背景
PostgreSQL limit N的成本估算，是通过计算总成本A，以及估算得到的总记录数B得到：
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(N/B)*A
大概意思就是占比的方法计算
对于单表查询，这种方法通常来说比较适用，但是如果数据分布有倾斜，实际上也并不一定适用，例如以下两种情况：
1、符合条件的数据占总记录数的50%，但是全部分布在表的末尾，那么limit 10000 条到底是走索引快还是走全表扫描快呢？
2、符合条件的数据占总记录数的50%，全部分布在表的头部，那么LIMIT 10000 条，肯定是全表扫描快了。
对于JOIN的情况，同样有类似的问题：
比如JOIN并且带条件时，LIMIT N，是走嵌套循环快，还是走MERGE 或 HASH JOIN快？
1、嵌套循环+where+LIMIT的成本计算方法，可以使用LIMIT占总估算记录数占比的方法得到，还算是比较合理。
2、MERGE JOIN+where+LIMIT的成本计算方法，必须考虑启动成本，例如WHERE条件在A表上（可以走索引直接从条件位置开始扫描），B表则需要从索引的开头开始扫描（到与A表的索引匹配时，也许需要扫描很多的索引ENTRY，这个启动成本可能会很高），启动成本，加上LIMIT条数在剩余的所有成本中的一个占比，得到的成本是一个比较合理的成本。
3、hash join+where+limit的成本计算方法，使用启动成本+LIMIT占总估算记录数占比的方法得到，优化器目前就是这么做的，比较合理。
然而，对于MERGE JOIN，目前在使用LIMIT时，PG没有加上这个启动成本，使得最后得到的执行计划可能不准确。
改进方法建议可以加入merge join启动成本。
PostgreSQL 例子
1、建表如下：
postgres=# create table test1(a int, b text, primary key(a));
CREATE TABLE
postgres=# create table test2(a int, b text, primary key(a));
CREATE TABLE
postgres=# alter table test1 add constraint testcheck foreign key(a) references test2(a);
ALTER TABLE
postgres=# insert into test2 select generate_series(1,1000000),'abcdefg';
INSERT 0 1000000
postgres=# insert into test1 select generate_series(1,1000000,2),'abcdefg';
INSERT 0 500000
analyze test1;
analyze test2;
2、查询SQL如下：
explain (analyze,verbose,timing,costs,buffers) select * from test2 left join test1 on test2.a = test1.a where test2.a > 500000 limit 10;
该语句中表结构比较特殊，两个关联字段都是主键，并且存在外键约束关系，查询计划如下：
QUERY PLAN
----------------------------------------------------------------------------------------------------------------------------------------------------
Limit (cost=0.73..0.89 rows=10 width=24) (actual time=54.729..54.739 rows=10 loops=1)
Output: test2.a, test2.b, test1.a, test1.b
Buffers: shared hit=2042
-> Merge Left Join (cost=0.73..7929.35 rows=498340 width=24) (actual time=54.728..54.735 rows=10 loops=1)
Output: test2.a, test2.b, test1.a, test1.b
Inner Unique: true
Merge Cond: (test2.a = test1.a)
Buffers: shared hit=2042
-> Index Scan using test2_pkey on public.test2 (cost=0.37..3395.42 rows=498340 width=12) (actual time=0.017..0.020 rows=10 loops=1)
Output: test2.a, test2.b
Index Cond: (test2.a > 500000)
Buffers: shared hit=4
-> Index Scan using test1_pkey on public.test1 (cost=0.37..2322.99 rows=500000 width=12) (actual time=0.006..34.120 rows=250006 loops=1)
Output: test1.a, test1.b
Buffers: shared hit=2038
Planning Time: 0.216 ms
Execution Time: 54.765 ms
(17 rows)
从执行计划上可以看出，根据test2表先查询出满足条件的10条记录，然后和test1表采用mergejoin关联，由于在估算的时候没有考虑到limit的影响，估算的行数非常大，是498340行，
实际采用nestloop效果会更好（关闭掉seqscan和megejoin）
postgres=# set enable_seqscan =off;
SET
postgres=# set enable_mergejoin =off;
SET
postgres=# explain (analyze,verbose,timing,costs,buffers) select * from test2 left join test1 on test2.a = test1.a where test2.a > 500000 limit 10;
QUERY PLAN
-----------------------------------------------------------------------------------------------------------------------------------------------
Limit (cost=0.73..4.53 rows=10 width=24) (actual time=0.040..0.060 rows=10 loops=1)
Output: test2.a, test2.b, test1.a, test1.b
Buffers: shared hit=39
-> Nested Loop Left Join (cost=0.73..189339.64 rows=498340 width=24) (actual time=0.039..0.057 rows=10 loops=1)
Output: test2.a, test2.b, test1.a, test1.b
Inner Unique: true
Buffers: shared hit=39
-> Index Scan using test2_pkey on public.test2 (cost=0.37..3395.42 rows=498340 width=12) (actual time=0.025..0.027 rows=10 loops=1)
Output: test2.a, test2.b
Index Cond: (test2.a > 500000)
Buffers: shared hit=4
-> Index Scan using test1_pkey on public.test1 (cost=0.37..0.37 rows=1 width=12) (actual time=0.002..0.002 rows=0 loops=10)
