数据库内核月报－ 2016/10 - PgSQL · 代码浅析 · PostgreSQL 9.6 聚合OP复用的优化分析 - 《数据库内核月报》

背景
9.6 聚合OP优化
对比测试
代码
小结

背景

聚合操作指将分组的数据聚合为一个结果输出。

聚合通常用在统计应用中，例如统计分组的最大值，最小值，记录数，平均值，方差，截距，相关性。

聚合也可能被用于文本分析或者图像分析等，例如最佳相似度，行列变换，聚合为数组或JSON，图像堆叠等。

因此聚合通常需要启动值，行的处理，以及结果的格式转换3个过程。

PostgreSQL的聚合也包含了以上三个过程，创建一个聚合函数的语法如下：

CREATE AGGREGATE name ( [ argmode ] [ argname ] arg_data_type [ , ... ] ) (
    SFUNC = sfunc,
    STYPE = state_data_type
    [ , SSPACE = state_data_size ]
    [ , FINALFUNC = ffunc ]
    [ , FINALFUNC_EXTRA ]
    [ , COMBINEFUNC = combinefunc ]
    [ , SERIALFUNC = serialfunc ]
    [ , DESERIALFUNC = deserialfunc ]
    [ , INITCOND = initial_condition ]
    [ , MSFUNC = msfunc ]
    [ , MINVFUNC = minvfunc ]
    [ , MSTYPE = mstate_data_type ]
    [ , MSSPACE = mstate_data_size ]
    [ , MFINALFUNC = mffunc ]
    [ , MFINALFUNC_EXTRA ]
    [ , MINITCOND = minitial_condition ]
    [ , SORTOP = sort_operator ]
    [ , PARALLEL = { SAFE | RESTRICTED | UNSAFE } ]
)

例子

CREATE AGGREGATE avg (float8)
(
    sfunc = float8_accum,
    stype = float8[],
    finalfunc = float8_avg,
    initcond = '{0,0,0}'
);

参考

https://www.postgresql.org/docs/9.6/static/xaggr.html

https://www.postgresql.org/docs/9.6/static/sql-createaggregate.html

PostgreSQL 聚合处理流程如图

使用initcond指定internal-state的初始值，没有则为空。
每条记录(作为next-data-values输入)，调用 sfunc( internal-state, next-data-values ) —> next-internal-state
输出的结果作为中间结果继续调用sfunc
ffunc( internal-state ) —> aggregate-value 可选，作为结果转换使用

9.6 聚合OP优化

如果initcond与sfunc一致，在同一个聚合分组内，sfunc只需要计算一遍所有记录，而不需要计算多遍。

https://git.postgresql.org/gitweb/?p=postgresql.git;a=commit;h=804163bc25e979fcd91b02e58fa2d1c6b587cc65

Share transition state between different aggregates when possible.
If there are two different aggregates in the query with same inputs, 
and the aggregates have the same initial condition and transition function,
only calculate the state value once, and only call the final functionsseparately. 
For example, AVG(x) and SUM(x) aggregates have the same transition function, which accumulates the sum and number of input tuples.
For a query like "SELECT AVG(x), SUM(x) FROM x", we can therefore accumulate the state function only once, which gives a nice speedup.
David Rowley, reviewed and edited by me.

我们可以通过以下SQL查看可以共享OP的聚合函数，rank一致的都可以共享。

postgres=# select rank() over (partition by 1 order by aggtransfn,agginitval),
           row_number() over (partition by aggtransfn,agginitval order by aggfnoid) rn,
           aggfnoid,aggtransfn,agginitval from pg_aggregate ;

