在之前的一篇月报中，我们已经简单地分析过PG的优化器（PgSQL · 源码分析 · PG优化器浅析），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_stats
WHERE 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
            = 0.100697
rows = 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_stats
WHERE tablename='tenk1' AND attname='stringu1';
null_frac         | 0
n_distinct        | 676
most_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]
            = 0.003
rows = 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=0.0025
cpu_tuple_cost=0.01
seq_page_cost=1
random_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动态规划，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。

原文：http://mysql.taobao.org/monthly/2017/02/07/