Output: test1.a, test1.b
Index Cond: (test2.a = test1.a)
Buffers: shared hit=35
Planning Time: 0.112 ms
Execution Time: 0.078 ms
(17 rows)
但是从评估的成本来看，merge join+limit 比 nestloop+limit更低，原因是nestloop的总成本更高(189339 比 7929)。所以优化器根据比例算法（未参照merge join的启动成本），认为在LIMIT的情况下，也是merge join成本更低。
实际情况是，MERGE JOIN的没带查询条件的B表，需要从索引的头部开始扫，而不是从指定位置开始扫。 因此实际情况是merge join是更慢的。
目前优化器使用hash join时，已经算上了startup cost，例子
postgres=# set enable_mergejoin =off;
SET
postgres=# set enable_seqscan =off;
SET
postgres=# set enable_nestloop =off;
SET
启动成本=3536.51
postgres=# explain (analyze,verbose,timing,costs,buffers) select * from test2 left join test1 on test2.a = test1.a where test2.a > 500000 limit 10;
QUERY PLAN
----------------------------------------------------------------------------------------------------------------------------------------------------------
Limit (cost=3536.51..3536.61 rows=10 width=24) (actual time=158.148..158.219 rows=10 loops=1)
Output: test2.a, test2.b, test1.a, test1.b
Buffers: shared hit=4079, temp written=1464
-> Hash Left Join (cost=3536.51..8135.83 rows=494590 width=24) (actual time=158.147..158.215 rows=10 loops=1)
Output: test2.a, test2.b, test1.a, test1.b
Inner Unique: true
Hash Cond: (test2.a = test1.a)
Buffers: shared hit=4079, temp written=1464
-> Index Scan using test2_pkey on public.test2 (cost=0.37..3369.86 rows=494590 width=12) (actual time=0.023..0.027 rows=26 loops=1)
Output: test2.a, test2.b
Index Cond: (test2.a > 500000)
Buffers: shared hit=4
-> Hash (cost=2322.99..2322.99 rows=500000 width=12) (actual time=156.848..156.849 rows=500000 loops=1)
Output: test1.a, test1.b
Buckets: 262144 Batches: 4 Memory Usage: 7418kB
Buffers: shared hit=4072, temp written=1464
-> Index Scan using test1_pkey on public.test1 (cost=0.37..2322.99 rows=500000 width=12) (actual time=0.011..72.506 rows=500000 loops=1)
Output: test1.a, test1.b
Buffers: shared hit=4072
Planning Time: 0.141 ms
Execution Time: 162.086 ms
(21 rows)
改进建议
针对test1表，需要估算a<500000有多少行，作为索引扫描的startup成本。
postgres=# explain select * from test1 where a<500000;
QUERY PLAN
---------------------------------------------------------------------------------
Index Scan using test1_pkey on test1 (cost=0.37..1702.83 rows=249893 width=12)
Index Cond: (a < 500000)
(2 rows)
postgres=# explain select * from test1;
QUERY PLAN
-------------------------------------------------------------
Seq Scan on test1 (cost=0.00..133.15 rows=500000 width=12)
(1 row)
所以，索引扫描test1（where a > 500000）的merge join启动成本应该有 1702，加上这个成本后，成本远大于NEST LOOP JOIN的成本，所以不会选择merge join。
Oracle 例子
create table test1(a int, b varchar2(4000), primary key(a));
create table test2(a int, b varchar2(4000), primary key(a));
alter table test1 add constraint testcheck foreign key(a) references test2(a);
insert into test2 select rownum, 'abcdefg' from dual connect by level <=1000000;
insert into test1 select * from (select rownum as rn, 'abcdefg' from dual connect by level <=1000000) t where mod(rn,2)=1;
exec DBMS_STATS.GATHER_TABLE_STATS('DIGOAL', 'TEST1', method_opt => 'FOR COLUMNS (a, b)');
exec DBMS_STATS.GATHER_TABLE_STATS('DIGOAL', 'TEST2', method_opt => 'FOR COLUMNS (a, b)');
查询SQL如下：
set autotrace on
set linesize 120
set pagesize 200
set wrap off
select * from test2 left join test1 on test2.a = test1.a where test2.a > 500000 and rownum<=10;
A B
---------- -------------------------------------------------------------------------------------------------------------
500001 abcdefg
500002 abcdefg
500003 abcdefg
500004 abcdefg
500005 abcdefg
500006 abcdefg
500007 abcdefg
500008 abcdefg
500009 abcdefg
500010 abcdefg
10 rows selected.
