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Implement restriction selectivity estimators for <@(spoint, scircle)
This implements restriction selectivity estimation for the <@ @> !<@ !@> family of operators on spoint and scircle. The selectivity is estimated to be (area of sphere circle) / (4 pi). Queries like `select * from sky where sky.star <@ scircle(const, radius)` will be able to properly estimate if using an index is appropriate depending on the size of radius. Secondly, a function spoint_dwithin(p1 spoint, p2 spoint, radius float8) is added that effectively returns `p1 <-> p2 <= radius`. But other than this two-operator expression, it has GIST index support so the optimizer can rewrite it to either `p1 <@ scircle(p2, radius)` or `p2 <@ scircle(p1, radius)`, i.e. it is symmetric in the first two arguments. This allows efficient matching queries without the user having to encode the join ordering in the query. On PostgreSQL 10/11, the spoint_dwithin function is created, but without the GIST support since that only appeared in PG12. The file expected/selectivity_1.out is used on PG10/11; it has <@ flipped around to @> in some plans.
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,155 @@ | ||
| -- spoint_dwithin function selectivity | ||
| set jit = off; -- suppress extra planning output | ||
| select explain('select * from spoint10k where spoint_dwithin(star, spoint(1,1), 1)'); | ||
| explain | ||
| ----------------------------------------------------------------------------------------------- | ||
| Bitmap Heap Scan on spoint10k (rows=2298 width=16) (actual rows=3009 loops=1) | ||
| Filter: spoint_dwithin(star, '(1 , 1)'::spoint, '1'::double precision) | ||
| Rows Removed by Filter: 1560 | ||
| Heap Blocks: exact=55 | ||
| -> Bitmap Index Scan on spoint10k_star_idx (rows=2298 width=0) (actual rows=4569 loops=1) | ||
| Index Cond: (star <@ '<(1 , 1) , 1>'::scircle) | ||
| (6 rows) | ||
|
|
||
| select explain('select * from spoint10k where spoint_dwithin(star, spoint(1,1), .1)'); | ||
| explain | ||
| ------------------------------------------------------------------------------------------- | ||
| Bitmap Heap Scan on spoint10k (rows=25 width=16) (actual rows=29 loops=1) | ||
| Filter: spoint_dwithin(star, '(1 , 1)'::spoint, '0.1'::double precision) | ||
| Rows Removed by Filter: 19 | ||
| Heap Blocks: exact=32 | ||
| -> Bitmap Index Scan on spoint10k_star_idx (rows=25 width=0) (actual rows=48 loops=1) | ||
| Index Cond: (star <@ '<(1 , 1) , 0.1>'::scircle) | ||
| (6 rows) | ||
|
|
||
| select explain('select * from spoint10k where spoint_dwithin(star, spoint(1,1), .01)'); | ||
| explain | ||
| --------------------------------------------------------------------------------------------- | ||
| Index Scan using spoint10k_star_idx on spoint10k (rows=1 width=16) (actual rows=1 loops=1) | ||
| Index Cond: (star <@ '<(1 , 1) , 0.01>'::scircle) | ||
| (2 rows) | ||
|
|
||
| select explain('select * from spoint10k where spoint_dwithin(spoint(1,1), star, 1)'); | ||
| explain | ||
| ----------------------------------------------------------------------------------------------- | ||
| Bitmap Heap Scan on spoint10k (rows=2298 width=16) (actual rows=3009 loops=1) | ||
| Filter: spoint_dwithin('(1 , 1)'::spoint, star, '1'::double precision) | ||
| Rows Removed by Filter: 1560 | ||
| Heap Blocks: exact=55 | ||
| -> Bitmap Index Scan on spoint10k_star_idx (rows=2298 width=0) (actual rows=4569 loops=1) | ||
| Index Cond: (star <@ '<(1 , 1) , 1>'::scircle) | ||
| (6 rows) | ||
|
|
||
