181 | (22684, 266),(22656, 181) + 213 | (24423, 255),(24360, 213) + 222 | (45989, 249),(45910, 222) (15 rows) -SELECT * FROM test_cube ORDER BY c~>4 DESC LIMIT 15; -- descending by 2nd coordinate or upper right corner - c -------------------------------- - (36311, 50073),(36258, 49987) - (30746, 50040),(30727, 49992) - (2168, 50012),(2108, 49914) - (21551, 49983),(21492, 49885) - (17954, 49975),(17865, 49915) - (3531, 49962),(3463, 49934) - (19128, 49932),(19112, 49849) - (31287, 49923),(31236, 49913) - (43925, 49912),(43888, 49878) - (29261, 49910),(29247, 49818) - (14913, 49873),(14849, 49836) - (20007, 49858),(19921, 49778) - (38266, 49852),(38233, 49844) - (37595, 49849),(37581, 49834) - (46151, 49848),(46058, 49830) +SELECT c~>4, c FROM test_cube ORDER BY c~>4 LIMIT 15; -- ascending by upper bound + ?column? | c +----------+--------------------------- + 0 | (100000) + 1 | (1, 1) + 50 | (30333, 50),(30273, 6) + 75 | (43301, 75),(43227, 43) + 142 | (19650, 142),(19630, 51) + 155 | (18037, 155),(17941, 109) + 160 | (2424, 160),(2424, 81) + 171 | (3449, 171),(3354, 108) + 187 | (759, 187),(662, 163) + 191 | (16906, 191),(16816, 139) + 208 | (28511, 208),(28479, 114) + 217 | (19946, 217),(19941, 118) + 249 | (45989, 249),(45910, 222) + 255 | (24423, 255),(24360, 213) + 266 | (22684, 266),(22656, 181) (15 rows) --- same thing for index with points -CREATE TABLE test_point(c cube); -INSERT INTO test_point(SELECT cube(array[c->1,c->2,c->3,c->4]) FROM test_cube); -CREATE INDEX ON test_point USING gist(c); -SELECT * FROM test_point ORDER BY c~>1, c~>2 LIMIT 15; -- ascending by 1st then by 2nd coordinate - c --------------------------- - (54, 38679, 3, 38602) - (83, 10271, 15, 10265) - (122, 46832, 64, 46762) - (154, 4019, 138, 3990) - (161, 24465, 107, 24374) - (162, 26040, 120, 25963) - (167, 17214, 92, 17184) - (207, 40886, 179, 40879) - (259, 1850, 175, 1820) - (270, 29508, 264, 29440) - (270, 32616, 226, 32607) - (288, 49588, 204, 49571) - (318, 31489, 235, 31404) - (326, 18837, 285, 18817) - (337, 455, 240, 359) +-- Same queries with sequential scan (should give the same results as above) +RESET enable_seqscan; +SET enable_indexscan = OFF; +SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5; + c | dist +-------------------------+------------------ + (337, 455),(240, 359) | 0 + (1, 1) | 140.007142674936 + (759, 187),(662, 163) | 162 + (948, 1201),(907, 1156) | 772.000647668122 + (1444, 403),(1346, 344) | 846 +(5 rows) + +SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5; + c | dist +-------------------------+------ + (337, 455),(240, 359) | 0 + (1, 1) | 99 + (759, 187),(662, 163) | 162 + (948, 1201),(907, 1156) | 656 + (1444, 403),(1346, 344) | 846 +(5 rows) + +SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5; + c | dist +-------------------------+------ + (337, 455),(240, 359) | 0 + (759, 187),(662, 163) | 162 + (1, 1) | 198 + (1444, 403),(1346, 344) | 846 + (369, 1457),(278, 1409) | 909 +(5 rows) + +SELECT c~>1, c FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by left bound + ?column? | c +----------+--------------------------- + 0 | (0, 100000) + 1 | (1, 1) + 3 | (54, 38679),(3, 38602) + 15 | (83, 10271),(15, 10265) + 64 | (122, 46832),(64, 46762) + 92 | (167, 17214),(92, 17184) + 107 | (161, 24465),(107, 24374) + 120 | (162, 26040),(120, 25963) + 138 | (154, 4019),(138, 3990) + 175 | (259, 1850),(175, 1820) + 179 | (207, 40886),(179, 40879) + 204 | (288, 49588),(204, 49571) + 226 | (270, 32616),(226, 32607) + 235 | (318, 31489),(235, 31404) + 240 | (337, 455),(240, 359) (15 rows) -SELECT * FROM test_point ORDER BY c~>4 DESC LIMIT 15; -- descending by 1st coordinate - c ------------------------------- - (30746, 50040, 30727, 49992) - (36311, 50073, 36258, 49987) - (3531, 49962, 3463, 49934) - (17954, 49975, 17865, 49915) - (2168, 50012, 2108, 49914) - (31287, 49923, 31236, 49913) - (21551, 49983, 21492, 49885) - (43925, 49912, 43888, 49878) - (19128, 49932, 19112, 49849) - (38266, 49852, 38233, 49844) - (14913, 49873, 14849, 