[Bug] There is a calculation logic error in the aggregate window query for overall standard deviation.
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Description
### Search before asking
- [X] I searched in the [issues](https://github.com/apache/iotdb/issues) and found nothing similar.
### Version
version 1.3.3 (Build: ad95a7e)
### Describe the bug and provide the minimal reproduce step
```
DROP DATABASE root.db0
CREATE TIMESERIES root.db0.t1.c0 INT32;
INSERT INTO root.db0.t1(timestamp, c0) VALUES (1641024000000, 72), (1641024005000, 112), (1641024010000, 152), (1641024015000, 192), (1641024020000, 232), (1641024025000, 272), (1641024030000, 312), (1641024035000, 352), (1641024040000, 392), (1641024045000, 432), (1641024050000, 472), (1641024055000, 512), (1641024060000, 552), (1641024065000, 592), (1641024070000, 632), (1641024075000, 672), (1641024080000, 712), (1641024085000, 752), (1641024090000, 792), (1641024095000, 832), (1641024100000, 872), (1641024105000, 912), (1641024110000, 952), (1641024115000, 992), (1641024120000, 1032), (1641024125000, 1072), (1641024130000, 1112), (1641024135000, 1152), (1641024140000, null), (1641024145000, 1232);
INSERT INTO root.db0.t1(timestamp, c0) VALUES (1641024150000, 1272), (1641024155000, 1312), (1641024160000, 1352), (1641024165000, 1392), (1641024170000, 1432), (1641024175000, 1472), (1641024180000, 1512), (1641024185000, 1552), (1641024190000, 1592), (1641024195000, 1632), (1641024200000, 1672), (1641024205000, 1712), (1641024210000, null), (1641024215000, 1792), (1641024220000, 1832), (1641024225000, 1872), (1641024230000, 1912), (1641024235000, 1952), (1641024240000, 1992), (1641024245000, 2032), (1641024250000, 2072), (1641024255000, 2112), (1641024260000, 2152), (1641024265000, 2192), (1641024270000, 2232), (1641024275000, 2272), (1641024280000, 2312), (1641024285000, 2352), (1641024290000, 2392), (1641024295000, 2432);
INSERT INTO root.db0.t1(timestamp, c0) VALUES (1641024300000, 2472), (1641024305000, 2512), (1641024310000, 2552), (1641024315000, 2592), (1641024320000, 2632), (1641024325000, 2672), (1641024330000, 2712), (1641024335000, 2752), (1641024340000, 2792), (1641024345000, null), (1641024350000, 2872), (1641024355000, 2912), (1641024360000, 2952), (1641024365000, 2992), (1641024370000, 3032), (1641024375000, 3072), (1641024380000, 3112), (1641024385000, 3152), (1641024390000, 3192), (1641024395000, 3232), (1641024400000, 3272), (1641024405000, 3312), (1641024410000, 3352), (1641024415000, 3392), (1641024420000, 3432), (1641024425000, 3472), (1641024430000, 3512), (1641024435000, 3552), (1641024440000, 3592), (1641024445000, 3632);
INSERT INTO root.db0.t1(timestamp, c0) VALUES (1641024450000, 3672), (1641024455000, null), (1641024460000, 3752), (1641024465000, null), (1641024470000, 3832), (1641024475000, 3872), (1641024480000, 3912), (1641024485000, 3952), (1641024490000, 3992), (1641024495000, 4032), (1641024500000, 4072), (1641024505000, 4112), (1641024510000, 4152), (1641024515000, 4192), (1641024520000, 4232), (1641024525000, 4272), (1641024530000, 4312), (1641024535000, 4352), (1641024540000, 4392), (1641024545000, 4432), (1641024550000, 4472), (1641024555000, 4512), (1641024560000, 4552), (1641024565000, 4592), (1641024570000, 4632), (1641024575000, 4672), (1641024580000, 4712), (1641024585000, 4752), (1641024590000, 4792), (1641024595000, 4832);
INSERT INTO root.db0.t1(timestamp, c0) VALUES (1641024600000, 4872), (1641024605000, 4912), (1641024610000, 4952), (1641024615000, 4992), (1641024620000, 5032), (1641024625000, 5072), (1641024630000, 5112), (1641024635000, 5152), (1641024640000, 5192), (1641024645000, 5232), (1641024650000, 5272), (1641024655000, 5312), (1641024660000, 5352), (1641024665000, 5392), (1641024670000, 5432), (1641024675000, 5472), (1641024680000, 5512), (1641024685000, 5552), (1641024690000, 5592), (1641024695000, 5632), (1641024700000, 5672), (1641024705000, 5712), (1641024710000, 5752), (1641024715000, 5792), (1641024720000, 5832), (1641024725000, 5872), (1641024730000, 5912), (1641024735000, 5952), (1641024740000, 5992), (1641024745000, 6032);