rank	rn	aggfnoid	aggtransfn	agginitval
1	1	pg_catalog.sum	float4pl	none
2	1	pg_catalog.avg	float4_accum	{0,0,0}
2	2	pg_catalog.variance	float4_accum	{0,0,0}
2	3	pg_catalog.stddev	float4_accum	{0,0,0}
2	4	pg_catalog.var_samp	float4_accum	{0,0,0}
2	5	pg_catalog.stddev_samp	float4_accum	{0,0,0}
2	6	pg_catalog.var_pop	float4_accum	{0,0,0}
2	7	pg_catalog.stddev_pop	float4_accum	{0,0,0}
9	1	pg_catalog.max	float4larger	none
10	1	pg_catalog.min	float4smaller	none
11	1	pg_catalog.sum	float8pl	none
12	1	pg_catalog.avg	float8_accum	{0,0,0}
12	2	pg_catalog.variance	float8_accum	{0,0,0}
12	3	pg_catalog.stddev	float8_accum	{0,0,0}
12	4	pg_catalog.var_samp	float8_accum	{0,0,0}
12	5	pg_catalog.stddev_samp	float8_accum	{0,0,0}
12	6	pg_catalog.var_pop	float8_accum	{0,0,0}
12	7	pg_catalog.stddev_pop	float8_accum	{0,0,0}
19	1	pg_catalog.max	float8larger	none
20	1	pg_catalog.min	float8smaller	none
21	1	pg_catalog.max	text_larger	none
22	1	pg_catalog.min	text_smaller	none
23	1	pg_catalog.max	array_larger	none
24	1	pg_catalog.min	array_smaller	none
25	1	pg_catalog.max	int4larger	none
25	2	pg_catalog.max	int4larger	none
27	1	pg_catalog.min	int4smaller	none
27	2	pg_catalog.min	int4smaller	none
29	1	pg_catalog.max	int2larger	none
30	1	pg_catalog.min	int2smaller	none
31	1	pg_catalog.sum	cash_pl	none
32	1	pg_catalog.max	cashlarger	none
33	1	pg_catalog.min	cashsmaller	none
34	1	pg_catalog.max	bpchar_larger	none
35	1	pg_catalog.min	bpchar_smaller	none
36	1	pg_catalog.max	date_larger	none
37	1	pg_catalog.min	date_smaller	none
38	1	pg_catalog.sum	interval_pl	none
39	1	pg_catalog.min	timestamptz_smaller	none
40	1	pg_catalog.max	timestamptz_larger	none
41	1	pg_catalog.min	interval_smaller	none
42	1	pg_catalog.max	interval_larger	none
43	1	pg_catalog.count	int8inc	0
44	1	pg_catalog.max	int8larger	none
45	1	pg_catalog.min	int8smaller	none
46	1	pg_catalog.max	time_larger	none
47	1	pg_catalog.min	time_smaller	none
48	1	pg_catalog.max	timetz_larger	none
49	1	pg_catalog.min	timetz_smaller	none
50	1	pg_catalog.bit_and	bitand	none
51	1	pg_catalog.bit_or	bitor	none
52	1	pg_catalog.min	numeric_smaller	none
53	1	pg_catalog.max	numeric_larger	none
54	1	pg_catalog.variance	numeric_accum	none
54	2	pg_catalog.stddev	numeric_accum	none
54	3	pg_catalog.var_samp	numeric_accum	none
54	4	pg_catalog.stddev_samp	numeric_accum	none
54	5	pg_catalog.var_pop	numeric_accum	none
54	6	pg_catalog.stddev_pop	numeric_accum	none
60	1	pg_catalog.variance	int2_accum	none
60	2	pg_catalog.stddev	int2_accum	none
60	3	pg_catalog.var_samp	int2_accum	none
60	4	pg_catalog.stddev_samp	int2_accum	none
60	5	pg_catalog.var_pop	int2_accum	none
60	6	pg_catalog.stddev_pop	int2_accum	none
66	1	pg_catalog.variance	int4_accum	none
66	2	pg_catalog.stddev	int4_accum	none
66	3	pg_catalog.var_samp	int4_accum	none
66	4	pg_catalog.stddev_samp	int4_accum	none
66	5	pg_catalog.var_pop	int4_accum	none
66	6	pg_catalog.stddev_pop	int4_accum	none
72	1	pg_catalog.variance	int8_accum	none
