[HACKERS] Declarative partitioning optimization for large amount of partitions

Hello.

I decided to figure out whether current implementation of declarative
partitioning has any bottlenecks when there is a lot of partitions. Here
is what I did [1].

```
-- init schema

\timing on

CREATE TABLE part_test (pk int not null, k int, v varchar(128)) PARTITION BY RANGE(pk);

do $$
declare   i integer;
begin   for i in 1 .. 10000   loop       raise notice 'i = %', i;       execute ('CREATE TABLE part_test_' || i ||
         ' PARTITION OF part_test FOR VALUES FROM (' ||                (1 + (i-1)*1000) || ') to (' || ( (i * 1000) +
1)|| ');'               );   end loop; 
end $$;

-- fill tables with some data

do $$
declare   i integer;
begin   for i in 1 .. 100*1000   loop       raise notice 'i = %', i;       execute ('insert into part_test values (
ceil(random()*(10000-1)*1000),ceil(random()*10000*1000), '''' || ceil(random()*10000*1000) );');   end loop; 
end $$;
```

Then:

```
# 2580 is some pk that exists
echo 'select * from part_test where pk = 2580;' > t.sql
pgbench -j 7 -c 7 -f t.sql -P 1 -T 300 eax
```

`perf top` showed to bottlenecks [2]. A stacktrace for the first one
looks like this [3]:

```
0x00000000007a42e2 in get_tabstat_entry (rel_id=25696, isshared=0 '\000') at pgstat.c:1689
1689                if (entry->t_id == rel_id)
#0  0x00000000007a42e2 in get_tabstat_entry (rel_id=25696, isshared=0 '\000') at pgstat.c:1689
#1  0x00000000007a4275 in pgstat_initstats (rel=0x7f4af3fd41f8) at pgstat.c:1666
#2  0x00000000004c7090 in relation_open (relationId=25696, lockmode=0) at heapam.c:1137
#3  0x00000000004c72c9 in heap_open (relationId=25696, lockmode=0) at heapam.c:1291
(skipped)
```

And here is a stacktrace for the second bottleneck [4]:

```
0x0000000000584fb1 in find_all_inheritors (parentrelId=16393, lockmode=1, numparents=0x0) at pg_inherits.c:199
199                forboth(lo, rels_list, li, rel_numparents)
#0  0x0000000000584fb1 in find_all_inheritors (parentrelId=16393, lockmode=1, numparents=0x0) at pg_inherits.c:199
#1  0x000000000077fc9f in expand_inherited_rtentry (root=0x1badcb8, rte=0x1b630b8, rti=1) at prepunion.c:1408
#2  0x000000000077fb67 in expand_inherited_tables (root=0x1badcb8) at prepunion.c:1335
#3  0x0000000000767526 in subquery_planner (glob=0x1b63cc0, parse=0x1b62fa0, parent_root=0x0, hasRecursion=0 '\000',
tuple_fraction=0)at planner.c:568 
(skipped)
```

The first one could be easily fixed by introducing a hash table
(rel_id -> pgStatList entry). Perhaps hash table should be used only
after some threshold. Unless there are any objections I will send a
corresponding patch shortly.

I didn't explored the second bottleneck closely yet but at first glance
it doesn't look much more complicated.

Please don't hesitate to share your thoughts regarding this matter.

[1] http://afiskon.ru/s/e3/5f47af9102_benchmark.txt
[2] http://afiskon.ru/s/00/2008c4ae66_temp.png
[3] http://afiskon.ru/s/23/650f0afc89_stack.txt
[4] http://afiskon.ru/s/03/a7e685a4db_stack2.txt

--
Best regards,
Aleksander Alekseev