Managing TOAST OID contention in Amazon RDS for PostgreSQL (original) (raw)

TOAST (The Oversized-Attribute Storage Technique) is a PostgreSQL feature designed to handle large data values that exceed the typical 8KB database block size. PostgreSQL doesn't allow physical rows to span multiple blocks. The block size acts as an upper limit on row size. TOAST overcomes this restriction by splitting large field values into smaller chunks. It stores them separately in a dedicated TOAST table linked to the main table. For more information, see thePostgreSQL TOAST storage mechanism and implementation documentation.

Topics

• Understanding TOAST operations
• Identifying performance challenges
• Recommendations
• Monitoring

Understanding TOAST operations

TOAST performs compression and stores large field values out of line. TOAST assigns a unique OID (Object Identifier) to each chunk of oversized data stored in the TOAST table. The main table stores the TOAST value ID and relation ID on the page to reference the corresponding row in the TOAST table. This allows PostgreSQL to efficiently locate and manage these TOAST chunks. However, as the TOAST table grows, the system risks exhausting available OIDs, leading to both performance degradation and potential downtime due to OID depletion.

Object identifiers in TOAST

An Object Identifier (OID) is a system-wide unique identifier used by PostgreSQL to reference database objects like tables, indexes, and functions. These identifiers play a vital role in PostgreSQL's internal operations, allowing the database to efficiently locate and manage objects.

For tables with eligible data sets for toasting, PostgreSQL assigns OIDs to uniquely identify each chunk of oversized data stored in the associated TOAST table. The system associates each chunk with a chunk_id, which helps PostgreSQL organize and locate these chunks efficiently within the TOAST table.

Identifying performance challenges

PostgreSQL's OID management relies on a global 32-bit counter so that it wraps around after generating 4 billion unique values. While the database cluster shares this counter, OID allocation involves two steps during TOAST operations:

• Global counter for allocation – The global counter assigns a new OID across the cluster.
• Local search for conflicts – The TOAST table ensures the new OID does not conflict with existing OIDs already used in that specific table.

Performance degradation can occur when:

• The TOAST table has high fragmentation or dense OID usage, leading to delays in assigning the OID.
• The system frequently allocates and reuses OIDs in environments with high data churn or wide tables that use TOAST extensively.

For more information, see the PostgreSQL TOAST table size limits and OID allocation documentation:

A global counter generates the OIDs and wraps around every 4 billion values, so that from time to time, the system generates an already-used value again. PostgreSQL detects that and tries again with the next OID. A slow INSERT could occur if there is a very long run of used OID values with no gaps in the TOAST table. These challenges become more pronounced as the OID space fills, leading to slower inserts and updates.

Identifying the problem

• Simple INSERT statements take significantly longer than usual in an inconsistent and random manner.
• Delays occur only for INSERT and UPDATE statements involving TOAST operations.
• The following log entries appear in PostgreSQL logs when the system struggles to find available OIDs in TOAST tables:

LOG: still searching for an unused OID in relation "pg_toast_20815"  
DETAIL: OID candidates have been checked 1000000 times, but no unused OID has been found yet.  

• Performance Insights indicates a high number of average active sessions (AAS) associated with LWLock:buffer_io and LWLock:OidGenLock wait events.
  You can run the following SQL query to identify long-running INSERT transactions with wait events:

SELECT  
    datname AS database_name,  
    usename AS database_user,  
    pid,  
    now() - pg_stat_activity.xact_start AS transaction_duration,  
    concat(wait_event_type, ':', wait_event) AS wait_event,  
    substr(query, 1, 30) AS TRANSACTION,  
    state  
FROM  
    pg_stat_activity  
WHERE (now() - pg_stat_activity.xact_start) > INTERVAL '60 seconds'  
    AND state IN ('active', 'idle in transaction', 'idle in transaction (aborted)', 'fastpath function call', 'disabled')  
    AND pid <> pg_backend_pid()  
AND lower(query) LIKE '%insert%'  
ORDER BY  
    transaction_duration DESC;  

Example query results displaying INSERT operations with extended wait times:

 database_name |  database_user  |  pid  | transaction_duration |     wait_event      |          transaction           | state  
---------------+-----------------+-------+----------------------+---------------------+--------------------------------+--------  
 postgres       | db_admin_user| 70965 | 00:10:19.484061      | LWLock:buffer_io    | INSERT INTO "products" (......... | active  
 postgres       | db_admin_user| 69878 | 00:06:14.976037      | LWLock:buffer_io    | INSERT INTO "products" (......... | active  
 postgres       | db_admin_user| 68937 | 00:05:13.942847      | :                   | INSERT INTO "products" (......... | active  

Isolating the problem

• Test small insert – Insert a record smaller than the toast_tuple_target threshold. Remember that compression is applied before TOAST storage. If this operates without performance issues, the problem is related to TOAST operations.
• Test new table – Create a new table with the same structure and insert a record larger than toast_tuple_target. If this works without issues, the problem is localized to the original table's OID allocation.

