[feature](agg function) support corr_welford agg function #49712

[Mryange]

pick #49712

In the past, due to performance considerations, the implementation of corr was relatively simple, avoiding division operations except in the final step.
However, this approach resulted in larger errors, so corr_welford was introduced to improve the accuracy of the calculations.

0.7605339114107809 corr_result
0.7605339114107733 corr_welford_result

What problem does this PR solve?

Issue Number: close #xxx

Related PR: #xxx

Problem Summary:

Release note

None

Check List (For Author)

• Test

  • Regression test
  • Unit Test
  • Manual test (add detailed scripts or steps below)
  • No need to test or manual test. Explain why:
    • This is a refactor/code format and no logic has been changed.
    • Previous test can cover this change.
    • No code files have been changed.
    • Other reason

• Behavior changed:

  • No.
  • Yes.

• Does this need documentation?

  • No.
  • Yes.

Check List (For Reviewer who merge this PR)

• Confirm the release note
• Confirm test cases
• Confirm document
• Add branch pick label

[hello-stephen]

Thank you for your contribution to Apache Doris.
Don't know what should be done next? See How to process your PR.

Please clearly describe your PR:

1. What problem was fixed (it's best to include specific error reporting information). How it was fixed.
2. Which behaviors were modified. What was the previous behavior, what is it now, why was it modified, and what possible impacts might there be.
3. What features were added. Why was this function added?
4. Which code was refactored and why was this part of the code refactored?
5. Which functions were optimized and what is the difference before and after the optimization?

[Mryange]

run buildall

[doris-robot]

TPC-H: Total hot run time: 40471 ms

machine: 'aliyun_ecs.c7a.8xlarge_32C64G'
scripts: https://github.com/apache/doris/tree/master/tools/tpch-tools
Tpch sf100 test result on commit de9f040a5bb3bcad0e4bd9f3b89fd7cd66e826ac, data reload: false
------ Round 1 ----------------------------------
q1	17615	6924	6693	6693
q2	2305	169	189	169
q3	11252	1205	1190	1190
q4	10286	724	693	693
q5	8664	2948	2957	2948
q6	223	132	132	132
q7	984	624	623	623
q8	9743	2007	2046	2007
q9	7098	6443	6460	6443
q10	7059	2244	2327	2244
q11	473	267	263	263
q12	408	217	205	205
q13	17760	2940	2985	2940
q14	246	207	214	207
q15	504	467	473	467
q16	659	600	599	599
q17	1000	551	542	542
q18	7400	6720	6647	6647
q19	1400	1061	1085	1061
q20	483	199	195	195
q21	4275	3290	3206	3206
q22	1081	997	1027	997
Total cold run time: 110918 ms
Total hot run time: 40471 ms
----- Round 2, with runtime_filter_mode=off -----
q1	6637	6549	6606	6549
q2	327	236	228	228
q3	2894	2956	2993	2956
q4	2092	1856	1779	1779
q5	5777	5705	5713	5705
q6	209	122	121	121
q7	2139	1747	1810	1747
q8	3308	3509	3570	3509
q9	8980	8891	8882	8882
q10	3584	3501	3526	3501
q11	582	494	480	480
q12	830	621	574	574
q13	7445	3110	3140	3110
q14	303	287	271	271
q15	513	463	447	447
q16	679	642	641	641
q17	1845	1627	1602	1602
q18	8291	7842	7622	7622
q19	1719	1625	1570	1570
q20	2093	1892	1916	1892
q21	5554	5052	5241	5052
q22	1104	987	974	974
Total cold run time: 66905 ms
Total hot run time: 59212 ms

[doris-robot]

