Added comments; added test [#CLICKHOUSE-2].

dbms/src/AggregateFunctions/AggregateFunctionStatisticsSimple.h

@@ -10,6 +10,18 @@
 #include <DataTypes/DataTypesNumber.h>
 
 
+/** This is simple, not numerically stable
+  *  implementations of variance/covariance/correlation functions.
+  *
+  * It is about two times faster than stable variants.
+  * Numerical errors may occur during summation.
+  *
+  * This implementation is selected as default,
+  *  because "you don't pay for what you don't need" principle.
+  *
+  * For more sophisticated implementation, look at AggregateFunctionStatistics.h
+  */
+
 namespace DB
 {
 

dbms/tests/queries/0_stateless/00181_aggregate_functions_statistics_stable.reference

+inf
+0
+inf
+0
+0
+0
+0
+0
+inf
+0
+0
+0
+inf
+0

dbms/tests/queries/0_stateless/00181_aggregate_functions_statistics_stable.sql

+DROP TABLE IF EXISTS test.series;
+
+CREATE TABLE test.series(i UInt32, x_value Float64, y_value Float64) ENGINE = Memory;
+
+INSERT INTO test.series(i, x_value, y_value) VALUES (1, 5.6,-4.4),(2, -9.6,3),(3, -1.3,-4),(4, 5.3,9.7),(5, 4.4,0.037),(6, -8.6,-7.8),(7, 5.1,9.3),(8, 7.9,-3.6),(9, -8.2,0.62),(10, -3,7.3);
+
+/* varSampStable */
+
+SELECT varSampStable(x_value) FROM (SELECT x_value FROM test.series LIMIT 0);
+SELECT varSampStable(x_value) FROM (SELECT x_value FROM test.series LIMIT 1);
+
+SELECT round(abs(res1 - res2), 6) FROM
+(
+SELECT
+    varSampStable(x_value) AS res1,
+    (sum(x_value * x_value) - ((sum(x_value) * sum(x_value)) / count())) / (count() - 1) AS res2
+FROM test.series
+);
+
+/* stddevSampStable */
+
+SELECT stddevSampStable(x_value) FROM (SELECT x_value FROM test.series LIMIT 0);
+SELECT stddevSampStable(x_value) FROM (SELECT x_value FROM test.series LIMIT 1);
+
+SELECT round(abs(res1 - res2), 6) FROM
+(
+SELECT
+    stddevSampStable(x_value) AS res1,
+    sqrt((sum(x_value * x_value) - ((sum(x_value) * sum(x_value)) / count())) / (count() - 1)) AS res2
+FROM test.series
+);
+
+/* varPopStable */
+
+SELECT varPopStable(x_value) FROM (SELECT x_value FROM test.series LIMIT 0);
+SELECT varPopStable(x_value) FROM (SELECT x_value FROM test.series LIMIT 1);
+
+SELECT round(abs(res1 - res2), 6) FROM
+(
+SELECT
+    varPopStable(x_value) AS res1,
+    (sum(x_value * x_value) - ((sum(x_value) * sum(x_value)) / count())) / count() AS res2
+FROM test.series
+);
+
+/* stddevPopStable */
+
+SELECT stddevPopStable(x_value) FROM (SELECT x_value FROM test.series LIMIT 0);
+SELECT stddevPopStable(x_value) FROM (SELECT x_value FROM test.series LIMIT 1);
+
+SELECT round(abs(res1 - res2), 6) FROM
+(
+SELECT
+    stddevPopStable(x_value) AS res1,
+    sqrt((sum(x_value * x_value) - ((sum(x_value) * sum(x_value)) / count())) / count()) AS res2
+FROM test.series
+);
+
+/* covarSampStable */
+
+SELECT covarSampStable(x_value, y_value) FROM (SELECT x_value, y_value FROM test.series LIMIT 0);
+SELECT covarSampStable(x_value, y_value) FROM (SELECT x_value, y_value FROM test.series LIMIT 1);
+
+SELECT round(abs(COVAR1 - COVAR2), 6)
+FROM
+(
+    SELECT
+        arrayJoin([1]) AS ID2,
+        covarSampStable(x_value, y_value) AS COVAR1
+    FROM test.series
+) ANY INNER JOIN
+(
+    SELECT
+        arrayJoin([1]) AS ID2,
+        sum(VAL) / (count() - 1) AS COVAR2
+    FROM
+    (
+        SELECT (X - AVG_X) * (Y - AVG_Y) AS VAL
+        FROM
+        (
+            SELECT
+                toUInt32(arrayJoin([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])) AS ID,
+                avg(x_value) AS AVG_X,
+                avg(y_value) AS AVG_Y
+            FROM test.series
+        ) ANY INNER JOIN
+        (
+            SELECT
+                i AS ID,
+                x_value AS X,
+                y_value AS Y
+            FROM test.series
+        ) USING ID
+    )
+) USING ID2;
+
+/* covarPopStable */
+
+SELECT covarPopStable(x_value, y_value) FROM (SELECT x_value, y_value FROM test.series LIMIT 0);
+SELECT covarPopStable(x_value, y_value) FROM (SELECT x_value, y_value FROM test.series LIMIT 1);
+
+SELECT round(abs(COVAR1 - COVAR2), 6)
+FROM
+(
+    SELECT
+        arrayJoin([1]) AS ID2,
+        covarPopStable(x_value, y_value) AS COVAR1
+    FROM test.series
+) ANY INNER JOIN
+(
+    SELECT
+        arrayJoin([1]) AS ID2,
+        sum(VAL) / count() AS COVAR2
+    FROM
+    (
+        SELECT (X - AVG_X) * (Y - AVG_Y) AS VAL
+        FROM
+        (
+            SELECT
+                toUInt32(arrayJoin([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])) AS ID,
+                avg(x_value) AS AVG_X,
+                avg(y_value) AS AVG_Y
+            FROM test.series
+        ) ANY INNER JOIN
+        (
+            SELECT
+                i AS ID,
+                x_value AS X,
+                y_value AS Y
+            FROM test.series
+        ) USING ID
+    )
+) USING ID2;
+
+/* corr */
+
+SELECT corrStable(x_value, y_value) FROM (SELECT x_value, y_value FROM test.series LIMIT 0);
+SELECT corrStable(x_value, y_value) FROM (SELECT x_value, y_value FROM test.series LIMIT 1);
+
+SELECT round(abs(corrStable(x_value, y_value) - covarPopStable(x_value, y_value) / (stddevPopStable(x_value) * stddevPopStable(y_value))), 6) FROM test.series;
+
+DROP TABLE test.series;