49836) - (37595, 49849, 37581, 49834) - (46151, 49848, 46058, 49830) - (29261, 49910, 29247, 49818) - (19233, 49824, 19185, 49794) +SELECT c~>2, c FROM test_cube ORDER BY c~>2 LIMIT 15; -- ascending by right bound + ?column? | c +----------+--------------------------- + 0 | (0, 100000) + 1 | (1, 1) + 54 | (54, 38679),(3, 38602) + 83 | (83, 10271),(15, 10265) + 122 | (122, 46832),(64, 46762) + 154 | (154, 4019),(138, 3990) + 161 | (161, 24465),(107, 24374) + 162 | (162, 26040),(120, 25963) + 167 | (167, 17214),(92, 17184) + 207 | (207, 40886),(179, 40879) + 259 | (259, 1850),(175, 1820) + 270 | (270, 29508),(264, 29440) + 270 | (270, 32616),(226, 32607) + 288 | (288, 49588),(204, 49571) + 318 | (318, 31489),(235, 31404) (15 rows) +SELECT c~>3, c FROM test_cube ORDER BY c~>3 LIMIT 15; -- ascending by lower bound + ?column? | c +----------+--------------------------- + 0 | (100000) + 1 | (1, 1) + 6 | (30333, 50),(30273, 6) + 43 | (43301, 75),(43227, 43) + 51 | (19650, 142),(19630, 51) + 81 | (2424, 160),(2424, 81) + 108 | (3449, 171),(3354, 108) + 109 | (18037, 155),(17941, 109) + 114 | (28511, 208),(28479, 114) + 118 | (19946, 217),(19941, 118) + 139 | (16906, 191),(16816, 139) + 163 | (759, 187),(662, 163) + 181 | (22684, 266),(22656, 181) + 213 | (24423, 255),(24360, 213) + 222 | (45989, 249),(45910, 222) +(15 rows) + +SELECT c~>4, c FROM test_cube ORDER BY c~>4 LIMIT 15; -- ascending by upper bound + ?column? | c +----------+--------------------------- + 0 | (100000) + 1 | (1, 1) + 50 | (30333, 50),(30273, 6) + 75 | (43301, 75),(43227, 43) + 142 | (19650, 142),(19630, 51) + 155 | (18037, 155),(17941, 109) + 160 | (2424, 160),(2424, 81) + 171 | (3449, 171),(3354, 108) + 187 | (759, 187),(662, 163) + 191 | (16906, 191),(16816, 139) + 208 | (28511, 208),(28479, 114) + 217 | (19946, 217),(19941, 118) + 249 | (45989, 249),(45910, 222) + 255 | (24423, 255),(24360, 213) + 266 | (22684, 266),(22656, 181) +(15 rows) + +RESET enable_indexscan; diff --git a/contrib/cube/expected/cube_2.out b/contrib/cube/expected/cube_2.out index 680a46b789..b3ad8b05d9 100644 --- a/contrib/cube/expected/cube_2.out +++ b/contrib/cube/expected/cube_2.out @@ -1495,25 +1495,25 @@ SELECT cube(array[40,50,60], array[10,20,30])~>1; SELECT cube(array[10,20,30], array[40,50,60])~>2; ?column? ---------- - 20 + 40 (1 row) SELECT cube(array[40,50,60], array[10,20,30])~>2; ?column? ---------- - 20 + 40 (1 row) SELECT cube(array[10,20,30], array[40,50,60])~>3; ?column? ---------- - 30 + 20 (1 row) SELECT cube(array[40,50,60], array[10,20,30])~>3; ?column? ---------- - 30 + 20 (1 row) SELECT cube(array[40,50,60], array[10,20,30])~>0; @@ -1521,7 +1521,7 @@ ERROR: cube index 0 is out of bounds SELECT cube(array[40,50,60], array[10,20,30])~>4; ?column? ---------- - 40 + 50 (1 row) SELECT cube(array[40,50,60], array[10,20,30])~>(-1); @@ -1552,25 +1552,28 @@ SELECT * FROM test_cube WHERE c && '(3000,1000),(0,0)' GROUP BY c ORDER BY c; (2424, 160),(2424, 81) (5 rows) --- kNN with index +-- Test kNN +INSERT INTO test_cube VALUES ('(1,1)'), ('(100000)'), ('(0, 100000)'); -- Some corner cases +SET enable_seqscan = false; +-- Test different metrics SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5; c | dist -------------------------+------------------ (337, 455),(240, 359) | 0 + (1, 1) | 140.007142674936 (759, 187),(662, 163) | 162 (948, 1201),(907, 1156) | 772.000647668122 (1444, 403),(1346, 344) | 846 - (369, 1457),(278, 1409) | 909 (5 rows) SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5; c | dist -------------------------+------ (337, 455),(240, 359) | 0 + (1, 1) | 99 (759, 187),(662, 163) | 162 (948, 1201),(907, 1156) | 656 (1444, 403),(1346, 344) | 846 - (369, 1457),(278, 1409) | 909 (5 rows) SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5; @@ -1578,133 +1581,203 @@ SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c -------------------------+------ (337, 455),(240, 359) | 0 (759, 187),(662, 163) | 162 + (1, 1) | 198 (1444, 403),(1346, 344) | 846 (369, 1457),(278, 1409) | 909 - (948, 1201),(907, 1156) | 1063 (5 rows) --- kNN-based sorting -SELECT * FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by 1st coordinate of lower left corner - c ---------------------------- - (54, 38679),(3, 38602) - (83, 10271),(15, 10265) - (122, 46832),(64, 46762) - (167, 17214),(92, 17184) - (161, 24465),(107, 24374) - (162, 26040),(120, 25963) - (154, 4019),(138, 3990) - (259, 1850),(175, 1820) - (207, 40886),(179, 40879) - (288, 49588),(204, 49571) - (270, 32616),(226, 32607) - (318, 31489),(235, 31404) - (337, 455),(240, 359) - (270, 29508),(264, 29440) - (369, 1457),(278, 1409) +-- Test sorting by coordinates +SELECT c~>1, c FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by left bound + ?column? | c +----------+--------------------------- + 0 | (0, 100000) + 1 | (1, 1) + 3 | (54, 38679),(3, 38602) + 15 | (83, 10271),(15, 10265) + 64 | (122, 46832),(64, 46762) + 92 | (167, 17214),(92, 17184) + 107 | (161, 24465),(107, 24374) + 120 | (162, 26040),(120, 25963) + 138 | (154, 4019),(138, 3990) + 175 | (259, 1850),(175, 1820) + 179 | (207, 40886),(179, 40879) + 204 | (288, 49588),(204, 49571) + 226 | (270, 32616),(226, 32607) + 235 | (318, 31489),(235, 31404) + 240 | (337, 455),(240, 359) (15 rows) -SELECT * FROM test_cube ORDER BY c~>4 LIMIT 15; -- ascending by 2nd coordinate or upper right corner - c ---------------------------- - (30333, 50),(30273, 6) - (43301, 75),(43227, 43) - (19650, 142),(19630, 51) - (2424, 160),(2424, 81) - (3449, 171),(3354, 108) - (18037, 155),(17941, 109) - (28511, 208),(28479, 114) - (19946, 217),(19941, 118) - (16906, 191),(16816, 139) - (759, 187),(662, 163) - (22684, 266),(22656, 181) - (24423, 255),(24360, 213) - (45989, 249),(45910, 222) - (11399, 377),(11360, 294) - (12162, 389),(12103, 309) +SELECT c~>2, c FROM test_cube ORDER BY c~>2 LIMIT 15; -- ascending by right bound + ?column? | c +----------+--------------------------- + 0 | (0, 100000) + 1 | (1, 1) + 54 | (54, 38679),(3, 38602) + 83 | (83, 10271),(15, 10265) + 122 | (122, 46832),(64, 46762) + 154 | (154, 4019),(138, 3990) + 161 | (161, 24465),(107, 24374) + 162 | (162, 26040),(120, 25963) + 167 | (167, 17214),(92, 17184) + 207 | (207, 40886),(179, 40879) + 259 | (259, 1850),(175, 1820) + 270 | (270, 29508),(264, 29440) + 270 | (270, 32616),(226, 32607) + 288 | (288, 49588),(204, 49571) + 318 | (318, 31489),(235, 31404) (15 rows) -SELECT * FROM test_cube ORDER BY c~>1 DESC LIMIT 15; -- descending by 1st coordinate of lower left corner - c -------------------------------- - (50027, 49230),(49951, 49214) - (49980, 35004),(49937, 34963) - (49985, 6436),(49927, 6338) - (49999, 27218),(49908, 27176) - (49954, 1340),(49905, 1294) - (49944, 25163),(49902, 25153) - (49981, 34876),(49898, 34786) - (49957, 43390),(49897, 43384) - (49853, 18504),(49848, 18503) - (49902, 41752),(49818, 41746) - (49907, 30225),(49810, 30158) - (49843, 5175),(49808, 5145) - (49887, 24274),(49805, 24184) - (49847, 7128),(49798, 7067) - (49820, 7990),(49771, 7967) +SELECT c~>3, c FROM test_cube ORDER BY c~>3 LIMIT 15; -- ascending by lower bound + ?column? | c +----------+--------------------------- + 0 | (100000) + 1 | (1, 1) + 6 | (30333, 50),(30273, 6) + 43 | (43301, 75),(43227, 43) + 51 | (19650, 142),(19630, 51) + 81 | (2424, 160),(2424, 81) + 108 | (3449, 171),(3354, 108) + 109 | (18037, 155),(17941, 109) + 114 | (28511, 208),(28479, 114) + 118 | (19946, 217),(19941, 118) + 139 | (16906, 191),(16816, 139) + 163 | (759, 187),(662, 163) + 181 | (22684, 266),(22656, 181) + 213 | (24423, 255),(24360, 213) + 222 | (45989, 249),(45910, 222) (15 rows) -SELECT * FROM test_cube ORDER BY c~>4 DESC LIMIT 15; -- descending by 2nd coordinate or upper right corner - c -------------------------------- - (36311, 50073),(36258, 49987) - (30746, 50040),(30727, 49992) - (2168, 50012),(2108, 49914) - (21551, 49983),(21492, 49885) - (17954, 49975),(17865, 49915) - (3531, 49962),(3463, 49934) - (19128, 49932),(19112, 49849) - (31287, 49923),(31236, 49913) - (43925, 49912),(43888, 49878) - (29261, 