Execution Plan
----------------------------------------------------------
Plan hash value: 3391785554
-----------------------------------------------------------------------------------------------
| Id | Operation | Name | Rows | Bytes | Cost (%CPU)| Time |
-----------------------------------------------------------------------------------------------
| 0 | SELECT STATEMENT | | 10 | 500 | 15 (0)| 00:00:01 |
|* 1 | COUNT STOPKEY | | | | | |
| 2 | NESTED LOOPS OUTER | | 10 | 500 | 15 (0)| 00:00:01 |
| 3 | TABLE ACCESS BY INDEX ROWID| TEST2 | 10 | 250 | 4 (0)| 00:00:01 |
|* 4 | INDEX RANGE SCAN | SYS_C00151146 | 9000 | | 3 (0)| 00:00:01 |
| 5 | TABLE ACCESS BY INDEX ROWID| TEST1 | 1 | 25 | 2 (0)| 00:00:01 |
|* 6 | INDEX UNIQUE SCAN | SYS_C00151145 | 1 | | 1 (0)| 00:00:01 |
-----------------------------------------------------------------------------------------------
Predicate Information (identified by operation id):
---------------------------------------------------
1 - filter(ROWNUM<=10)
4 - access("TEST2"."A">500000)
6 - access("TEST2"."A"="TEST1"."A"(+))
filter("TEST1"."A"(+)>500000)
Statistics
----------------------------------------------------------
0 recursive calls
0 db block gets
25 consistent gets
0 physical reads
0 redo size
937 bytes sent via SQL*Net to client
500 bytes received via SQL*Net from client
2 SQL*Net roundtrips to/from client
0 sorts (memory)
0 sorts (disk)
10 rows processed
Oracle 选择了nestloop join。
使用HINT，让Oracle使用merge join，看看成本是多少，是否与修正PostgreSQL merge join启动成本接近。
select /*+ USE_MERGE(test2,test1) */ * from test2 left join test1 on test2.a = test1.a where test2.a > 500000 and rownum<=10;
Execution Plan
----------------------------------------------------------
Plan hash value: 492577188
------------------------------------------------------------------------------------------------
| Id | Operation | Name | Rows | Bytes | Cost (%CPU)| Time |
------------------------------------------------------------------------------------------------
| 0 | SELECT STATEMENT | | 10 | 750 | 29 (7)| 00:00:01 |
|* 1 | COUNT STOPKEY | | | | | |
| 2 | MERGE JOIN OUTER | | 10 | 750 | 29 (7)| 00:00:01 |
| 3 | TABLE ACCESS BY INDEX ROWID | TEST2 | 10 | 250 | 4 (0)| 00:00:01 |
|* 4 | INDEX RANGE SCAN | SYS_C00151146 | 9000 | | 3 (0)| 00:00:01 |
|* 5 | SORT JOIN | | 25000 | 610K| 25 (8)| 00:00:01 |
| 6 | TABLE ACCESS BY INDEX ROWID| TEST1 | 25000 | 610K| 23 (0)| 00:00:01 |
|* 7 | INDEX RANGE SCAN | SYS_C00151145 | 4500 | | 11 (0)| 00:00:01 |
------------------------------------------------------------------------------------------------
Predicate Information (identified by operation id):
---------------------------------------------------
1 - filter(ROWNUM<=10)
4 - access("TEST2"."A">500000)
5 - access("TEST2"."A"="TEST1"."A"(+))
filter("TEST2"."A"="TEST1"."A"(+))
7 - access("TEST1"."A"(+)>500000)
Statistics
----------------------------------------------------------
1 recursive calls
0 db block gets
1099 consistent gets
