{"action":"created","comment":{"url":"https://api.github.com/repos/pingcap/tidb/pulls/comments/236965217","pull_request_review_id":179151600,"id":236965217,"node_id":"MDI0OlB1bGxSZXF1ZXN0UmV2aWV3Q29tbWVudDIzNjk2NTIxNw==","diff_hunk":"@@ -0,0 +1,187 @@\n+// Copyright 2018 PingCAP, Inc.\n+//\n+// Licensed under the Apache License, Version 2.0 (the \"License\");\n+// you may not use this file except in compliance with the License.\n+// You may obtain a copy of the License at\n+//\n+//     http://www.apache.org/licenses/LICENSE-2.0\n+//\n+// Unless required by applicable law or agreed to in writing, software\n+// distributed under the License is distributed on an \"AS IS\" BASIS,\n+// See the License for the specific language governing permissions and\n+// limitations under the License.\n+\n+package aggfuncs\n+\n+import (\n+\t\"github.com/pingcap/errors\"\n+\t\"github.com/pingcap/tidb/sessionctx\"\n+\t\"github.com/pingcap/tidb/types\"\n+\t\"github.com/pingcap/tidb/util/chunk\"\n+\t\"github.com/pingcap/tidb/util/set\"\n+)\n+\n+// varianceKind stands for kind of population standard deviation/sample variance aggregate functions.\n+type varianceKind int\n+\n+const (\n+\tkindNone varianceKind = iota\n+\tkindVarPop\n+\tkindVarSamp\n+\tkindStdPop\n+\tkinkStdSamp\n+)\n+\n+// All the following function implementations return the float64 result,\n+// which store the partial results in \"partialResult4VarianceFloat64\".\n+//\n+// \"baseVarianceFloat64\" is wrapped by:\n+// - \"varianceOriginal4Float64\"\n+// - \"variancePartial4Float64\"\n+type baseVarianceFloat64 struct {\n+\tbaseAggFunc\n+\tvarianceKind\n+}\n+\n+type partialResult4VarianceFloat64 struct {\n+\tcount    int64\n+\tsum      float64\n+\tvariance float64 // $$\\sum_{k=i}^{j}{(a_k-avg_{ij})^2}$$ (this is actually n times the variance)","path":"executor/aggfuncs/func_variance.go","position":49,"original_position":49,"commit_id":"ce8f27b9dbf640fca5aef584610cdc72b677db5f","original_commit_id":"ce8f27b9dbf640fca5aef584610cdc72b677db5f","user":{"login":"zz-jason","id":5268763,"node_id":"MDQ6VXNlcjUyNjg3NjM=","avatar_url":"https://avatars0.githubusercontent.com/u/5268763?v=4","gravatar_id":"","url":"https://api.github.com/users/zz-jason","html_url":"https://github.com/zz-jason","followers_url":"https://api.github.com/users/zz-jason/followers","following_url":"https://api.github.com/users/zz-jason/following{/other_user}","gists_url":"https://api.github.com/users/zz-jason/gists{/gist_id}","starred_url":"https://api.github.com/users/zz-jason/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/zz-jason/subscriptions","organizations_url":"https://api.github.com/users/zz-jason/orgs","repos_url":"https://api.github.com/users/zz-jason/repos","events_url":"https://api.github.com/users/zz-jason/events{/privacy}","received_events_url":"https://api.github.com/users/zz-jason/received_events","type":"User","site_admin":false},"body":"Uh.. How about use the normal form to express the math formula? For example:\r\n```\r\nsum((a[i]-avg)^2)\r\n```","created_at":"2018-11-28T07:26:27Z","updated_at":"2018-11-28T07:51:59Z","html_url":"https://github.com/pingcap/tidb/pull/7718#discussion_r236965217","pull_request_url":"https://api.github.com/repos/pingcap/tidb/pulls/7718","author_association":"MEMBER","_links":{"self":{"href":"https://api.github.com/repos/pingcap/tidb/pulls/comments/236965217"},"html":{"href":"https://github.com/pingcap/tidb/pull/7718#discussion_r236965217"},"pull_request":{"href":"https://api.github.com/repos/pingcap/tidb/pulls/7718"}}},"pull_request":{"url":"https://api.github.com/repos/pingcap/tidb/pulls/7718","id":215825597,"node_id":"MDExOlB1bGxSZXF1ZXN0MjE1ODI1NTk3","html_url":"https://github.com/pingcap/tidb/pull/7718","diff_url":"https://github.com/pingcap/tidb/pull/7718.diff","patch_url":"https://github.com/pingcap/tidb/pull/7718.patch","issue_url":"https://api.github.com/repos/pingcap/tidb/issues/7718","number":7718,"state":"open","locked":false,"title":" expression: support agg function var_pop","user":{"login":"mccxj","id":98360,"node_id":"MDQ6VXNlcjk4MzYw","avatar_url":"https://avatars0.githubusercontent.com/u/98360?v=4","gravatar_id":"","url":"https://api.github.com/users/mccxj","html_url":"https://github.com/mccxj","followers_url":"https://api.github.com/users/mccxj/followers","following_url":"https://api.github.com/users/mccxj/following{/other_user}","gists_url":"https://api.github.com/users/mccxj/gists{/gist_id}","starred_url":"https://api.github.com/users/mccxj/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/mccxj/subscriptions","organizations_url":"https://api.github.com/users/mccxj/orgs","repos_url":"https://api.github.com/users/mccxj/repos","events_url":"https://api.github.com/users/mccxj/events{/privacy}","received_events_url":"https://api.github.com/users/mccxj/received_events","type":"User","site_admin":false},"body":"### What problem does this PR solve? <!