49910),(29247, 49818) - (14913, 49873),(14849, 49836) - (20007, 49858),(19921, 49778) - (38266, 49852),(38233, 49844) - (37595, 49849),(37581, 49834) - (46151, 49848),(46058, 49830) +SELECT c~>4, c FROM test_cube ORDER BY c~>4 LIMIT 15; -- ascending by upper bound + ?column? | c +----------+--------------------------- + 0 | (100000) + 1 | (1, 1) + 50 | (30333, 50),(30273, 6) + 75 | (43301, 75),(43227, 43) + 142 | (19650, 142),(19630, 51) + 155 | (18037, 155),(17941, 109) + 160 | (2424, 160),(2424, 81) + 171 | (3449, 171),(3354, 108) + 187 | (759, 187),(662, 163) + 191 | (16906, 191),(16816, 139) + 208 | (28511, 208),(28479, 114) + 217 | (19946, 217),(19941, 118) + 249 | (45989, 249),(45910, 222) + 255 | (24423, 255),(24360, 213) + 266 | (22684, 266),(22656, 181) (15 rows) --- same thing for index with points -CREATE TABLE test_point(c cube); -INSERT INTO test_point(SELECT cube(array[c->1,c->2,c->3,c->4]) FROM test_cube); -CREATE INDEX ON test_point USING gist(c); -SELECT * FROM test_point ORDER BY c~>1, c~>2 LIMIT 15; -- ascending by 1st then by 2nd coordinate - c --------------------------- - (54, 38679, 3, 38602) - (83, 10271, 15, 10265) - (122, 46832, 64, 46762) - (154, 4019, 138, 3990) - (161, 24465, 107, 24374) - (162, 26040, 120, 25963) - (167, 17214, 92, 17184) - (207, 40886, 179, 40879) - (259, 1850, 175, 1820) - (270, 29508, 264, 29440) - (270, 32616, 226, 32607) - (288, 49588, 204, 49571) - (318, 31489, 235, 31404) - (326, 18837, 285, 18817) - (337, 455, 240, 359) +-- Same queries with sequential scan (should give the same results as above) +RESET enable_seqscan; +SET enable_indexscan = OFF; +SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5; + c | dist +-------------------------+------------------ + (337, 455),(240, 359) | 0 + (1, 1) | 140.007142674936 + (759, 187),(662, 163) | 162 + (948, 1201),(907, 1156) | 772.000647668122 + (1444, 403),(1346, 344) | 846 +(5 rows) + +SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5; + c | dist +-------------------------+------ + (337, 455),(240, 359) | 0 + (1, 1) | 99 + (759, 187),(662, 163) | 162 + (948, 1201),(907, 1156) | 656 + (1444, 403),(1346, 344) | 846 +(5 rows) + +SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5; + c | dist +-------------------------+------ + (337, 455),(240, 359) | 0 + (759, 187),(662, 163) | 162 + (1, 1) | 198 + (1444, 403),(1346, 344) | 846 + (369, 1457),(278, 1409) | 909 +(5 rows) + +SELECT c~>1, c FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by left bound + ?column? | c +----------+--------------------------- + 0 | (0, 100000) + 1 | (1, 1) + 3 | (54, 38679),(3, 38602) + 15 | (83, 10271),(15, 10265) + 64 | (122, 46832),(64, 46762) + 92 | (167, 17214),(92, 17184) + 107 | (161, 24465),(107, 24374) + 120 | (162, 26040),(120, 25963) + 138 | (154, 4019),(138, 3990) + 175 | (259, 1850),(175, 1820) + 179 | (207, 40886),(179, 40879) + 204 | (288, 49588),(204, 49571) + 226 | (270, 32616),(226, 32607) + 235 | (318, 31489),(235, 31404) + 240 | (337, 455),(240, 359) (15 rows) -SELECT * FROM test_point ORDER BY c~>4 DESC LIMIT 15; -- descending by 1st coordinate - c ------------------------------- - (30746, 50040, 30727, 49992) - (36311, 50073, 36258, 49987) - (3531, 49962, 3463, 49934) - (17954, 49975, 17865, 49915) - (2168, 50012, 2108, 49914) - (31287, 49923, 31236, 49913) - (21551, 49983, 21492, 49885) - (43925, 49912, 43888, 49878) - (19128, 49932, 19112, 49849) - (38266, 49852, 38233, 49844) - (14913, 49873, 14849, 49836) - (37595, 49849, 37581, 49834) - (46151, 49848, 46058, 49830) - (29261, 49910, 29247, 49818) - (19233, 49824, 19185, 49794) +SELECT c~>2, c FROM test_cube ORDER BY c~>2 LIMIT 15; -- ascending by right bound + ?column? | c +----------+--------------------------- + 0 | (0, 100000) + 1 | (1, 1) + 54 | (54, 38679),(3, 38602) + 83 | (83, 10271),(15, 10265) + 122 | (122, 46832),(64, 46762) + 154 | (154, 4019),(138, 3990) + 161 | (161, 24465),(107, 24374) + 162 | (162, 26040),(120, 25963) + 167 | (167, 17214),(92, 17184) + 207 | (207, 40886),(179, 