Recommendations

The following approaches can help resolve TOAST OID contention issues.

• Data cleanup and archive – Review and delete any obsolete or unnecessary data to free up OIDs for future use, or archive the data. Consider the following limitations:
  • Limited scalability, as future cleanup might not always be possible.
  • Possible long-running VACUUM operation to remove the resulting dead tuples.
• Write to a new table – Create a new table for future inserts and use a UNION ALL view to combine old and new data for queries. This view presents the combined data from both old and new tables, allowing queries to access them as a single table. Consider the following limitations:
  • Updates on the old table might still cause OID exhaustion.
• Partition or Shard – Partition the table or shard data for better scalability and performance. Consider the following limitations:
  • Increased complexity in query logic and maintenance, potential need for application changes to handle partitioned data correctly.

Monitoring

Using system tables

You can use PostgreSQL's system tables to monitor growth of OID usage.

Warning

Depending on the number of OIDs in the TOAST table, it may take time to complete. We recommend that you schedule monitoring during off-business hours to minimize impact.

The following anonymous block counts the number of distinct OIDs used in each TOAST table and displays the parent table information:

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rspace="0em">′</mo></msup><mi>P</mi><mi>a</mi><mi>r</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mi>c</mi><mi>h</mi><mi>e</mi><mi>m</mi><mi>a</mi><mo>:</mo><mi>E</mi><mi>N</mi><mi>D</mi><mi>I</mi><mi>F</mi><mo separator="true">;</mo><mi>E</mi><mi>N</mi><mi>D</mi><mi>L</mi><mi>O</mi><mi>O</mi><mi>P</mi><mo separator="true">;</mo><mi>E</mi><mi>N</mi><mi>D</mi></mrow><annotation encoding="application/x-tex">DECLARE
    r record;
    o bigint;
    parent_table text;
    parent_schema text;
BEGIN
    SET LOCAL client_min_messages TO notice;
    FOR r IN
    SELECT
        c.oid,
        c.oid::regclass AS toast_table
    FROM
        pg_class c
    WHERE
        c.relkind = &#x27;t&#x27;
        AND c.relowner != 10 LOOP
            -- Fetch the number of distinct used OIDs (chunk IDs) from the TOAST table
            EXECUTE &#x27;SELECT COUNT(DISTINCT chunk_id) FROM &#x27; || r.toast_table INTO o;
            -- If there are used OIDs, find the associated parent table and its schema
            IF o &lt;&gt; 0 THEN
                SELECT
                    n.nspname,
                    c.relname INTO parent_schema,
                    parent_table
                FROM
                    pg_class c
                    JOIN pg_namespace n ON c.relnamespace = n.oid
                WHERE
                    c.reltoastrelid = r.oid;
                -- Raise a concise NOTICE message
                RAISE NOTICE &#x27;Parent schema: % | Parent table: % | Toast table: % | Number of used OIDs: %&#x27;, parent_schema, parent_table, r.toast_table, TO_CHAR(o, &#x27;FM9,999,999,999,999&#x27;);
            END IF;
        END LOOP;
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mathnormal">ess</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">es</span><span class="mord mathnormal" style="margin-right:0.02778em;">TO</span><span class="mord mathnormal">n</span><span class="mord mathnormal">o</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">ce</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">FOR</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.05764em;">NSE</span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.13889em;">ECT</span><span class="mord mathnormal">c</span><span class="mord">.</span><span class="mord mathnormal">o</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">c</span><span class="mord">.</span><span class="mord mathnormal">o</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">::</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.9963em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">re</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mord mathnormal">A</span><span class="mord mathnormal">St</span><span class="mord 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class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ssc</span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="mord mathnormal" style="margin-right:0.05764em;">ERE</span><span class="mord mathnormal">c</span><span class="mord">.</span><span class="mord mathnormal">re</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">kin</span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel"><span class="mrel">=</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8019em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8019em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8019em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mord mathnormal">Dc</span><span class="mord">.</span><span class="mord mathnormal">re</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.02778em;">er</span><span class="mclose">!</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord">10</span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.13889em;">OOP</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0519em;vertical-align:-0.25em;"></span><span class="mord">−</span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mord mathnormal">e</span><span class="mord mathnormal">t</span><span class="mord mathnormal">c</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord mathnormal">u</span><span class="mord mathnormal">mb</span><span class="mord mathnormal">ero</span><span class="mord mathnormal">fd</span><span class="mord mathnormal">i</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal">in</span><span class="mord mathnormal">c</span><span class="mord mathnormal">t</span><span class="mord mathnormal">u</span><span class="mord mathnormal">se</span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal">Ds</span><span class="mopen">(</span><span class="mord mathnormal">c</span><span class="mord mathnormal">h</span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.03148em;">nk</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal">Ds</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">ro</span><span class="mord