72	2	pg_catalog.stddev	int8_accum	none
72	3	pg_catalog.var_samp	int8_accum	none
72	4	pg_catalog.stddev_samp	int8_accum	none
72	5	pg_catalog.var_pop	int8_accum	none
72	6	pg_catalog.stddev_pop	int8_accum	none
78	1	pg_catalog.sum	int2_sum	none
79	1	pg_catalog.sum	int4_sum	none
80	1	pg_catalog.avg	interval_accum	{0 second,0 second}
81	1	pg_catalog.bit_and	int2and	none
82	1	pg_catalog.bit_or	int2or	none
83	1	pg_catalog.bit_and	int4and	none
84	1	pg_catalog.bit_or	int4or	none
85	1	pg_catalog.bit_and	int8and	none
86	1	pg_catalog.bit_or	int8or	none
87	1	pg_catalog.avg	int2_avg_accum	{0,0}
88	1	pg_catalog.avg	int4_avg_accum	{0,0}
89	1	pg_catalog.max	oidlarger	none
90	1	pg_catalog.min	oidsmaller	none
91	1	pg_catalog.min	timestamp_smaller	none
92	1	pg_catalog.max	timestamp_larger	none
93	1	pg_catalog.array_agg	array_agg_transfn	none
94	1	bool_and	booland_statefunc	none
94	2	every	booland_statefunc	none
96	1	bool_or	boolor_statefunc	none
97	1	pg_catalog.avg	int8_avg_accum	none
97	2	pg_catalog.sum	int8_avg_accum	none
99	1	pg_catalog.max	tidlarger	none
100	1	pg_catalog.min	tidsmaller	none
101	1	pg_catalog.count	int8inc_any	0
102	1	regr_count	int8inc_float8_float8	0
103	1	regr_sxx	float8_regr_accum	{0,0,0,0,0,0}
103	2	regr_syy	float8_regr_accum	{0,0,0,0,0,0}
103	3	regr_sxy	float8_regr_accum	{0,0,0,0,0,0}
103	4	regr_avgx	float8_regr_accum	{0,0,0,0,0,0}
103	5	regr_avgy	float8_regr_accum	{0,0,0,0,0,0}
103	6	regr_r2	float8_regr_accum	{0,0,0,0,0,0}
103	7	regr_slope	float8_regr_accum	{0,0,0,0,0,0}
103	8	regr_intercept	float8_regr_accum	{0,0,0,0,0,0}
103	9	covar_pop	float8_regr_accum	{0,0,0,0,0,0}
103	10	covar_samp	float8_regr_accum	{0,0,0,0,0,0}
103	11	corr	float8_regr_accum	{0,0,0,0,0,0}
114	1	pg_catalog.avg	numeric_avg_accum	none
114	2	pg_catalog.sum	numeric_avg_accum	none
116	1	xmlagg	xmlconcat2	none
117	1	json_agg	json_agg_transfn	none
118	1	json_object_agg	json_object_agg_transfn	none
119	1	jsonb_agg	jsonb_agg_transfn	none
120	1	jsonb_object_agg	jsonb_object_agg_transfn	none
121	1	pg_catalog.min	enum_smaller	none
122	1	pg_catalog.max	enum_larger	none
123	1	pg_catalog.string_agg	string_agg_transfn	none
124	1	pg_catalog.string_agg	bytea_string_agg_transfn	none
125	1	pg_catalog.max	network_larger	none
126	1	pg_catalog.min	network_smaller	none
127	1	pg_catalog.percentile_disc	ordered_set_transition	none
127	2	pg_catalog.percentile_cont	ordered_set_transition	none
127	3	pg_catalog.percentile_cont	ordered_set_transition	none
127	4	pg_catalog.percentile_disc	ordered_set_transition	none
127	5	pg_catalog.percentile_cont	ordered_set_transition	none
127	6	pg_catalog.percentile_cont	ordered_set_transition	none
127	7	mode	ordered_set_transition	none
134	1	pg_catalog.rank	ordered_set_transition_multi	none
134	2	pg_catalog.percent_rank	ordered_set_transition_multi	none
134	3	pg_catalog.cume_dist	ordered_set_transition_multi	none
134	4	pg_catalog.dense_rank	ordered_set_transition_multi	none
138	1	pg_catalog.array_agg	array_agg_array_transfn	none