40879) + 259 | (259, 1850),(175, 1820) + 270 | (270, 29508),(264, 29440) + 270 | (270, 32616),(226, 32607) + 288 | (288, 49588),(204, 49571) + 318 | (318, 31489),(235, 31404) (15 rows) +SELECT c~>3, c FROM test_cube ORDER BY c~>3 LIMIT 15; -- ascending by lower bound + ?column? | c +----------+--------------------------- + 0 | (100000) + 1 | (1, 1) + 6 | (30333, 50),(30273, 6) + 43 | (43301, 75),(43227, 43) + 51 | (19650, 142),(19630, 51) + 81 | (2424, 160),(2424, 81) + 108 | (3449, 171),(3354, 108) + 109 | (18037, 155),(17941, 109) + 114 | (28511, 208),(28479, 114) + 118 | (19946, 217),(19941, 118) + 139 | (16906, 191),(16816, 139) + 163 | (759, 187),(662, 163) + 181 | (22684, 266),(22656, 181) + 213 | (24423, 255),(24360, 213) + 222 | (45989, 249),(45910, 222) +(15 rows) + +SELECT c~>4, c FROM test_cube ORDER BY c~>4 LIMIT 15; -- ascending by upper bound + ?column? | c +----------+--------------------------- + 0 | (100000) + 1 | (1, 1) + 50 | (30333, 50),(30273, 6) + 75 | (43301, 75),(43227, 43) + 142 | (19650, 142),(19630, 51) + 155 | (18037, 155),(17941, 109) + 160 | (2424, 160),(2424, 81) + 171 | (3449, 171),(3354, 108) + 187 | (759, 187),(662, 163) + 191 | (16906, 191),(16816, 139) + 208 | (28511, 208),(28479, 114) + 217 | (19946, 217),(19941, 118) + 249 | (45989, 249),(45910, 222) + 255 | (24423, 255),(24360, 213) + 266 | (22684, 266),(22656, 181) +(15 rows) + +RESET enable_indexscan; diff --git a/contrib/cube/expected/cube_3.out b/contrib/cube/expected/cube_3.out index 8ad92221ad..4a6c5f613e 100644 --- a/contrib/cube/expected/cube_3.out +++ b/contrib/cube/expected/cube_3.out @@ -1495,25 +1495,25 @@ SELECT cube(array[40,50,60], array[10,20,30])~>1; SELECT cube(array[10,20,30], array[40,50,60])~>2; ?column? ---------- - 20 + 40 (1 row) SELECT cube(array[40,50,60], array[10,20,30])~>2; ?column? ---------- - 20 + 40 (1 row) SELECT cube(array[10,20,30], array[40,50,60])~>3; ?column? ---------- - 30 + 20 (1 row) SELECT cube(array[40,50,60], array[10,20,30])~>3; ?column? ---------- - 30 + 20 (1 row) SELECT cube(array[40,50,60], array[10,20,30])~>0; @@ -1521,7 +1521,7 @@ ERROR: cube index 0 is out of bounds SELECT cube(array[40,50,60], array[10,20,30])~>4; ?column? ---------- - 40 + 50 (1 row) SELECT cube(array[40,50,60], array[10,20,30])~>(-1); @@ -1552,25 +1552,28 @@ SELECT * FROM test_cube WHERE c && '(3000,1000),(0,0)' GROUP BY c ORDER BY c; (2424, 160),(2424, 81) (5 rows) --- kNN with index +-- Test kNN +INSERT INTO test_cube VALUES ('(1,1)'), ('(100000)'), ('(0, 100000)'); -- Some corner cases +SET enable_seqscan = false; +-- Test different metrics SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5; c | dist -------------------------+------------------ (337, 455),(240, 359) | 0 + (1, 1) | 140.007142674936 (759, 187),(662, 163) | 162 (948, 1201),(907, 1156) | 772.000647668122 (1444, 403),(1346, 344) | 846 - (369, 1457),(278, 1409) | 909 (5 rows) SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5; c | dist -------------------------+------ (337, 455),(240, 359) | 0 + (1, 1) | 99 (759, 187),(662, 163) | 162 (948, 1201),(907, 1156) | 656 (1444, 403),(1346, 344) | 846 - (369, 1457),(278, 1409) | 909 (5 rows) SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5; @@ -1578,133 +1581,203 @@ SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c -------------------------+------ (337, 455),(240, 359) | 0 (759, 187),(662, 163) | 162 + (1, 1) | 198 (1444, 403),(1346, 344) | 846 (369, 1457),(278, 1409) | 909 - (948, 1201),(907, 1156) | 1063 (5 rows) --- kNN-based sorting -SELECT * FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by 1st coordinate of lower left corner - c ---------------------------- - (54, 38679),(3, 38602) - (83, 10271),(15, 10265) - (122, 46832),(64, 46762) - (167, 17214),(92, 17184) - (161, 24465),(107, 24374) - (162, 26040),(120, 25963) - (154, 4019),(138, 3990) - (259, 1850),(175, 1820) - (207, 40886),(179, 40879) - (288, 49588),(204, 49571) - (270, 32616),(226, 32607) - (318, 31489),(235, 31404) - (337, 455),(240, 359) - (270, 