mathnormal">m</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.02778em;">TO</span><span class="mord mathnormal">A</span><span class="mord mathnormal">STt</span><span class="mord mathnormal">ab</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.07153em;">EXEC</span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8019em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.05764em;">SE</span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.02778em;">ECTCO</span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="mord mathnormal" style="margin-right:0.13889em;">NT</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.13889em;">ST</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.13889em;">NCT</span><span class="mord mathnormal">c</span><span class="mord mathnormal">h</span><span class="mord mathnormal">u</span><span class="mord mathnormal">n</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">d</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.02778em;">FRO</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">M</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8019em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord">∣∣</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord">.</span><span class="mord mathnormal">t</span><span class="mord mathnormal">o</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">ab</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.02778em;">NTO</span><span class="mord mathnormal">o</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord mathnormal">ere</span><span class="mord mathnormal">a</span><span class="mord mathnormal">re</span><span class="mord mathnormal">u</span><span class="mord mathnormal">se</span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal">Ds</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">in</span><span class="mord mathnormal">d</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ssoc</span><span class="mord mathnormal">ia</span><span class="mord mathnormal">t</span><span class="mord mathnormal">e</span><span class="mord mathnormal">d</span><span class="mord mathnormal">p</span><span class="mord mathnormal">a</span><span class="mord mathnormal">re</span><span class="mord mathnormal">n</span><span class="mord mathnormal">tt</span><span class="mord mathnormal">ab</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mord mathnormal">an</span><span class="mord mathnormal">d</span><span class="mord mathnormal">i</span><span class="mord mathnormal">t</span><span class="mord mathnormal">ssc</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mord mathnormal">o</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="mord mathnormal" style="margin-right:0.05764em;">ENSE</span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.13889em;">ECT</span><span class="mord mathnormal">n</span><span class="mord">.</span><span class="mord mathnormal">n</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">nam</span><span class="mord mathnormal">e</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">c</span><span class="mord">.</span><span class="mord mathnormal">re</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">nam</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal">NTOp</span><span class="mord mathnormal">a</span><span class="mord mathnormal">re</span><span class="mord mathnormal">n</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">c</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">ma</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">a</span><span class="mord mathnormal">re</span><span class="mord mathnormal">n</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">ab</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mord mathnormal">FROMp</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ssc</span><span class="mord mathnormal" style="margin-right:0.09618em;">J</span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal">Np</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">am</span><span class="mord mathnormal">es</span><span class="mord mathnormal">p</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ce</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.10903em;">ON</span><span class="mord mathnormal">c</span><span class="mord">.</span><span class="mord mathnormal">re</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">nam</span><span class="mord mathnormal">es</span><span class="mord mathnormal">p</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ce</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">n</span><span class="mord">.</span><span class="mord mathnormal">o</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="mord mathnormal" style="margin-right:0.05764em;">ERE</span><span class="mord mathnormal">c</span><span class="mord">.</span><span class="mord mathnormal">re</span><span class="mord mathnormal">lt</span><span class="mord mathnormal">o</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal">re</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord">.</span><span class="mord mathnormal">o</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.9963em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mord mathnormal">ai</span><span class="mord mathnormal">se</span><span class="mord mathnormal">a</span><span class="mord mathnormal">co</span><span class="mord mathnormal">n</span><span class="mord mathnormal">c</span><span class="mord mathnormal">i</span><span class="mord mathnormal">se</span><span class="mord mathnormal" style="margin-right:0.13889em;">NOT</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.05764em;">CE</span><span class="mord mathnormal">m</span><span class="mord mathnormal">ess</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.13889em;">SENOT</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8019em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mord mathnormal">a</span><span class="mord mathnormal">re</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span><span class="mord mathnormal">sc</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">ma</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">EN</span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">EN</span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.13889em;">OOP</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">EN</span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span></span></span></span></span>;

