MIME-Version: 1.0 (Mimestream 1.3.8)
From: James Brown <james@instrumentl.com>
Date: Thu, 29 Aug 2024 19:49:27 -0700
Message-ID: <CA+7GS+Ff3PWbeJNbi7e6Nqfgh4HOTzyNoyGsBwFeivkUKDUwBA@mail.gmail.com>
Subject: optimizing a join against a windowed function
To: pgsql-general@lists.postgresql.org
Cc: Gabriel Sinkin <gabe@instrumentl.com>
Content-Type: multipart/alternative; boundary="000000000000c621360620dda304"
Archived-At: <https://www.postgresql.org/message-id/CA%2B7GS%2BFf3PWbeJNbi7e6Nqfgh4HOTzyNoyGsBwFeivkUKDUwBA%40mail.gmail.com>
Precedence: bulk

--000000000000c621360620dda304
Content-Type: text/plain; charset="UTF-8"

Hello:

I'm attempting to figure out whether an optimizer behavior I'm seeing is a
PostgreSQL bug or expected behavior. The scenario:

I have two tables: one named taxpayers which has a goodish number of
columns an an integer PK id, and one named insights, which has
a taxpayer_id foreign key to taxpayers, a year, and (again) a lot of other
columns. There's an index on insights (taxpayer_id, year DESC). I'm
executing the following SQL:

```
SELECT taxpayers.id, insight_id
   FROM taxpayers
   JOIN (
       WITH ordered_insights AS (
           SELECT taxpayer_id, id, RANK() OVER (PARTITION BY taxpayer_id
ORDER BY year DESC) AS rank
           FROM insights
           WHERE year IS NOT NULL
       )
       SELECT taxpayer_id, id AS insight_id
       FROM ordered_insights
       WHERE rank = 1
   ) latest_insights ON latest_insights.taxpayer_id = taxpayers.id
WHERE taxpayers.id IN (?, ?)
```

(this is simplified example; the real code has the subselect in a view so
that it can execute this kind of join from an ORM; it also joins quite a
few tables downstream after this)

If there's only a single value in the IN clause, the EXPLAIN plan looks
great:

Nested Loop  (cost=0.86..53.30 rows=1 width=16)
  ->  Index Only Scan using taxpayers_pkey on taxpayers  (cost=0.43..8.45
rows=1 width=8)
        Index Cond: (id = 650974)
  ->  Subquery Scan on ordered_insights  (cost=0.43..44.83 rows=1 width=16)
        Filter: (ordered_insights.rank = 1)
        ->  WindowAgg  (cost=0.43..44.71 rows=10 width=28)
              Run Condition: (rank() OVER (?) <= 1)
              ->  Index Scan using index_insights_on_taxpayer_id_year_desc
on insights  (cost=0.43..44.53 rows=10 width=20)
                    Index Cond: ((taxpayer_id = 650974) AND (year IS NOT
NULL))
(9 rows)

However, if there are multiple rows in the IN clause, the optimizer decides
to execute the subselect against the entire giant table, and it is not
great:

Hash Join  (cost=2611586.97..2800201.15 rows=1 width=16)
  Hash Cond: (ordered_insights.taxpayer_id = taxpayers.id)
  ->  Subquery Scan on ordered_insights  (cost=2611570.10..2799818.65
rows=28961 width=16)
        Filter: (ordered_insights.rank = 1)
        ->  WindowAgg  (cost=2611570.10..2727415.36 rows=5792263 width=28)
              Run Condition: (rank() OVER (?) <= 1)
              ->  Sort  (cost=2611570.10..2626050.76 rows=5792263 width=20)
                    Sort Key: insights.taxpayer_id, insights.year DESC
                    ->  Seq Scan on insights  (cost=0.00..1723354.01
rows=5792263 width=20)
                          Filter: (year IS NOT NULL)
  ->  Hash  (cost=16.85..16.85 rows=2 width=8)
        ->  Index Only Scan using taxpayers_pkey on taxpayers
 (cost=0.43..16.85 rows=2 width=8)
              Index Cond: (id = ANY ('{650974,243848}'::bigint[]))

If I add in a second repetitive WHERE clause, it goes back to being happy,
but that feels a bit like a hack:

# EXPLAIN SELECT taxpayers.id, insight_id
   FROM taxpayers
   JOIN (
       WITH ordered_insights AS (
           SELECT taxpayer_id, id, RANK() OVER (PARTITION BY taxpayer_id
ORDER BY year DESC) AS rank
           FROM insights
           WHERE year IS NOT NULL
       )
       SELECT taxpayer_id, id AS insight_id
       FROM ordered_insights
       WHERE rank = 1
   ) latest_insights ON latest_insights.taxpayer_id = taxpayers.id
WHERE taxpayers.id IN (650974, 243848) AND latest_insights.taxpayer_id IN
(650974, 243848);
                                                        QUERY PLAN

-----------------------------------------------------------------------------------------------------------------------------
Nested Loop  (cost=0.86..110.57 rows=1 width=16)
  Join Filter: (taxpayers.id = ordered_insights.taxpayer_id)
  ->  Subquery Scan on ordered_insights  (cost=0.43..93.69 rows=1 width=16)
        Filter: (ordered_insights.rank = 1)
        ->  WindowAgg  (cost=0.43..93.42 rows=21 width=28)
              Run Condition: (rank() OVER (?) <= 1)
              ->  Index Scan using index_insights_on_taxpayer_id_year_desc
on insights  (cost=0.43..93.06 rows=21 width=20)
                    Index Cond: ((taxpayer_id = ANY
('{650974,243848}'::bigint[])) AND (year IS NOT NULL))
  ->  Index Only Scan using taxpayers_pkey on taxpayers  (cost=0.43..16.85
rows=2 width=8)
        Index Cond: (id = ANY ('{650974,243848}'::bigint[]))

This feels like a bug to me, but maybe I'm missing something obvious. I
don't really get why the optimizer wouldn't be able to infer the second
condition given that I'm doing a join on a non-nullable integer column (so
there's no NaN nonsense to worry about), but maybe I'm missing something
obvious.

I've reproduced this on PostgreSQL 15.7 and 17beta3.

Thanks for any insights y'all can provide!

-- 
James Brown

--000000000000c621360620dda304
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: base64
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--000000000000c621360620dda304--