29508),(264, 29440) - (369, 1457),(278, 1409) +-- Test sorting by coordinates +SELECT c~>1, c FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by left bound + ?column? | c +----------+--------------------------- + 0 | (0, 100000) + 1 | (1, 1) + 3 | (54, 38679),(3, 38602) + 15 | (83, 10271),(15, 10265) + 64 | (122, 46832),(64, 46762) + 92 | (167, 17214),(92, 17184) + 107 | (161, 24465),(107, 24374) + 120 | (162, 26040),(120, 25963) + 138 | (154, 4019),(138, 3990) + 175 | (259, 1850),(175, 1820) + 179 | (207, 40886),(179, 40879) + 204 | (288, 49588),(204, 49571) + 226 | (270, 32616),(226, 32607) + 235 | (318, 31489),(235, 31404) + 240 | (337, 455),(240, 359) (15 rows) -SELECT * FROM test_cube ORDER BY c~>4 LIMIT 15; -- ascending by 2nd coordinate or upper right corner - c ---------------------------- - (30333, 50),(30273, 6) - (43301, 75),(43227, 43) - (19650, 142),(19630, 51) - (2424, 160),(2424, 81) - (3449, 171),(3354, 108) - (18037, 155),(17941, 109) - (28511, 208),(28479, 114) - (19946, 217),(19941, 118) - (16906, 191),(16816, 139) - (759, 187),(662, 163) - (22684, 266),(22656, 181) - (24423, 255),(24360, 213) - (45989, 249),(45910, 222) - (11399, 377),(11360, 294) - (12162, 389),(12103, 309) +SELECT c~>2, c FROM test_cube ORDER BY c~>2 LIMIT 15; -- ascending by right bound + ?column? | c +----------+--------------------------- + 0 | (0, 100000) + 1 | (1, 1) + 54 | (54, 38679),(3, 38602) + 83 | (83, 10271),(15, 10265) + 122 | (122, 46832),(64, 46762) + 154 | (154, 4019),(138, 3990) + 161 | (161, 24465),(107, 24374) + 162 | (162, 26040),(120, 25963) + 167 | (167, 17214),(92, 17184) + 207 | (207, 40886),(179, 40879) + 259 | (259, 1850),(175, 1820) + 270 | (270, 29508),(264, 29440) + 270 | (270, 32616),(226, 32607) + 288 | (288, 49588),(204, 49571) + 318 | (318, 31489),(235, 31404) (15 rows) -SELECT * FROM test_cube ORDER BY c~>1 DESC LIMIT 15; -- descending by 1st coordinate of lower left corner - c -------------------------------- - (50027, 49230),(49951, 49214) - (49980, 35004),(49937, 34963) - (49985, 6436),(49927, 6338) - (49999, 27218),(49908, 27176) - (49954, 1340),(49905, 1294) - (49944, 25163),(49902, 25153) - (49981, 34876),(49898, 34786) - (49957, 43390),(49897, 43384) - (49853, 18504),(49848, 18503) - (49902, 41752),(49818, 41746) - (49907, 30225),(49810, 30158) - (49843, 5175),(49808, 5145) - (49887, 24274),(49805, 24184) - (49847, 7128),(49798, 7067) - (49820, 7990),(49771, 7967) +SELECT c~>3, c FROM test_cube ORDER BY c~>3 LIMIT 15; -- ascending by lower bound + ?column? | c +----------+--------------------------- + 0 | (100000) + 1 | (1, 1) + 6 | (30333, 50),(30273, 6) + 43 | (43301, 75),(43227, 43) + 51 | (19650, 142),(19630, 51) + 81 | (2424, 160),(2424, 81) + 108 | (3449, 171),(3354, 108) + 109 | (18037, 155),(17941, 109) + 114 | (28511, 208),(28479, 114) + 118 | (19946, 217),(19941, 118) + 139 | (16906, 191),(16816, 139) + 163 | (759, 187),(662, 163) + 181 | (22684, 266),(22656, 181) + 213 | (24423, 255),(24360, 213) + 222 | (45989, 249),(45910, 222) (15 rows) -SELECT * FROM test_cube ORDER BY c~>4 DESC LIMIT 15; -- descending by 2nd coordinate or upper right corner - c -------------------------------- - (36311, 50073),(36258, 49987) - (30746, 50040),(30727, 49992) - (2168, 50012),(2108, 49914) - (21551, 49983),(21492, 49885) - (17954, 49975),(17865, 49915) - (3531, 49962),(3463, 49934) - (19128, 49932),(19112, 49849) - (31287, 49923),(31236, 49913) - (43925, 49912),(43888, 49878) - (29261, 49910),(29247, 49818) - (14913, 49873),(14849, 49836) - (20007, 49858),(19921, 49778) - (38266, 49852),(38233, 49844) - (37595, 49849),(37581, 49834) - (46151, 49848),(46058, 49830) +SELECT c~>4, c FROM test_cube ORDER BY c~>4 LIMIT 15; -- ascending by upper bound + ?column? | c +----------+--------------------------- + 0 | (100000) + 1 | (1, 1) + 50 | (30333, 50),(30273, 6) + 75 | (43301, 75),(43227, 43) + 142 | (19650, 142),(19630, 51) + 155 | (18037, 155),(17941, 109) + 160 | (2424, 160),(2424, 81) + 171 | (3449, 171),(3354, 108) + 187 | (759, 187),(662, 163) + 191 | (16906, 191),(16816, 139) + 208 | (28511, 208),(28479, 114) + 217 | (19946, 217),(19941, 118) + 249 | (45989, 249),(45910, 222) + 255 | (24423, 255),(24360, 213) + 266 | (22684, 266),(22656, 181) (15 rows) --- same thing for index with points -CREATE TABLE test_point(c cube); -INSERT INTO test_point(SELECT cube(array[c->1,c->2,c->3,c->4]) FROM test_cube); -CREATE INDEX ON test_point USING gist(c); -SELECT * FROM test_point ORDER BY c~>1, c~>2 LIMIT 15; -- ascending by 1st then by 2nd coordinate - c --------------------------- - (54, 38679, 3, 38602) - (83, 10271, 15, 10265) - (122, 46832, 64, 46762) - (154, 4019, 138, 3990) - (161, 24465, 107, 24374) - (162, 26040, 120, 25963) - (167, 17214, 92, 17184) - (207, 40886, 179, 40879) - (259, 1850, 175, 1820) - (270, 29508, 264, 29440) - (270, 32616, 226, 32607) - (288, 49588, 204, 49571) - (318, 31489, 235, 31404) - (326, 18837, 285, 18817) - (337, 455, 240, 359) +-- Same queries with sequential scan (should give the same results as above) +RESET enable_seqscan; +SET enable_indexscan = OFF; +SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5; + c | dist +-------------------------+------------------ + (337, 455),(240, 359) | 0 + (1, 1) | 140.007142674936 + (759, 187),(662, 163) | 162 + (948, 1201),(907, 1156) | 772.000647668122 + (1444, 403),(1346, 344) | 846 +(5 rows) + +SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5; + c | dist +-------------------------+------ + (337, 455),(240, 359) | 0 + (1, 1) | 99 + (759, 187),(662, 163) | 162 + (948, 1201),(907, 1156) | 656 + (1444, 403),(1346, 344) | 846 +(5 rows) + +SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5; + c | dist +-------------------------+------ + (337, 455),(240, 359) | 0 + (759, 187),(662, 163) | 162 + (1, 1) | 198 + (1444, 403),(1346, 344) | 846 + (369, 1457),(278, 1409) | 909 +(5 rows) + +SELECT c~>1, c FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by left bound + ?column? | c +----------+--------------------------- + 0 | (0, 100000) + 1 | (1, 1) + 3 | (54, 38679),(3, 38602) + 15 | (83, 10271),(15, 10265) + 64 | (122, 46832),(64, 46762) + 92 | (167, 17214),(92, 17184) + 107 | (161, 24465),(107, 24374) + 120 | (162, 26040),(120, 25963) + 138 | (154, 4019),(138, 3990) + 175 | (259, 1850),(175, 1820) + 179 | (207, 40886),(179, 40879) + 204 | (288, 49588),(204, 49571) + 226 | (270, 32616),(226, 32607) + 235 | (318, 31489),(235, 31404) + 240 | (337, 455),(240, 359) (15 rows) -SELECT * FROM test_point ORDER BY c~>4 DESC LIMIT 15; -- descending by 1st coordinate - c ------------------------------- - (30746, 50040, 30727, 49992) - (36311, 50073, 36258, 49987) - (3531, 49962, 3463, 49934) - (17954, 49975, 17865, 49915) - (2168, 50012, 2108, 49914) - (31287, 49923, 31236, 49913) - (21551, 49983, 21492, 49885) - (43925, 49912, 43888, 49878) - (19128, 49932, 19112, 49849) - (38266, 49852, 38233, 49844) - (14913, 49873, 14849, 49836) - (37595, 49849, 37581, 49834) - (46151, 49848, 46058, 49830) - (29261, 49910, 29247, 49818) - (19233, 49824, 19185, 49794) +SELECT c~>2, c FROM test_cube ORDER BY c~>2 LIMIT 15; -- ascending by right bound + ?column? | c +----------+--------------------------- + 0 | (0, 100000) + 1 | (1, 1) + 54 | (54, 38679),(3, 38602) + 83 | (83, 10271),(15, 10265) + 122 | (122, 46832),(64, 46762) + 154 | (154, 4019),(138, 3990) + 161 | (161, 24465),(107, 24374) + 162 | (162, 26040),(120, 25963) + 167 | (167, 17214),(92, 17184) + 207 | (207, 40886),(179, 40879) + 259 | (259, 1850),(175, 1820) + 270 | (270, 29508),(264, 29440) + 270 | (270, 32616),(226, 32607) + 288 | (288, 49588),(204, 49571) + 318 | (318, 31489),(235, 31404) (15 rows) +SELECT c~>3, c FROM test_cube ORDER BY c~>3 LIMIT 15; -- ascending by lower bound + ?column? | c +----------+--------------------------- + 0 | (100000) + 1 | (1, 1) + 6 | (30333, 50),(30273, 6) + 43 | (43301, 75),(43227, 43) + 51 | (19650, 142),(19630, 51) + 81 | (2424, 160),(2424, 81) + 108 | (3449, 171),(3354, 108) + 109 | (18037, 155),(17941, 109) + 114 | (28511, 208),(28479, 114) + 118 | (19946, 217),(19941, 118) + 139 | (16906, 191),(16816, 139) + 163 | (759, 187),(662, 163) + 181 | (22684, 266),(22656, 181) + 213 | (24423, 255),(24360, 213) + 222 | (45989, 249),(45910, 222) +(15 rows) + +SELECT c~>4, c FROM test_cube ORDER BY c~>4 LIMIT 15; -- ascending by upper bound + ?column? | c +----------+--------------------------- + 0 | (100000) + 1 | (1, 1) + 50 | (30333, 50),(30273, 6) + 75 | (43301, 75),(43227, 43) + 142 | (19650, 142),(19630, 51) + 155 | (18037, 155),(17941, 109) + 160 | (2424, 160),(2424, 81) + 171 | (3449, 171),(3354, 108) + 187 | (759, 187),(662, 163) + 191 | (16906, 191),(16816, 139) + 208 | (28511, 208),(28479, 114) + 217 | (19946, 217),(19941, 118) + 249 | (45989, 249),(45910, 222) + 255 | (24423, 255),(24360, 213) + 266 | (22684, 266),(22656, 181) +(15 rows) + +RESET enable_indexscan; diff --git a/contrib/cube/sql/cube.sql b/contrib/cube/sql/cube.sql index df5e1b286b..46b93375b6 100644 --- a/contrib/cube/sql/cube.sql +++ b/contrib/cube/sql/cube.sql @@ -372,20 +372,29 @@ SELECT * FROM test_cube WHERE c && '(3000,1000),(0,0)' ORDER BY c; -- Test sorting SELECT * FROM test_cube WHERE c && '(3000,1000),(0,0)' GROUP BY c ORDER BY c; --- kNN with index +-- Test kNN +INSERT INTO test_cube VALUES ('(1,1)'), ('(100000)'), ('(0, 100000)'); -- Some corner cases +SET enable_seqscan = false; + +-- Test different metrics SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5; SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5; SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5; --- kNN-based sorting -SELECT * FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by 1st coordinate of lower left corner -SELECT * FROM test_cube ORDER BY c~>4 LIMIT 15; -- ascending by 2nd coordinate or upper right corner -SELECT * FROM test_cube ORDER BY c~>1 DESC LIMIT 15; -- descending by 1st coordinate of lower left corner -SELECT * FROM test_cube ORDER BY c~>4 DESC LIMIT 15; -- descending by 2nd coordinate or upper right corner +-- Test sorting by coordinates +SELECT c~>1, c FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by left bound +SELECT c~>2, c FROM test_cube ORDER BY c~>2 LIMIT 15; -- ascending by right bound +SELECT c~>3, c FROM test_cube ORDER BY c~>3 LIMIT 15; -- ascending by lower bound +SELECT c~>4, c FROM test_cube ORDER BY c~>4 LIMIT 15; -- ascending by upper bound --- same thing for index with points -CREATE TABLE test_point(c cube); -INSERT INTO test_point(SELECT cube(array[c->1,c->2,c->3,c->4]) FROM test_cube); -CREATE INDEX ON test_point USING gist(c); -SELECT * FROM test_point ORDER BY c~>1, c~>2 LIMIT 15; -- ascending by 1st then by 2nd coordinate -SELECT * FROM test_point ORDER BY c~>4 DESC LIMIT 15; -- descending by 1st coordinate +-- Same queries with sequential scan (should give the same results as above) +RESET enable_seqscan; +SET enable_indexscan = OFF; +SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5; +SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5; +SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5; +SELECT c~>1, c FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by left bound +SELECT c~>2, c FROM test_cube ORDER BY c~>2 LIMIT 15; -- ascending by right bound +SELECT c~>3, c FROM test_cube ORDER BY c~>3 LIMIT 15; -- ascending by lower bound +SELECT c~>4, c FROM test_cube ORDER BY c~>4 LIMIT 15; -- ascending by upper bound +RESET enable_indexscan; diff --git a/doc/src/sgml/cube.sgml b/doc/src/sgml/cube.sgml index 1ffc40f1a5..3d503719c5 100644 --- a/doc/src/sgml/cube.sgml +++ b/doc/src/sgml/cube.sgml @@ -186,10 +186,11 @@ a ~> n float8 - Get n-th coordinate in normalized cube - representation, in which the coordinates have been rearranged into - the form lower left — upper right; that is, the - smaller endpoint along each dimension appears first. + Get n-th coordinate of cube in following way: + n = 2 * k - 1 means lower bound of k-th + dimension, n = 2 * k means upper bound of + k-th dimension. This operator is designed + for KNN-GiST support.