Example output displaying OID usage statistics by TOAST table:

NOTICE:  Parent schema: public | Parent table: my_table | Toast table: pg_toast.pg_toast_16559 | Number of used OIDs: 45,623,317
NOTICE:  Parent schema: public | Parent table: my_table1 | Toast table: pg_toast.pg_toast_45639925 | Number of used OIDs: 10,000
NOTICE:  Parent schema: public | Parent table: my_table2 | Toast table: pg_toast.pg_toast_45649931 | Number of used OIDs: 1,000,000
DO

The following anonymous block retrieves the maximum assigned OID for each non-empty TOAST table:

DO <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>D</mi><mi>E</mi><mi>C</mi><mi>L</mi><mi>A</mi><mi>R</mi><mi>E</mi><mi>r</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>o</mi><mi>r</mi><mi>d</mi><mo separator="true">;</mo><mi>o</mi><mi>b</mi><mi>i</mi><mi>g</mi><mi>i</mi><mi>n</mi><mi>t</mi><mo separator="true">;</mo><mi>p</mi><mi>a</mi><mi>r</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mi>t</mi></msub><mi>a</mi><mi>b</mi><mi>l</mi><mi>e</mi><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi><mo separator="true">;</mo><mi>p</mi><mi>a</mi><mi>r</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mi>s</mi></msub><mi>c</mi><mi>h</mi><mi>e</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi><mo separator="true">;</mo><mi>B</mi><mi>E</mi><mi>G</mi><mi>I</mi><mi>N</mi><mi>S</mi><mi>E</mi><mi>T</mi><mi>L</mi><mi>O</mi><mi>C</mi><mi>A</mi><mi>L</mi><mi>c</mi><mi>l</mi><mi>i</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mi>m</mi></msub><mi>i</mi><msub><mi>n</mi><mi>m</mi></msub><mi>e</mi><mi>s</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi><mi>T</mi><mi>O</mi><mi>n</mi><mi>o</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>e</mi><mo separator="true">;</mo><mi>F</mi><mi>O</mi><mi>R</mi><mi>r</mi><mi>I</mi><mi>N</mi><mi>S</mi><mi>E</mi><mi>L</mi><mi>E</mi><mi>C</mi><mi>T</mi><mi>c</mi><mi mathvariant="normal">.</mi><mi>o</mi><mi>i</mi><mi>d</mi><mo separator="true">,</mo><mi>c</mi><mi mathvariant="normal">.</mi><mi>o</mi><mi>i</mi><mi>d</mi><mo>:</mo><mo>:</mo><mi>r</mi><mi>e</mi><mi>g</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>A</mi><mi>S</mi><mi>t</mi><mi>o</mi><mi>a</mi><mi>s</mi><msub><mi>t</mi><mi>t</mi></msub><mi>a</mi><mi>b</mi><mi>l</mi><mi>e</mi><mi>F</mi><mi>R</mi><mi>O</mi><mi>M</mi><mi>p</mi><msub><mi>g</mi><mi>c</mi></msub><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>c</mi><mi>W</mi><mi>H</mi><mi>E</mi><mi>R</mi><mi>E</mi><mi>c</mi><mi mathvariant="normal">.</mi><mi>r</mi><mi>e</mi><mi>l</mi><mi>k</mi><mi>i</mi><mi>n</mi><mi>d</mi><msup><mo>=</mo><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><msup><mi>t</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mi>A</mi><mi>N</mi><mi>D</mi><mi>c</mi><mi mathvariant="normal">.</mi><mi>r</mi><mi>e</mi><mi>l</mi><mi>o</mi><mi>w</mi><mi>n</mi><mi>e</mi><mi>r</mi><mo stretchy="false">!</mo><mo>=</mo><mn>10</mn><mi>L</mi><mi>O</mi><mi>O</mi><mi>P</mi><mo>−</mo><mo>−</mo><mi>F</mi><mi>e</mi><mi>t</mi><mi>c</mi><mi>h</mi><mi>t</mi><mi>h</mi><mi>e</mi><mi>m</mi><mi>a</mi><mi>x</mi><mo stretchy="false">(</mo><mi>c</mi><mi>h</mi><mi>u</mi><mi>n</mi><msub><mi>k</mi><mi>i</mi></msub><mi>d</mi><mo stretchy="false">)</mo><mi>f</mi><mi>r</mi><mi>o</mi><mi>m</mi><mi>t</mi><mi>h</mi><mi>e</mi><mi>T</mi><mi>O</mi><mi>A</mi><mi>S</mi><mi>T</mi><mi>t</mi><mi>a</mi><mi>b</mi><mi>l</mi><mi>e</mi><mi>E</mi><mi>X</mi><mi>E</mi><mi>C</mi><mi>U</mi><mi>T</mi><msup><mi>E</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mi>S</mi><mi>E</mi><mi>L</mi><mi>E</mi><mi>C</mi><mi>T</mi><mi>m</mi><mi>a</mi><mi>x</mi><mo stretchy="false">(</mo><mi>c</mi><mi>h</mi><mi>u</mi><mi>n</mi><msub><mi>k</mi><mi>i</mi></msub><mi>d</mi><mo stretchy="false">)</mo><mi>F</mi><mi>R</mi><mi>O</mi><msup><mi>M</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mi mathvariant="normal">∣</mi><mi mathvariant="normal">∣</mi><mi>r</mi><mi mathvariant="normal">.</mi><mi>t</mi><mi>o</mi><mi>a</mi><mi>s</mi><msub><mi>t</mi><mi>t</mi></msub><mi>a</mi><mi>b</mi><mi>l</mi><mi>e</mi><mi>I</mi><mi>N</mi><mi>T</mi><mi>O</mi><mi>o</mi><mo separator="true">;</mo><mo>−</mo><mo>−</mo><mi>I</mi><mi>f</mi><mi>t</mi><mi>h</mi><mi>e</mi><mi>r</mi><msup><mi>e</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mi>s</mi><mi>a</mi><mi>t</mi><mi>l</mi><mi>e</mi><mi>a</mi><mi>s</mi><mi>t</mi><mi>o</mi><mi>n</mi><mi>e</mi><mi>T</mi><mi>O</mi><mi>A</mi><mi>S</mi><mi>T</mi><mi>e</mi><mi>d</mi><mi>c</mi><mi>h</mi><mi>u</mi><mi>n</mi><mi>k</mi><mo separator="true">,</mo><mi>f</mi><mi>i</mi><mi>n</mi><mi>d</mi><mi>t</mi><mi>h</mi><mi>e</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>p</mi><mi>a</mi><mi>r</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>t</mi><mi>a</mi><mi>b</mi><mi>l</mi><mi>e</mi><mi>a</mi><mi>n</mi><mi>d</mi><mi>i</mi><mi>t</mi><mi>s</mi><mi>s</mi><mi>c</mi><mi>h</mi><mi>e</mi><mi>m</mi><mi>a</mi><mi>I</mi><mi>F</mi><mi>o</mi><mi>I</mi><mi>S</mi><mi>N</mi><mi>O</mi><mi>T</mi><mi>N</mi><mi>U</mi><mi>L</mi><mi>L</mi><mi>T</mi><mi>H</mi><mi>E</mi><mi>N</mi><mi>S</mi><mi>E</mi><mi>L</mi><mi>E</mi><mi>C</mi><mi>T</mi><mi>n</mi><mi mathvariant="normal">.