我接下来抽取几个数据统计相关的，验证9.6的优化效果

  103 |  1 | regr_sxx                   | float8_regr_accum            | {0,0,0,0,0,0}
  103 |  2 | regr_syy                   | float8_regr_accum            | {0,0,0,0,0,0}
  103 |  3 | regr_sxy                   | float8_regr_accum            | {0,0,0,0,0,0}
  103 |  4 | regr_avgx                  | float8_regr_accum            | {0,0,0,0,0,0}
  103 |  5 | regr_avgy                  | float8_regr_accum            | {0,0,0,0,0,0}
  103 |  6 | regr_r2                    | float8_regr_accum            | {0,0,0,0,0,0}
  103 |  7 | regr_slope                 | float8_regr_accum            | {0,0,0,0,0,0}
  103 |  8 | regr_intercept             | float8_regr_accum            | {0,0,0,0,0,0}
  103 |  9 | covar_pop                  | float8_regr_accum            | {0,0,0,0,0,0}
  103 | 10 | covar_samp                 | float8_regr_accum            | {0,0,0,0,0,0}
  103 | 11 | corr                       | float8_regr_accum            | {0,0,0,0,0,0}

这几个聚合函数的用法如下

https://www.postgresql.org/docs/9.6/static/functions-aggregate.html

Function	Argument Type	Return Type	Partial Mode	Description
corr(Y, X)	double precision	double precision	Yes	correlation coefficient
covar_pop(Y, X)	double precision	double precision	Yes	population covariance
covar_samp(Y, X)	double precision	double precision	Yes	sample covariance
regr_avgx(Y, X)	double precision	double precision	Yes	average of the independent variable (sum(X)/N)
regr_avgy(Y, X)	double precision	double precision	Yes	average of the dependent variable (sum(Y)/N)
regr_intercept(Y, X)	double precision	double precision	Yes	y-intercept of the least-squares-fit linear equation determined by the (X, Y) pairs
regr_r2(Y, X)	double precision	double precision	Yes	square of the correlation coefficient
regr_slope(Y, X)	double precision	double precision	Yes	slope of the least-squares-fit linear equation determined by the (X, Y) pairs
regr_sxx(Y, X)	double precision	double precision	Yes	sum(X^2) - sum(X)^2/N (“sum of squares” of the independent variable)
regr_sxy(Y, X)	double precision	double precision	Yes	sum(XY) - sum(X) sum(Y)/N (“sum of products” of independent times dependent variable)
regr_syy(Y, X)	double precision	double precision	Yes	sum(Y^2) - sum(Y)^2/N (“sum of squares” of the dependent variable)

对比测试

测试5000万条记录

postgres=# create table agg_test(x float8, y float8);
postgres=# insert into agg_test select 10000*random(), 10000*random() from generate_series(1,50000000);

1. 9.6 非并行
聚合计算耗费了7.1秒

postgres=# show max_parallel_workers_per_gather ;
 max_parallel_workers_per_gather 
---------------------------------
 0
(1 row)
postgres=# explain (analyze,verbose,timing,costs,buffers) select corr(y,x), covar_pop(y,x), covar_samp(y,x), regr_avgx(y,x), regr_avgy(y,x), regr_intercept(y,x), regr_r2(y,x), regr_slope(y,x), regr_sxx(y,x), regr_sxy(y,x), regr_syy(y,x) from agg_test ;
                                                                                            QUERY PLAN                                                                                            
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 Aggregate  (cost=2145276.13..2145276.14 rows=1 width=88) (actual time=11703.472..11703.472 rows=1 loops=1)
   Output: corr(y, x), covar_pop(y, x), covar_samp(y, x), regr_avgx(y, x), regr_avgy(y, x), regr_intercept(y, x), regr_r2(y, x), regr_slope(y, x), regr_sxx(y, x), regr_sxy(y, x), regr_syy(y, x)
   Buffers: shared hit=270271
   ->  Seq Scan on public.agg_test  (cost=0.00..770272.36 rows=50000136 width=16) (actual time=0.010..4594.588 rows=50000000 loops=1)
         Output: x, y
         Buffers: shared hit=270271
 Planning time: 0.082 ms
 Execution time: 11703.541 ms
(8 rows)

