`STDDEV_POP` / `VAR_*` over `BIGINT UNSIGNED` near `2^64` wrong on `UNION ALL`
- Dominant language
- Go
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Description
## Bug Report
On a base table (or a materialized copy of a `UNION ALL`), TiDB correctly returns `0.0`. Over a **≥3-way `UNION ALL`** of the same rows (e.g. `MOD(sh,4)=0/1/2/3` partitions), the same aggregates return a **nonzero** value (`STDDEV_POP` ≈ `443.405`). A 2-way `UNION ALL` still returns `0.0`. MySQL 9.7.2 and MariaDB 11.4 return `0.0` for the 4-way form.
### 1. Minimal reproduce step (Required)
```sql
CREATE TABLE u (sh BIGINT UNSIGNED);
INSERT INTO u VALUES
(18446744073709551614),
(18446744073709551613),
(18446744073709551612),
(18446744073709551611),
(18446744073709551610),
(18446744073709551609),
(18446744073709551608),
(18446744073709551607);
SELECT STDDEV_POP(sh) FROM u;
-- 0.0
SELECT STDDEV_POP(sh) FROM (
SELECT sh FROM u WHERE MOD(sh, 4) = 0
UNION ALL SELECT sh FROM u WHERE MOD(sh, 4) = 1
UNION ALL SELECT sh FROM u WHERE MOD(sh, 4) = 2
UNION ALL SELECT sh FROM u WHERE MOD(sh, 4) = 3
) AS x;
-- 443.40500673763256
```
### 2. What did you expect to see? (Required)
### 3. What did you see instead (Required)
### 4. What is your TiDB version? (Required)
`tidb 8.0.11-TiDB-v8.5.0`
Contributor guide
Research direction
Start by running the provided SQL reproduction and compare the base-table result with the four-way UNION ALL result, then inspect the database aggregation and UNION ALL execution paths. Done means STDDEV_POP and the related VAR_* aggregates return 0.0 for the reproduced BIGINT UNSIGNED values, including the four-way UNION ALL query.
Written by the indexing model from the issue text.
Assessment
- Tech stack
- go, sql
- Domain
- databases
- Issue type
- Bug
- Difficulty
- 4/5
- Estimated time
- 3-5 days
- Activity status
- Quiet
- Clarity
- Clearly specified
- Newbie friendliness
- 52/100