</mi><mi>n</mi><mi>s</mi><mi>p</mi><mi>n</mi><mi>a</mi><mi>m</mi><mi>e</mi><mo separator="true">,</mo><mi>c</mi><mi mathvariant="normal">.</mi><mi>r</mi><mi>e</mi><mi>l</mi><mi>n</mi><mi>a</mi><mi>m</mi><mi>e</mi><mi>I</mi><mi>N</mi><mi>T</mi><mi>O</mi><mi>p</mi><mi>a</mi><mi>r</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mi>s</mi></msub><mi>c</mi><mi>h</mi><mi>e</mi><mi>m</mi><mi>a</mi><mo separator="true">,</mo><mi>p</mi><mi>a</mi><mi>r</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mi>t</mi></msub><mi>a</mi><mi>b</mi><mi>l</mi><mi>e</mi><mi>F</mi><mi>R</mi><mi>O</mi><mi>M</mi><mi>p</mi><msub><mi>g</mi><mi>c</mi></msub><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>c</mi><mi>J</mi><mi>O</mi><mi>I</mi><mi>N</mi><mi>p</mi><msub><mi>g</mi><mi>n</mi></msub><mi>a</mi><mi>m</mi><mi>e</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>e</mi><mi>n</mi><mi>O</mi><mi>N</mi><mi>c</mi><mi mathvariant="normal">.</mi><mi>r</mi><mi>e</mi><mi>l</mi><mi>n</mi><mi>a</mi><mi>m</mi><mi>e</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>e</mi><mo>=</mo><mi>n</mi><mi mathvariant="normal">.</mi><mi>o</mi><mi>i</mi><mi>d</mi><mi>W</mi><mi>H</mi><mi>E</mi><mi>R</mi><mi>E</mi><mi>c</mi><mi mathvariant="normal">.</mi><mi>r</mi><mi>e</mi><mi>l</mi><mi>t</mi><mi>o</mi><mi>a</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>e</mi><mi>l</mi><mi>i</mi><mi>d</mi><mo>=</mo><mi>r</mi><mi mathvariant="normal">.</mi><mi>o</mi><mi>i</mi><mi>d</mi><mo separator="true">;</mo><mo>−</mo><mo>−</mo><mi>R</mi><mi>a</mi><mi>i</mi><mi>s</mi><mi>e</mi><mi>a</mi><mi>c</mi><mi>o</mi><mi>n</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>e</mi><mi>N</mi><mi>O</mi><mi>T</mi><mi>I</mi><mi>C</mi><mi>E</mi><mi>m</mi><mi>e</mi><mi>s</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>R</mi><mi>A</mi><mi>I</mi><mi>S</mi><mi>E</mi><mi>N</mi><mi>O</mi><mi>T</mi><mi>I</mi><mi>C</mi><msup><mi>E</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mi>P</mi><mi>a</mi><mi>r</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mi>c</mi><mi>h</mi><mi>e</mi><mi>m</mi><mi>a</mi><mo>:</mo><mi>E</mi><mi>N</mi><mi>D</mi><mi>I</mi><mi>F</mi><mo separator="true">;</mo><mi>E</mi><mi>N</mi><mi>D</mi><mi>L</mi><mi>O</mi><mi>O</mi><mi>P</mi><mo separator="true">;</mo><mi>E</mi><mi>N</mi><mi>D</mi></mrow><annotation encoding="application/x-tex">DECLARE
    r record;
    o bigint;
    parent_table text;
    parent_schema text;
BEGIN
    SET LOCAL client_min_messages TO notice;
    FOR r IN
    SELECT
        c.oid,
        c.oid::regclass AS toast_table
    FROM
        pg_class c
    WHERE
        c.relkind = &#x27;t&#x27;
        AND c.relowner != 10 LOOP
            -- Fetch the max(chunk_id) from the TOAST table
            EXECUTE &#x27;SELECT max(chunk_id) FROM &#x27; || r.toast_table INTO o;
            -- If there&#x27;s at least one TOASTed chunk, find the associated parent table and its schema
            IF o IS NOT NULL THEN
                SELECT
                    n.nspname,
                    c.relname INTO parent_schema,
                    parent_table
                FROM
                    pg_class c
                    JOIN pg_namespace n ON c.relnamespace = n.oid
                WHERE
                    c.reltoastrelid = r.oid;
                -- Raise a concise NOTICE message
                RAISE NOTICE &#x27;Parent schema: % | Parent table: % | Toast table: % | Max chunk_id: %&#x27;, parent_schema, parent_table, r.toast_table, TO_CHAR(o, &#x27;FM9,999,999,999,999&#x27;);
            END IF;
        END LOOP;
END</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.07153em;">EC</span><span class="mord mathnormal">L</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05764em;">RE</span><span class="mord mathnormal" style="margin-right:0.02778em;">rrecor</span><span class="mord mathnormal">d</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">o</span><span class="mord mathnormal">bi</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">in</span><span class="mord mathnormal">t</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">a</span><span class="mord mathnormal">re</span><span class="mord mathnormal">n</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">ab</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mord mathnormal">t</span><span class="mord mathnormal">e</span><span class="mord mathnormal">x</span><span class="mord mathnormal">t</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">a</span><span class="mord mathnormal">re</span><span class="mord mathnormal">n</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">c</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">e</span><span class="mord mathnormal">x</span><span class="mord