| select explain('select * from spoint10k where spoint_dwithin(spoint(1,1), star, .1)'); | ||
| explain | ||
| ------------------------------------------------------------------------------------------- | ||
| Bitmap Heap Scan on spoint10k (rows=25 width=16) (actual rows=29 loops=1) | ||
| Filter: spoint_dwithin('(1 , 1)'::spoint, star, '0.1'::double precision) | ||
| Rows Removed by Filter: 19 | ||
| Heap Blocks: exact=32 | ||
| -> Bitmap Index Scan on spoint10k_star_idx (rows=25 width=0) (actual rows=48 loops=1) | ||
| Index Cond: (star <@ '<(1 , 1) , 0.1>'::scircle) | ||
| (6 rows) | ||
|
|
||
| select explain('select * from spoint10k where spoint_dwithin(spoint(1,1), star, .01)'); | ||
| explain | ||
| --------------------------------------------------------------------------------------------- | ||
| Index Scan using spoint10k_star_idx on spoint10k (rows=1 width=16) (actual rows=1 loops=1) | ||
| Index Cond: (star <@ '<(1 , 1) , 0.01>'::scircle) | ||
| (2 rows) | ||
|
|
||
| select explain('select * from spoint10k a join spoint10k b on spoint_dwithin(a.star, b.star, 1)', do_analyze := 'false'); | ||
| explain | ||
| --------------------------------------------------------------------------------------- | ||
| Nested Loop (rows=22984885 width=32) | ||
| -> Seq Scan on spoint10k a (rows=10000 width=16) | ||
| -> Index Scan using spoint10k_star_idx on spoint10k b (rows=2298 width=16) | ||
| Index Cond: (star OPERATOR(public.<@) scircle(a.star, '1'::double precision)) | ||
| (4 rows) | ||
|
|
||
| select explain('select * from spoint10k a join spoint10k b on spoint_dwithin(a.star, b.star, .1)'); | ||
| explain | ||
| ----------------------------------------------------------------------------------------------------------- | ||
| Nested Loop (rows=249792 width=32) (actual rows=505342 loops=1) | ||
| -> Seq Scan on spoint10k a (rows=10000 width=16) (actual rows=10000 loops=1) | ||
| -> Index Scan using spoint10k_star_idx on spoint10k b (rows=25 width=16) (actual rows=51 loops=10000) | ||
| Index Cond: (star OPERATOR(public.<@) scircle(a.star, '0.1'::double precision)) | ||
| Rows Removed by Index Recheck: 31 | ||
| (5 rows) | ||
|
|
||
| select explain('select * from spoint10k a join spoint10k b on spoint_dwithin(a.star, b.star, .01)'); | ||
| explain | ||
| --------------------------------------------------------------------------------------------------------- | ||
| Nested Loop (rows=2500 width=32) (actual rows=17614 loops=1) | ||
| -> Seq Scan on spoint10k a (rows=10000 width=16) (actual rows=10000 loops=1) | ||
| -> Index Scan using spoint10k_star_idx on spoint10k b (rows=1 width=16) (actual rows=2 loops=10000) | ||
| Index Cond: (star OPERATOR(public.<@) scircle(a.star, '0.01'::double precision)) | ||
| Rows Removed by Index Recheck: 1 | ||
| (5 rows) | ||
|
|
||
| -- spoint_dwithin is symmetric in the first two arguments | ||
| select explain('select * from spoint10k a join spoint10k b on spoint_dwithin(a.star, b.star, .01) | ||
| where spoint_dwithin(a.star, spoint(1,1), .1)'); | ||
| explain | ||
| ------------------------------------------------------------------------------------------------------ | ||
| Nested Loop (rows=6 width=32) (actual rows=33 loops=1) | ||
| -> Bitmap Heap Scan on spoint10k a (rows=25 width=16) (actual rows=29 loops=1) | ||
| Filter: spoint_dwithin(star, '(1 , 1)'::spoint, '0.1'::double precision) | ||
| Rows Removed by Filter: 19 | ||
| Heap Blocks: exact=32 | ||
| -> Bitmap Index Scan on spoint10k_star_idx (rows=25 width=0) (actual rows=48 loops=1) | ||
| Index Cond: (star <@ '<(1 , 1) , 0.1>'::scircle) | ||