0 physical reads
0 redo size
937 bytes sent via SQL*Net to client
500 bytes received via SQL*Net from client
2 SQL*Net roundtrips to/from client
1 sorts (memory)
0 sorts (disk)
10 rows processed
小结
1、PostgreSQL 在计算merge join+limit的成本时，优化器有优化的空间，可以考虑把启动成本算进来，提高优化器选择带limit输出的SQL的JOIN方法的正确性。
2、如果是inner join，通过query rewrite可以对merge join进行优化，跳过不符合条件的头部INDEX SCAN。
postgres=# explain (analyze,verbose,timing,costs,buffers) select * from test2 join test1 on test2.a = test1.a where test2.a > 500000 limit 10;
QUERY PLAN
----------------------------------------------------------------------------------------------------------------------------------------------------
Limit (cost=0.77..1.09 rows=10 width=24) (actual time=54.626..54.638 rows=10 loops=1)
Output: test2.a, test2.b, test1.a, test1.b
Buffers: shared hit=2042
-> Merge Join (cost=0.77..7895.19 rows=247295 width=24) (actual time=54.625..54.635 rows=10 loops=1)
Output: test2.a, test2.b, test1.a, test1.b
Inner Unique: true
Merge Cond: (test2.a = test1.a)
Buffers: shared hit=2042
-> Index Scan using test2_pkey on public.test2 (cost=0.37..3369.86 rows=494590 width=12) (actual time=0.017..0.020 rows=19 loops=1)
Output: test2.a, test2.b
Index Cond: (test2.a > 500000)
Buffers: shared hit=4
-> Index Scan using test1_pkey on public.test1 (cost=0.37..2322.99 rows=500000 width=12) (actual time=0.008..34.009 rows=250010 loops=1)
Output: test1.a, test1.b
Buffers: shared hit=2038
Planning Time: 0.244 ms
Execution Time: 54.669 ms
(17 rows)
sql rewrite:
可以做到内核里面，这样就不需要改SQL了。效果如下，超好。
postgres=# explain (analyze,verbose,timing,costs,buffers) select * from test2 join test1 on test2.a = test1.a where test2.a > 500000 and test1.a > 500000limit 10;
QUERY PLAN
-----------------------------------------------------------------------------------------------------------------------------------------------
Limit (cost=0.75..1.30 rows=10 width=24) (actual time=0.035..0.048 rows=10 loops=1)
Output: test2.a, test2.b, test1.a, test1.b
Buffers: shared hit=8
-> Merge Join (cost=0.75..6711.51 rows=123700 width=24) (actual time=0.034..0.044 rows=10 loops=1)
Output: test2.a, test2.b, test1.a, test1.b
Inner Unique: true
Merge Cond: (test2.a = test1.a)
Buffers: shared hit=8
-> Index Scan using test2_pkey on public.test2 (cost=0.37..3369.86 rows=494590 width=12) (actual time=0.015..0.019 rows=19 loops=1)
Output: test2.a, test2.b
Index Cond: (test2.a > 500000)
Buffers: shared hit=4
-> Index Scan using test1_pkey on public.test1 (cost=0.37..1704.30 rows=250106 width=12) (actual time=0.015..0.017 rows=10 loops=1)
Output: test1.a, test1.b
Index Cond: (test1.a > 500000)
Buffers: shared hit=4
Planning Time: 0.276 ms
Execution Time: 0.074 ms
(18 rows)
参考
《PostgreSQL 优化器案例之 - order by limit 索引选择问题》
src/backend/optimizer/path/costsize.c
原文地址：https://github.com/digoal/blog/blob/master/201810/20181004_03.md
新闻名称：PostgreSQLJOINlimit优化器成本计算改进-mergejoinstartupcost优化
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