INSERT INTO root.db0.t1(timestamp, c0) VALUES (1641024750000, 6072), (1641024755000, 6112), (1641024760000, 6152), (1641024765000, 6192), (1641024770000, 6232), (1641024775000, 6272), (1641024780000, 6312), (1641024785000, 6352), (1641024790000, 6392), (1641024795000, 6432), (1641024800000, 6472), (1641024805000, 6512), (1641024810000, 6552), (1641024815000, 6592), (1641024820000, 6632), (1641024825000, 6672), (1641024830000, 6712), (1641024835000, 6752), (1641024840000, 6792), (1641024845000, 6832), (1641024850000, 6872), (1641024855000, 6912), (1641024860000, 6952), (1641024865000, 6992), (1641024870000, 7032), (1641024875000, 7072), (1641024880000, 7112), (1641024885000, 7152), (1641024890000, 7192), (1641024895000, 7232);
INSERT INTO root.db0.t1(timestamp, c0) VALUES (1641024900000, 7272), (1641024905000, 7312), (1641024910000, 7352), (1641024915000, 7392), (1641024920000, null), (1641024925000, 7472), (1641024930000, 7512), (1641024935000, 7552), (1641024940000, 7592), (1641024945000, 7632), (1641024950000, 7672), (1641024955000, 7712), (1641024960000, 7752), (1641024965000, 7792), (1641024970000, 7832), (1641024975000, 7872), (1641024980000, 7912), (1641024985000, 7952), (1641024990000, 7992), (1641024995000, 8032), (1641025000000, 8072), (1641025005000, 8112), (1641025010000, 8152), (1641025015000, 8192), (1641025020000, 8232), (1641025025000, 8272), (1641025030000, 8312), (1641025035000, 8352), (1641025040000, 8392), (1641025045000, 8432);
INSERT INTO root.db0.t1(timestamp, c0) VALUES (1641025050000, 8472), (1641025055000, 8512), (1641025060000, 8552), (1641025065000, 8592), (1641025070000, 8632), (1641025075000, 8672), (1641025080000, 8712), (1641025085000, 8752), (1641025090000, 8792), (1641025095000, 8832), (1641025100000, 8872), (1641025105000, 8912), (1641025110000, 8952), (1641025115000, 8992), (1641025120000, 9032), (1641025125000, 9072), (1641025130000, 9112), (1641025135000, 9152), (1641025140000, null), (1641025145000, 9232), (1641025150000, 9272), (1641025155000, 9312), (1641025160000, 9352), (1641025165000, 9392), (1641025170000, 9432), (1641025175000, 9472), (1641025180000, 9512), (1641025185000, 9552), (1641025190000, 9592), (1641025195000, 9632);
INSERT INTO root.db0.t1(timestamp, c0) VALUES (1641025200000, 9672), (1641025205000, 9712), (1641025210000, 9752), (1641025215000, 9792), (1641025220000, 9832), (1641025225000, 9872), (1641025230000, 9912), (1641025235000, 9952), (1641025240000, 9992), (1641025245000, 10032), (1641025250000, 10072), (1641025255000, 10112), (1641025260000, 10152), (1641025265000, 10192), (1641025270000, 10232), (1641025275000, 10272), (1641025280000, 10312), (1641025285000, 10352), (1641025290000, 10392), (1641025295000, 10432), (1641025300000, 10472), (1641025305000, 10512), (1641025310000, 10552), (1641025315000, 10592), (1641025320000, 10632), (1641025325000, 10672), (1641025330000, 10712), (1641025335000, 10752), (1641025340000, 10792), (1641025345000, 10832);
INSERT INTO root.db0.t1(timestamp, c0) VALUES (1641025350000, 10872), (1641025355000, 10912), (1641025360000, 10952), (1641025365000, 10992), (1641025370000, 11032), (1641025375000, 11072), (1641025380000, 11112), (1641025385000, 11152), (1641025390000, 11192), (1641025395000, 11232), (1641025400000, 11272), (1641025405000, 11312), (1641025410000, 11352), (1641025415000, 11392), (1641025420000, 11432), (1641025425000, 11472), (1641025430000, 11512), (1641025435000, 11552), (1641025440000, 11592), (1641025445000, 11632), (1641025450000, 11672), (1641025455000, 11712), (1641025460000, 11752), (1641025465000, 11792), (1641025470000, 11832), (1641025475000, 11872), (1641025480000, 11912), (1641025485000, 11952), (1641025490000, 11992), (1641025495000, 12032);