| -> Index Scan using spoint10k_star_idx on spoint10k b (rows=1 width=16) (actual rows=1 loops=29) | ||
| Index Cond: (star OPERATOR(public.<@) scircle(a.star, '0.01'::double precision)) | ||
| Rows Removed by Index Recheck: 0 | ||
| (10 rows) | ||
|
|
||
| select explain('select * from spoint10k a join spoint10k b on spoint_dwithin(b.star, a.star, .01) | ||
| where spoint_dwithin(a.star, spoint(1,1), .1)'); | ||
| explain | ||
| ------------------------------------------------------------------------------------------------------ | ||
| Nested Loop (rows=6 width=32) (actual rows=33 loops=1) | ||
| -> Bitmap Heap Scan on spoint10k a (rows=25 width=16) (actual rows=29 loops=1) | ||
| Filter: spoint_dwithin(star, '(1 , 1)'::spoint, '0.1'::double precision) | ||
| Rows Removed by Filter: 19 | ||
| Heap Blocks: exact=32 | ||
| -> Bitmap Index Scan on spoint10k_star_idx (rows=25 width=0) (actual rows=48 loops=1) | ||
| Index Cond: (star <@ '<(1 , 1) , 0.1>'::scircle) | ||
| -> Index Scan using spoint10k_star_idx on spoint10k b (rows=1 width=16) (actual rows=1 loops=29) | ||
| Index Cond: (star OPERATOR(public.<@) scircle(a.star, '0.01'::double precision)) | ||
| Rows Removed by Index Recheck: 0 | ||
| (10 rows) | ||
|
|
||
| -- both sides indexable, check if the planner figures out the better choice | ||
| select explain('select * from spoint10k a join spoint10k b on spoint_dwithin(a.star, b.star, .01) | ||
| where spoint_dwithin(a.star, spoint(1,1), .1) and spoint_dwithin(b.star, spoint(1,1), .05)'); | ||
| explain | ||
| ------------------------------------------------------------------------------------------------------------------------------------- | ||
| Nested Loop (rows=1 width=32) (actual rows=16 loops=1) | ||
| -> Bitmap Heap Scan on spoint10k b (rows=6 width=16) (actual rows=12 loops=1) | ||
| Filter: spoint_dwithin(star, '(1 , 1)'::spoint, '0.05'::double precision) | ||
| Rows Removed by Filter: 4 | ||
| Heap Blocks: exact=14 | ||
| -> Bitmap Index Scan on spoint10k_star_idx (rows=6 width=0) (actual rows=16 loops=1) | ||
| Index Cond: (star <@ '<(1 , 1) , 0.05>'::scircle) | ||
| -> Index Scan using spoint10k_star_idx on spoint10k a (rows=1 width=16) (actual rows=1 loops=12) | ||
| Index Cond: ((star OPERATOR(public.<@) scircle(b.star, '0.01'::double precision)) AND (star <@ '<(1 , 1) , 0.1>'::scircle)) | ||
| Rows Removed by Index Recheck: 0 | ||
| (10 rows) | ||
|
|
||
| select explain('select * from spoint10k a join spoint10k b on spoint_dwithin(a.star, b.star, .01) | ||
| where spoint_dwithin(a.star, spoint(1,1), .05) and spoint_dwithin(b.star, spoint(1,1), .1)'); | ||
| explain | ||
| ------------------------------------------------------------------------------------------------------------------------------------- | ||
| Nested Loop (rows=1 width=32) (actual rows=16 loops=1) | ||
| -> Bitmap Heap Scan on spoint10k a (rows=6 width=16) (actual rows=12 loops=1) | ||
| Filter: spoint_dwithin(star, '(1 , 1)'::spoint, '0.05'::double precision) | ||
| Rows Removed by Filter: 4 | ||
| Heap Blocks: exact=14 | ||
| -> Bitmap Index Scan on spoint10k_star_idx (rows=6 width=0) (actual rows=16 loops=1) | ||
| Index Cond: (star <@ '<(1 , 1) , 0.05>'::scircle) | ||
| -> Index Scan using spoint10k_star_idx on spoint10k b (rows=1 width=16) (actual rows=1 loops=12) | ||
| Index Cond: ((star OPERATOR(public.<@) scircle(a.star, '0.01'::double precision)) AND (star <@ '<(1 , 1) , 0.1>'::scircle)) | ||
| Rows Removed by Index Recheck: 0 | ||
| (10 rows) | ||
|
|
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