TPC-DS: Total hot run time: 190653 ms

machine: 'aliyun_ecs.c7a.8xlarge_32C64G'
scripts: https://github.com/apache/doris/tree/master/tools/tpcds-tools
TPC-DS sf100 test result on commit de9f040a5bb3bcad0e4bd9f3b89fd7cd66e826ac, data reload: false
query1	998	376	371	371
query2	6513	2003	1968	1968
query3	6713	216	220	216
query4	33945	23517	23434	23434
query5	4354	467	438	438
query6	278	182	168	168
query7	4616	318	305	305
query8	270	217	212	212
query9	9596	2610	2595	2595
query10	481	268	263	263
query11	18502	15160	15441	15160
query12	155	102	101	101
query13	1652	440	431	431
query14	9249	6632	6521	6521
query15	234	171	182	171
query16	8057	486	406	406
query17	1650	591	548	548
query18	2109	298	307	298
query19	202	158	147	147
query20	120	103	106	103
query21	204	99	98	98
query22	4426	4340	4304	4304
query23	34371	33282	33562	33282
query24	12767	2871	2952	2871
query25	733	389	399	389
query26	1896	169	169	169
query27	3019	347	333	333
query28	7841	2420	2395	2395
query29	1044	436	427	427
query30	327	171	161	161
query31	1028	800	807	800
query32	97	57	58	57
query33	778	275	283	275
query34	1027	492	536	492
query35	868	713	712	712
query36	1097	938	938	938
query37	173	73	70	70
query38	3954	3793	3796	3793
query39	1476	1438	1446	1438
query40	293	101	100	100
query41	53	51	50	50
query42	118	103	101	101
query43	521	476	480	476
query44	1278	790	793	790
query45	188	171	168	168
query46	1157	757	742	742
query47	1960	1806	1859	1806
query48	481	376	389	376
query49	1307	420	411	411
query50	825	423	427	423
query51	7329	7021	7150	7021
query52	108	99	97	97
query53	273	193	188	188
query54	1226	475	472	472
query55	81	77	80	77
query56	273	255	259	255
query57	1257	1118	1074	1074
query58	233	211	213	211
query59	3072	2871	2800	2800
query60	275	254	256	254
query61	114	107	128	107
query62	865	654	657	654
query63	223	195	190	190
query64	5233	668	651	651
query65	3302	3192	3193	3192
query66	1419	322	304	304
query67	15718	15758	15697	15697
query68	3522	591	583	583
query69	398	262	271	262
query70	1171	1141	1084	1084
query71	325	261	252	252
query72	6120	4256	4200	4200
query73	765	353	356	353
query74	9967	9399	9209	9209
query75	3345	2656	2689	2656
query76	1980	1068	1067	1067
query77	386	305	285	285
query78	10397	9687	9584	9584
query79	1187	600	585	585
query80	870	475	462	462
query81	540	242	238	238
query82	1261	94	95	94
query83	211	154	157	154
query84	251	86	96	86
query85	1192	361	371	361
query86	325	302	285	285
query87	4403	4310	4226	4226
query88	3430	2404	2384	2384
query89	405	295	296	295
query90	2157	187	186	186
query91	188	147	152	147
query92	61	50	54	50
query93	1088	554	542	542
query94	827	294	308	294
query95	363	264	259	259
query96	606	286	284	284
query97	3328	3158	3163	3158
query98	213	208	202	202
query99	1522	1352	1279	1279
Total cold run time: 298806 ms
Total hot run time: 190653 ms

[doris-robot]

ClickBench: Total hot run time: 32.16 s

machine: 'aliyun_ecs.c7a.8xlarge_32C64G'
scripts: https://github.com/apache/doris/tree/master/tools/clickbench-tools
ClickBench test result on commit de9f040a5bb3bcad0e4bd9f3b89fd7cd66e826ac, data reload: false
query1	0.04	0.03	0.03
query2	0.07	0.03	0.03
query3	0.23	0.06	0.06
query4	1.62	0.10	0.10
query5	0.51	0.51	0.54
query6	1.14	0.73	0.73
query7	0.02	0.02	0.01
query8	0.04	0.03	0.04
query9	0.57	0.49	0.50
query10	0.57	0.55	0.56
query11	0.14	0.11	0.10
query12	0.13	0.11	0.12
query13	0.61	0.59	0.59
query14	2.73	2.82	2.75
query15	0.91	0.83	0.82
query16	0.39	0.40	0.38
query17	0.99	1.03	1.03
query18	0.25	0.22	0.21
query19	1.85	1.89	2.00
query20	0.01	0.01	0.02
query21	15.35	0.59	0.58
query22	2.71	2.78	1.86
query23	16.97	1.02	0.88
query24	2.76	0.70	1.48
query25	0.16	0.31	0.12
query26	0.38	0.14	0.13
query27	0.04	0.05	0.04
query28	10.51	0.50	0.46
query29	12.58	3.30	3.30
query30	0.24	0.06	0.06
query31	2.86	0.38	0.39
query32	3.22	0.46	0.47
query33	2.97	3.03	3.01
query34	17.20	4.46	4.49
query35	4.50	4.50	4.54
query36	0.68	0.50	0.48
query37	0.09	0.06	0.07
query38	0.05	0.04	0.04
query39	0.03	0.02	0.03
query40	0.16	0.12	0.12
query41	0.07	0.02	0.02
query42	0.04	0.02	0.02
query43	0.04	0.03	0.03
Total cold run time: 106.43 s
Total hot run time: 32.16 s

[Mryange]

run buildall

[Mryange]

run feut

[hello-stephen]

BE UT Coverage Report

Increment line coverage 3.33% (4/120) 🎉

Increment coverage report
Complete coverage report

Category	Coverage
Function Coverage	40.21% (10557/26257)
Line Coverage	30.98% (89300/288288)
Region Coverage	30.11% (46069/152990)
Branch Coverage	26.61% (23546/88470)

[Mryange]

run feut

[dataroaring]

LGTM

[github-actions]

PR approved by at least one committer and no changes requested.

[github-actions]

PR approved by anyone and no changes requested.