INSERT INTO root.db0.t1(timestamp, c0) VALUES (1641025500000, 12072), (1641025505000, 12112), (1641025510000, 12152), (1641025515000, 12192), (1641025520000, 12232), (1641025525000, 12272), (1641025530000, 12312), (1641025535000, 12352), (1641025540000, 12392), (1641025545000, 12432), (1641025550000, 12472), (1641025555000, 12512), (1641025560000, 12552), (1641025565000, 12592), (1641025570000, 12632), (1641025575000, 12672), (1641025580000, 12712), (1641025585000, 12752), (1641025590000, 12792), (1641025595000, 12832), (1641025600000, 12872), (1641025605000, 12912), (1641025610000, 12952), (1641025615000, 12992), (1641025620000, 13032), (1641025625000, 13072), (1641025630000, 13112), (1641025635000, 13152), (1641025640000, 13192), (1641025645000, 13232);
INSERT INTO root.db0.t1(timestamp, c0) VALUES (1641025650000, null), (1641025655000, 13312), (1641025660000, 13352), (1641025665000, 13392), (1641025670000, null), (1641025675000, 13472), (1641025680000, 13512), (1641025685000, 13552), (1641025690000, 13592), (1641025695000, 13632), (1641025700000, 13672), (1641025705000, 13712), (1641025710000, 13752), (1641025715000, 13792), (1641025720000, 13832), (1641025725000, 13872), (1641025730000, 13912), (1641025735000, 13952);
# query 1
SELECT STDDEV_POP(c0) FROM root.db0.t1 GROUP BY ([1641023357064, 1641025073925),2545s,854s)
# query 2
SELECT STDDEV_POP(c0) FROM root.db0.t1 GROUP BY ([1641023357064, 1641025073925),2545s,1708s)
# query 3
SELECT STDDEV_POP(c0) FROM root.db0.t1 GROUP BY([1641025065064, 1641025073925),2545s)
```
### What did you expect to see?
The expected result set for Query 1 is: 2489.867388014679 1987.3425863588686 **0.0**
The expected result set for Query 2 is: 2489.867388014679 0.0
The expected result set for Query 3 is: 0.0
### What did you see instead?
The actual result set returned by Query 1 is: 2489.867388014679 1987.3425863588686 **NaN**
The actual result set returned by Query 2 is: 2489.867388014679 **3.1714797501871533E-4**
The actual result set returned by Query 3 is: 0.0
### Anything else?
Dear IoTDB team, In the three queries above, we perform **standard deviation window aggregation** on the `root.db0.t1.c1` time series.
- Query 1 has an aggregation start time of `1641023357064` and an end time of `1641025073925`, with each aggregation window size being `2545s` and a window sliding distance of `854s`.
- Query 2 uses the same aggregation time range as Query 1 but doubles the sliding distance of Query 1.
- Query 3 changes the start time to `1641025065064` (`1641025065064 = 1641023357064 + 854000 + 854000`).
By analyzing the actual result sets returned by the three queries, we found discrepancies in the aggregation values of the last window. Additionally, Query 1 triggered a **numeric overflow** error.
### Are you willing to submit a PR?
- [ ] I'm willing to submit a PR!
Contributor guide
Research direction
Start by reproducing the three STDDEV_POP window queries from the issue on IoTDB 1.3.3 and compare the final-window results with the stated expectations. Trace the aggregate-window standard-deviation path and verify that single-value windows return 0.0 without numeric overflow or NaN; done means all three queries produce the expected results.
Written by the indexing model from the issue text.
Assessment
- Tech stack
- java, sql
- Domain
- data, databases
- Issue type
- Bug
- Difficulty
- 4/5
- Estimated time
- 3-5 days
- Activity status
- Stale
- Clarity
- Mostly clear
- Newbie friendliness
- 35/100