2. 9.5
聚合计算耗费了36.1秒

postgres=# explain (analyze,verbose,timing,costs,buffers) select corr(y,x), covar_pop(y,x), covar_samp(y,x), regr_avgx(y,x), regr_avgy(y,x), regr_intercept(y,x), regr_r2(y,x), regr_slope(y,x), regr_sxx(y,x), regr_sxy(y,x), regr_syy(y,x) from agg_test ;
                                                                                            QUERY PLAN                                                                                            
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 Aggregate  (cost=2145276.13..2145276.14 rows=1 width=16) (actual time=40563.668..40563.669 rows=1 loops=1)
   Output: corr(y, x), covar_pop(y, x), covar_samp(y, x), regr_avgx(y, x), regr_avgy(y, x), regr_intercept(y, x), regr_r2(y, x), regr_slope(y, x), regr_sxx(y, x), regr_sxy(y, x), regr_syy(y, x)
   Buffers: shared hit=270271
   ->  Seq Scan on public.agg_test  (cost=0.00..770272.36 rows=50000136 width=16) (actual time=0.009..4481.032 rows=50000000 loops=1)
         Output: x, y
         Buffers: shared hit=270271
 Planning time: 0.063 ms
 Execution time: 40563.742 ms
(8 rows)

3. 9.6 并行
聚合计算约耗费0.2秒

postgres=# set max_parallel_workers_per_gather =128;
postgres=# set force_parallel_mode =on;  
postgres=# alter table agg_test set (parallel_workers =32);
postgres=# explain (analyze,verbose,timing,costs,buffers) select corr(y,x), covar_pop(y,x), covar_samp(y,x), regr_avgx(y,x), regr_avgy(y,x), regr_intercept(y,x), regr_r2(y,x), regr_slope(y,x), regr_sxx(y,x), regr_sxy(y,x), regr_syy(y,x) from agg_test ;
                                                                                                                                                      QUERY PLAN                                                 
 Finalize Aggregate  (cost=329869.02..329869.03 rows=1 width=88) (actual time=456.718..456.718 rows=1 loops=1)
   Output: corr(y, x), covar_pop(y, x), covar_samp(y, x), regr_avgx(y, x), regr_avgy(y, x), regr_intercept(y, x), regr_r2(y, x), regr_slope(y, x), regr_sxx(y, x), regr_sxy(y, x), regr_syy(y, x)
   Buffers: shared hit=275071
   ->  Gather  (cost=329864.90..329868.11 rows=32 width=352) (actual time=456.567..456.612 rows=33 loops=1)
         Output: (PARTIAL corr(y, x)), (PARTIAL covar_pop(y, x)), (PARTIAL covar_samp(y, x)), (PARTIAL regr_avgx(y, x)), (PARTIAL regr_avgy(y, x)), (PARTIAL regr_intercept(y, x)), (PARTIAL regr_r2(y, x)), (PARTIAL regr_slope(y, x)), (PARTIAL regr_sxx(y, x)), (PARTIAL regr_sxy(y, x)), (PARTIAL regr_syy(y, x))
         Workers Planned: 32
         Workers Launched: 32
         Buffers: shared hit=275071
         ->  Partial Aggregate  (cost=328864.90..328864.91 rows=1 width=352) (actual time=451.769..451.769 rows=1 loops=33)
               Output: PARTIAL corr(y, x), PARTIAL covar_pop(y, x), PARTIAL covar_samp(y, x), PARTIAL regr_avgx(y, x), PARTIAL regr_avgy(y, x), PARTIAL regr_intercept(y, x), PARTIAL regr_r2(y, x), PARTIAL regr_slope(y, x), PARTIAL regr_sxx(y, x), PARTIAL regr_sxy(y, x), PARTIAL regr_syy(y, x)
               Buffers: shared hit=270655
               Worker 0: actual time=448.888..448.888 rows=1 loops=1
                 Buffers: shared hit=8265
               Worker 1: actual time=449.881..449.881 rows=1 loops=1
                 Buffers: shared hit=8357
               Worker 2: actual time=450.175..450.176 rows=1 loops=1
                 Buffers: shared hit=8295
               Worker 3: actual time=450.306..450.306 rows=1 loops=1
                 Buffers: shared hit=8357
               Worker 4: actual time=449.567..449.567 rows=1 loops=1
                 Buffers: shared hit=6844
               Worker 5: actual time=450.467..450.467 rows=1 loops=1
                 Buffers: shared hit=8360
               Worker 6: actual time=450.574..450.574 rows=1 loops=1
                 Buffers: shared hit=7898
               Worker 7: actual time=450.665..450.665 rows=1 loops=1
                 Buffers: shared hit=8397
               Worker 8: actual time=450.719..450.719 rows=1 loops=1
                 Buffers: shared hit=8084
               Worker 9: actual time=450.922..450.922 rows=1 loops=1
                 Buffers: shared hit=8405
               Worker 10: actual time=451.004..451.004 rows=1 loops=1
                 Buffers: shared hit=5421
               Worker 11: actual time=451.175..451.175 rows=1 loops=1
                 Buffers: shared hit=8431
               Worker 12: actual time=451.316..451.316 rows=1 loops=1
                 Buffers: shared hit=8276
               Worker 13: actual time=451.457..451.457 rows=1 loops=1
                 Buffers: shared hit=8431
               Worker 14: actual time=451.506..451.506 rows=1 loops=1
                 Buffers: shared hit=8163
               Worker 15: actual time=451.670..451.670 rows=1 loops=1
                 Buffers: shared hit=7959
               Worker 16: actual time=451.797..451.797 rows=1 loops=1
                 Buffers: shared hit=8428
               Worker 17: actual time=451.875..451.875 rows=1 loops=1
                 Buffers: shared hit=8265
               Worker 18: actual time=451.982..451.982 rows=1 loops=1
                 Buffers: shared hit=8444
               Worker 19: actual time=452.127..452.127 rows=1 loops=1
                 Buffers: shared hit=7717
               Worker 20: actual time=452.232..452.232 rows=1 loops=1
                 Buffers: shared hit=8450
               Worker 21: actual time=452.331..452.331 rows=1 loops=1
                 Buffers: shared hit=8304