--add issue link with summary if exists-->\r\n\r\nSee https://github.com/pingcap/tidb/issues/7623\r\n\r\nPR for parser https://github.com/pingcap/parser/pull/53\r\n\r\nPR for tikv https://github.com/tikv/tikv/pull/3835\r\n\r\n### What is changed and how it works?\r\n\r\n```\r\nmysql> create table t(a int(11), b float, c double, d decimal(6,2));\r\nQuery OK, 0 rows affected (0.01 sec)\r\n\r\nmysql> select var_pop(a), var_pop(b), var_pop(c), var_pop(d) from t;\r\n+------------+------------+------------+------------+\r\n| var_pop(a) | var_pop(b) | var_pop(c) | var_pop(d) |\r\n+------------+------------+------------+------------+\r\n|       NULL |       NULL |       NULL |       NULL |\r\n+------------+------------+------------+------------+\r\n1 row in set (0.00 sec)\r\n\r\nmysql> insert into t values(1, 2.5, 3.5, 6.25), (2, 3.5, 4.5, 8.55);\r\nQuery OK, 2 rows affected (0.00 sec)\r\n\r\nmysql> select var_pop(a), var_pop(b), var_pop(c), var_pop(d) from t;\r\n+------------+------------+------------+------------+\r\n| var_pop(a) | var_pop(b) | var_pop(c) | var_pop(d) |\r\n+------------+------------+------------+------------+\r\n|       0.25 |       0.25 |       0.25 |       1.32 |\r\n+------------+------------+------------+------------+\r\n1 row in set (0.01 sec)\r\n\r\nmysql> select var_pop(a), var_pop(b), variance(a), variance(b) from t;\r\n+------------+------------+-------------+-------------+\r\n| var_pop(a) | var_pop(b) | variance(a) | variance(b) |\r\n+------------+------------+-------------+-------------+\r\n|       0.25 |       0.25 |        0.25 |        0.25 |\r\n+------------+------------+-------------+-------------+\r\n1 row in set (0.01 sec)\r\n\r\nmysql> select var_pop(a), var_pop(b), var_pop(c), var_pop(d) from t group by a;\r\n+------------+------------+------------+------------+\r\n| var_pop(a) | var_pop(b) | var_pop(c) | var_pop(d) |\r\n+------------+------------+------------+------------+\r\n|          0 |          0 |          0 |       0.00 |\r\n|          0 |          0 |          0 |       0.00 |\r\n+------------+------------+------------+------------+\r\n2 rows in set (0.00 sec)\r\n\r\nmysql> insert into t values(1, 3.5, 4.5, 5.25);\r\nQuery OK, 1 row affected (0.00 sec)\r\n\r\n-- run with --column-type-info\r\nmysql> select a, var_pop(a), var_pop(b), var_pop(c), var_pop(d) from t group by a;\r\nField   1:  `a`\r\nCatalog:    `def`\r\nDatabase:   `test`\r\nTable:      `t`\r\nOrg_table:  `t`\r\nType:       LONG\r\nCollation:  binary (63)\r\nLength:     11\r\nMax_length: 1\r\nDecimals:   0\r\nFlags:      NUM \r\n\r\nField   2:  `var_pop(a)`\r\nCatalog:    `def`\r\nDatabase:   ``\r\nTable:      ``\r\nOrg_table:  ``\r\nType:       DOUBLE\r\nCollation:  binary (63)\r\nLength:     23\r\nMax_length: 1\r\nDecimals:   0\r\nFlags:      BINARY NUM \r\n\r\nField   3:  `var_pop(b)`\r\nCatalog:    `def`\r\nDatabase:   ``\r\nTable:      ``\r\nOrg_table:  ``\r\nType:       DOUBLE\r\nCollation:  binary (63)\r\nLength:     23\r\nMax_length: 4\r\nDecimals:   31\r\nFlags:      BINARY NUM \r\n\r\nField   4:  `var_pop(c)`\r\nCatalog:    `def`\r\nDatabase:   ``\r\nTable:      ``\r\nOrg_table:  ``\r\nType:       DOUBLE\r\nCollation:  binary (63)\r\nLength:     23\r\nMax_length: 4\r\nDecimals:   31\r\nFlags:      BINARY NUM \r\n\r\nField   5:  `var_pop(d)`\r\nCatalog:    `def`\r\nDatabase:   ``\r\nTable:      ``\r\nOrg_table:  ``\r\nType:       DOUBLE\r\nCollation:  binary (63)\r\nLength:     23\r\nMax_length: 4\r\nDecimals:   2\r\nFlags:      BINARY NUM \r\n\r\n\r\n+------+------------+------------+------------+------------+\r\n| a    | var_pop(a) | var_pop(b) | var_pop(c) | var_pop(d) |\r\n+------+------------+------------+------------+------------+\r\n|    2 |          0 |          0 |          0 |       0.00 |\r\n|    1 |          0 |       0.25 |       0.25 |       0.25 |\r\n+------+------------+------------+------------+------------+\r\n2 rows in set (0.00 sec)\r\n\r\n```\r\n\r\n### Check List <!--REMOVE the items that are not applicable-->\r\n\r\nTests 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