mathnormal">t</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">BEG</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.13889em;">NSET</span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">OC</span><span class="mord mathnormal">A</span><span class="mord mathnormal">L</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">i</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">ess</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">es</span><span class="mord mathnormal" style="margin-right:0.02778em;">TO</span><span class="mord mathnormal">n</span><span class="mord mathnormal">o</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">ce</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">FOR</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.05764em;">NSE</span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.13889em;">ECT</span><span class="mord mathnormal">c</span><span class="mord">.</span><span class="mord mathnormal">o</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">c</span><span class="mord">.</span><span class="mord mathnormal">o</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">::</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.9963em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">re</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mord mathnormal">A</span><span class="mord mathnormal">St</span><span class="mord mathnormal">o</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">ab</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mord mathnormal">FROMp</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ssc</span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="mord mathnormal" style="margin-right:0.05764em;">ERE</span><span class="mord mathnormal">c</span><span class="mord">.</span><span class="mord mathnormal">re</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">kin</span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel"><span class="mrel">=</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8019em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8019em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8019em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mord mathnormal">Dc</span><span class="mord">.</span><span class="mord mathnormal">re</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.02778em;">er</span><span class="mclose">!</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord">10</span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.13889em;">OOP</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0519em;vertical-align:-0.25em;"></span><span class="mord">−</span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mord mathnormal">e</span><span class="mord mathnormal">t</span><span class="mord mathnormal">c</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">x</span><span class="mopen">(</span><span class="mord mathnormal">c</span><span class="mord mathnormal">h</span><span class="mord mathnormal">u</span><span class="mord mathnormal">n</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">d</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">ro</span><span class="mord mathnormal">m</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.02778em;">TO</span><span class="mord mathnormal">A</span><span class="mord mathnormal">STt</span><span class="mord mathnormal">ab</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.07153em;">EXEC</span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8019em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.05764em;">SE</span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.13889em;">ECT</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">x</span><span class="mopen">(</span><span class="mord mathnormal">c</span><span class="mord mathnormal">h</span><span class="mord mathnormal">u</span><span class="mord mathnormal">n</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">d</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.02778em;">FRO</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">M</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8019em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord">∣∣</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord">.</span><span class="mord mathnormal">t</span><span class="mord mathnormal">o</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">ab</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.02778em;">NTO</span><span class="mord mathnormal">o</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.9963em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord mathnormal" style="margin-right:0.02778em;">er</span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8019em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord mathnormal">s</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.01968em;">tl</span><span class="mord mathnormal">e</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal">o</span><span class="mord