               Worker 22: actual time=452.450..452.450 rows=1 loops=1
                 Buffers: shared hit=8455
               Worker 23: actual time=452.592..452.592 rows=1 loops=1
                 Buffers: shared hit=8367
               Worker 24: actual time=452.679..452.679 rows=1 loops=1
                 Buffers: shared hit=8460
               Worker 25: actual time=452.814..452.815 rows=1 loops=1
                 Buffers: shared hit=8445
               Worker 26: actual time=452.969..452.969 rows=1 loops=1
                 Buffers: shared hit=8465
               Worker 27: actual time=452.999..452.999 rows=1 loops=1
                 Buffers: shared hit=8454
               Worker 28: actual time=453.193..453.193 rows=1 loops=1
                 Buffers: shared hit=8462
               Worker 29: actual time=452.985..452.985 rows=1 loops=1
                 Buffers: shared hit=8437
               Worker 30: actual time=453.482..453.483 rows=1 loops=1
                 Buffers: shared hit=8348
               Worker 31: actual time=453.505..453.505 rows=1 loops=1
                 Buffers: shared hit=8182
               ->  Parallel Seq Scan on public.agg_test  (cost=0.00..285896.04 rows=1562504 width=16) (actual time=0.046..248.331 rows=1515152 loops=33)
                     Output: y, x
                     Buffers: shared hit=270655
                     Worker 0: actual time=0.058..247.983 rows=1526805 loops=1
                       Buffers: shared hit=8265
                     Worker 1: actual time=0.047..249.121 rows=1543825 loops=1
                       Buffers: shared hit=8357
                     Worker 2: actual time=0.047..249.206 rows=1532355 loops=1
                       Buffers: shared hit=8295
                     Worker 3: actual time=0.047..249.914 rows=1543825 loops=1
                       Buffers: shared hit=8357
                     Worker 4: actual time=0.069..244.072 rows=1263920 loops=1
                       Buffers: shared hit=6844
                     Worker 5: actual time=0.046..250.046 rows=1544380 loops=1
                       Buffers: shared hit=8360
                     Worker 6: actual time=0.047..247.860 rows=1458910 loops=1
                       Buffers: shared hit=7898
                     Worker 7: actual time=0.045..249.471 rows=1551225 loops=1
                       Buffers: shared hit=8397
                     Worker 8: actual time=0.047..247.850 rows=1493320 loops=1
                       Buffers: shared hit=8084
                     Worker 9: actual time=0.049..249.905 rows=1552705 loops=1
                       Buffers: shared hit=8405
                     Worker 10: actual time=0.048..240.578 rows=1000665 loops=1
                       Buffers: shared hit=5421
                     Worker 11: actual time=0.043..249.234 rows=1557515 loops=1
                       Buffers: shared hit=8431
                     Worker 12: actual time=0.044..248.830 rows=1528840 loops=1
                       Buffers: shared hit=8276
                     Worker 13: actual time=0.046..249.576 rows=1557515 loops=1
                       Buffers: shared hit=8431
                     Worker 14: actual time=0.043..248.819 rows=1507935 loops=1
                       Buffers: shared hit=8163
                     Worker 15: actual time=0.046..248.303 rows=1470195 loops=1
                       Buffers: shared hit=7959
                     Worker 16: actual time=0.045..249.997 rows=1556960 loops=1
                       Buffers: shared hit=8428
                     Worker 17: actual time=0.046..249.282 rows=1526805 loops=1
                       Buffers: shared hit=8265
                     Worker 18: actual time=0.043..249.849 rows=1559785 loops=1
                       Buffers: shared hit=8444
                     Worker 19: actual time=0.047..247.241 rows=1425425 loops=1
                       Buffers: shared hit=7717
                     Worker 20: actual time=0.043..250.134 rows=1561030 loops=1
                       Buffers: shared hit=8450
                     Worker 21: actual time=0.044..249.316 rows=1534020 loops=1
                       Buffers: shared hit=8304
                     Worker 22: actual time=0.043..250.169 rows=1561955 loops=1
                       Buffers: shared hit=8455
                     Worker 23: actual time=0.045..249.550 rows=1545675 loops=1
                       Buffers: shared hit=8367
                     Worker 24: actual time=0.044..250.062 rows=1562880 loops=1
                       Buffers: shared hit=8460
                     Worker 25: actual time=0.043..250.298 rows=1560105 loops=1
                       Buffers: shared hit=8445
                     Worker 26: actual time=0.043..249.939 rows=1563805 loops=1
                       Buffers: shared hit=8465
                     Worker 27: actual time=0.049..250.511 rows=1561770 loops=1
                       Buffers: shared hit=8454
                     Worker 28: actual time=0.045..250.523 rows=1563250 loops=1
                       Buffers: shared hit=8462
                     Worker 29: actual time=0.049..250.492 rows=1558625 loops=1
                       Buffers: shared hit=8437
                     Worker 30: actual time=0.053..247.131 rows=1542160 loops=1
                       Buffers: shared hit=8348
                     Worker 31: actual time=0.053..249.789 rows=1511450 loops=1
                       Buffers: shared hit=8182
 Planning time: 0.101 ms
 Execution time: 483.888 ms
(144 rows)

