在之前的一篇月报中，我们已经简单地分析过PG的优化器（），着重分析了SQL逻辑优化，也就是尽量对SQL进行等价或者推倒变换，以达到更有效率的执行计划。本次月报将会深入分析PG优化器原理，着重物理查询优化，包括表的扫描方式选择、多表组合方式、多表组合顺序等。

表扫描方式

表扫描方式主要包含顺序扫描、索引扫描以及Tid扫描等方式，不同的扫描方式

• Seq scan，顺序扫描物理数据页

postgres=> explain select * from t1 ;                     QUERY PLAN----------------------------------------------------- Seq Scan on t1  (cost=0.00..14.52 rows=952 width=8)

• Index scan，先通过索引值获得物理数据的位置，再到物理页读取

postgres=> explain select * from t1 where a1 = 10;                             QUERY PLAN-------------------------------------------------------------------- Index Scan using t1_a1_key on t1  (cost=0.28..8.29 rows=1 width=8)   Index Cond: (a1 = 10)

• Tid scan，通过page号和item号直接定位到物理数据

postgres=> explain select * from t1 where ctid='(1,10)';                    QUERY PLAN-------------------------------------------------- Tid Scan on t1  (cost=0.00..4.01 rows=1 width=8)   TID Cond: (ctid = '(1,10)'::tid)

选择度计算

• 全表扫描选择度计算

全表扫描时每条记录都会返回，所以选择度为1，所以rows=10000

EXPLAIN SELECT * FROM tenk1;                         QUERY PLAN------------------------------------------------------------- Seq Scan on tenk1  (cost=0.00..458.00 rows=10000 width=244) SELECT relpages, reltuples FROM pg_class WHERE relname = 'tenk1'; relpages | reltuples----------+-----------      358 |     10000

• 整型大于或者小于选择度计算

EXPLAIN SELECT * FROM tenk1 WHERE unique1 < 1000;                                   QUERY PLAN-------------------------------------------------------------------------------- Bitmap Heap Scan on tenk1  (cost=24.06..394.64 rows=1007 width=244)   Recheck Cond: (unique1 < 1000)   ->  Bitmap Index Scan on tenk1_unique1  (cost=0.00..23.80 rows=1007 width=0)         Index Cond: (unique1 < 1000)SELECT histogram_bounds FROM pg_statsWHERE tablename='tenk1' AND attname='unique1';                   histogram_bounds------------------------------------------------------ {0,993,1997,3050,4040,5036,5957,7057,8029,9016,9995}selectivity = (1 + (1000 - bucket[2].min)/(bucket[2].max - bucket[2].min))/num_buckets            = (1 + (1000 - 993)/(1997 - 993))/10            = 0.100697rows = rel_cardinality * selectivity     = 10000 * 0.100697     = 1007  (rounding off)

• 字符串等值选择度计算

EXPLAIN SELECT * FROM tenk1 WHERE stringu1 = 'CRAAAA';                        QUERY PLAN---------------------------------------------------------- Seq Scan on tenk1  (cost=0.00..483.00 rows=30 width=244)   Filter: (stringu1 = 'CRAAAA'::name)SELECT null_frac, n_distinct, most_common_vals, most_common_freqs FROM pg_statsWHERE tablename='tenk1' AND attname='stringu1';null_frac         | 0n_distinct        | 676most_common_vals|{EJAAAA,BBAAAA,CRAAAA,FCAAAA,FEAAAA,GSAAAA,JOAAAA,MCAAAA,NAAAAA,WGAAAA}most_common_freqs | {0.00333333,0.003,0.003,0.003,0.003,0.003,0.003,0.003,0.003,0.003}selectivity = mcf[3]            = 0.003rows = 10000 * 0.003     = 30

备注：如果值不在most_common_vals里面，计算公式为：

selectivity = (1 - sum(mvf))/(num_distinct - num_mcv)

• cost计算

代价模型:总代价=CPU代价+IO代价+启动代价

postgres=> explain select * from t1 where a1 > 10;                     QUERY PLAN----------------------------------------------------- Seq Scan on t1  (cost=0.00..16.90 rows=942 width=8)   Filter: (a1 > 10)(2 rows)其中：postgres=> select relpages, reltuples from pg_class where relname = 't1'; relpages | reltuples----------+-----------        5 |       952(1 row)cpu_operator_cost=0.0025cpu_tuple_cost=0.01seq_page_cost=1random_page_cost=4

总cost = cpu_tuple_cost * 952 + seq_page_cost * 5 + cpu_operator_cost * 952

= 16.90 其他扫描方式cost计算可以参考如下函数：

postgres=> select amcostestimate,amname from pg_am ;  amcostestimate  | amname------------------+-------- btcostestimate   | btree hashcostestimate | hash gistcostestimate | gist gincostestimate  | gin spgcostestimate  | spgist(5 rows)

表组合方式

• Nest Loop

SELECT  * FROM     t1 L, t2 R WHERE  L.id=R.id

假设：

M = 20000 pages in L, pL = 40 rows per page,

N = 400 pages in R, pR = 20 rows per page.

select relpages, reltuples from pg_class where relname=‘t1’

L和R进行join

for l in L do  for r in R do    if rid == lid  then ret += (r, s)

对于外表L每一个元组扫描内表R所有的元组

总IO代价: M + (pL * M) * N = 20000 + (4020000)400 = 320020000

• MergeJoin

主要分为3步:

(1) Sort L on lid 代价MlogM

(2) Sort R on rid 代价NlogN

(3) Merge the sorted L and R on lid and rid 代价M+N

• HashJoin

使用HashJoin的前提是其中假设一个表可以完全放在内存中，实际过程中可能统计信息有偏差，优化器认为一个表可以放到内存中，事实上数据在内存中放不下，需要使用临时文件，这样会降低性能。

表的组合顺序

不同的组合顺序将会产生不同的代价，想要获得最佳的组合顺序，如果枚举所有组合顺序，那么将会有N!的排列组合，计算量对于优化器来说难以承受。PG优化器使用两种算法计算更优的组合顺序，动态规划和遗传算法。对于连接比较少的情况使用动态规划，否则使用遗传算法。

• 动态规划求解过程

PG优化器主要考虑将执行计划树生成以下三种形式:

动态规划的思想可以参考百度百科，主要将待求解问题分解成若干个子问题，先求解子问题，然后从这些子问题的解得到原问题的解。具体应用在表组合顺序上，则是先考虑单表最优访问访问，然后考虑两种组合，再考虑多表组合，最终得到更优的解。