mathnormal">n</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.02778em;">TO</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.13889em;">ST</span><span class="mord mathnormal">e</span><span class="mord mathnormal">d</span><span class="mord mathnormal">c</span><span class="mord mathnormal">h</span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.03148em;">nk</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">in</span><span class="mord mathnormal">d</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ssoc</span><span class="mord mathnormal">ia</span><span class="mord mathnormal">t</span><span class="mord mathnormal">e</span><span class="mord mathnormal">d</span><span class="mord mathnormal">p</span><span class="mord mathnormal">a</span><span class="mord mathnormal">re</span><span class="mord mathnormal">n</span><span class="mord mathnormal">tt</span><span class="mord mathnormal">ab</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mord mathnormal">an</span><span class="mord mathnormal">d</span><span class="mord mathnormal">i</span><span class="mord mathnormal">t</span><span class="mord mathnormal">ssc</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.10903em;">SNOTN</span><span class="mord mathnormal">ULL</span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="mord mathnormal" style="margin-right:0.05764em;">ENSE</span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.13889em;">ECT</span><span class="mord mathnormal">n</span><span class="mord">.</span><span class="mord mathnormal">n</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">nam</span><span class="mord mathnormal">e</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">c</span><span class="mord">.</span><span class="mord mathnormal">re</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">nam</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal">NTOp</span><span class="mord mathnormal">a</span><span class="mord mathnormal">re</span><span class="mord mathnormal">n</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">c</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">ma</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">a</span><span class="mord mathnormal">re</span><span class="mord mathnormal">n</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">ab</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mord mathnormal">FROMp</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ssc</span><span class="mord mathnormal" style="margin-right:0.09618em;">J</span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal">Np</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">am</span><span class="mord mathnormal">es</span><span class="mord mathnormal">p</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ce</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.10903em;">ON</span><span class="mord mathnormal">c</span><span class="mord">.</span><span class="mord mathnormal">re</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">nam</span><span class="mord mathnormal">es</span><span class="mord mathnormal">p</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ce</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">n</span><span class="mord">.</span><span class="mord mathnormal">o</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="mord mathnormal" style="margin-right:0.05764em;">ERE</span><span class="mord mathnormal">c</span><span class="mord">.</span><span class="mord mathnormal">re</span><span class="mord mathnormal">lt</span><span class="mord mathnormal">o</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal">re</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord">.</span><span class="mord mathnormal">o</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.9963em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mord mathnormal">ai</span><span class="mord mathnormal">se</span><span class="mord mathnormal">a</span><span class="mord mathnormal">co</span><span class="mord mathnormal">n</span><span class="mord mathnormal">c</span><span class="mord mathnormal">i</span><span class="mord mathnormal">se</span><span class="mord mathnormal" style="margin-right:0.13889em;">NOT</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.05764em;">CE</span><span class="mord mathnormal">m</span><span class="mord mathnormal">ess</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.13889em;">SENOT</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8019em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mord mathnormal">a</span><span class="mord mathnormal">re</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span><span class="mord mathnormal">sc</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">ma</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">EN</span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">EN</span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.13889em;">OOP</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">EN</span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span></span></span></span></span>;