9.6的优化效果很明显，在没有使用并行的情况下，聚合操作已经有约5倍的性能提升。

结果对比

版本	9.6	9.5	9.6并行(32)
5000万记录(11个聚合函数)耗时(秒)	7.1	36.1	0.2

代码

https://git.postgresql.org/gitweb/?p=postgresql.git;a=commit;h=804163bc25e979fcd91b02e58fa2d1c6b587cc65

涉及如下

src/backend/executor/execQual.c         diff | blob | blame | history
src/backend/executor/nodeAgg.c          diff | blob | blame | history
src/backend/executor/nodeWindowAgg.c            diff | blob | blame | history
src/backend/parser/parse_agg.c          diff | blob | blame | history
src/include/nodes/execnodes.h           diff | blob | blame | history
src/include/parser/parse_agg.h          diff | blob | blame | history
src/test/regress/expected/aggregates.out                diff | blob | blame | history
src/test/regress/sql/aggregates.sql             diff | blob | blame | history

小结

在统计学中，大多数的统计算法的中间结果都是可以共用的，例如sum,avg; 方差,相关性,count,sum等运算;

PostgreSQL 9.6很好的抓住了这样的特征，对初始条件一致，中间算法一致的聚合函数，在同一个分组中数据只需要计算一遍，大大降低了CPU的开销，提高了统计效率。

这个思路与LLVM有一些神似的地方，不过LLVM的适用场景更广。