Example output displaying maximum chunk IDs for TOAST tables:

NOTICE:  Parent schema: public | Parent table: my_table | Toast table: pg_toast.pg_toast_16559 | Max chunk_id: 45,639,907
NOTICE:  Parent schema: public | Parent table: my_table1 | Toast table: pg_toast.pg_toast_45639925 | Max chunk_id: 45,649,929
NOTICE:  Parent schema: public | Parent table: my_table2 | Toast table: pg_toast.pg_toast_45649931 | Max chunk_id: 46,649,935
DO

Using Performance Insights

The wait events LWLock:buffer_io and LWLock:OidGenLock appear in Performance Insights during operations that require assigning new Object Identifiers (OIDs). High Average Active Sessions (AAS) for these events typically point to contention during OID assignment and resource management. This is particularly common in environments with high data churn, extensive large data usage, or frequent object creation.

LWLock:buffer_io

LWLock:buffer_io is a wait event that occurs when a PostgreSQL session is waiting for I/O operations on a shared buffer to complete. This typically happens when the database reads data from disk into memory or writes modified pages from memory to disk. The BufferIO wait event ensures consistency by preventing multiple processes from accessing or modifying the same buffer while I/O operations are in progress. High occurrences of this wait event may indicate disk bottlenecks or excessive I/O activity in the database workload.

During TOAST operations:

• PostgreSQL allocates OIDs for large objects and ensures their uniqueness by scanning the TOAST table's index.
• Large TOAST indexes may require accessing multiple pages to verify OID uniqueness. This results in increased disk I/O, especially when the buffer pool cannot cache all required pages.

The size of the index directly affects the number of buffer pages that need to be accessed during these operations. Even if the index is not bloated, its sheer size can increase buffer I/O, particularly in high-concurrency or high-churn environments. For more information, see LWLock:BufferIO wait event troubleshooting guide.

LWLock:OidGenLock

OidGenLock is a wait event that occurs when a PostgreSQL session is waiting to allocate a new object identifier (OID). This lock ensures that OIDs are generated sequentially and safely, allowing only one process to generate OIDs at a time.

During TOAST operations:

• OID allocation for chunks in TOAST table – PostgreSQL assigns OIDs to chunks in TOAST tables when managing large data records. Each OID must be unique to prevent conflicts in the system catalog.
• High concurrency – Since access to OID generator is sequential, when multiple sessions are concurrently creating objects that require OIDs, contention for OidGenLock can occur. This increases the likelihood of sessions waiting for OID allocation to complete.
• Dependency on system catalog access – Allocating OIDs requires updates to shared system catalog tables likepg_class and pg_type. If these tables experience heavy activity (due to frequent DDL operations), it can increase lock contention forOidGenLock.
• High OID allocation demand – TOAST heavy workloads with large data records require constant OID allocation, increasing contention.

Additional factors that increase OID contention:

• Frequent object creation – Workloads that frequently create and drop objects, such as temporary tables, amplify contention on the global OID counter.
• Global counter locking – The global OID counter is accessed serially to ensure uniqueness, creating a single point of contention in high-concurrency environments.