From f8fa079d8c157dc44817be48824fdff09fb6b59a Mon Sep 17 00:00:00 2001
From: Teodor Sigaev <teodor@sigaev.ru>
Date: Thu, 20 Feb 2025 19:00:02 +0300
Subject: [PATCH] Estimate the selectivity as quadratic mean of non-null
 fraction divided by number of distinct values and set of MCV selectivities.
 Use quadratic mean because it includes the squared deviation (error) as well
 and here it would be nice to compute upper limit of estimation to prevent
 wrong choose of nested loop, for example.

---
 src/backend/utils/adt/selfuncs.c | 43 +++++++++++++++++++++-----------
 1 file changed, 29 insertions(+), 14 deletions(-)

diff --git a/src/backend/utils/adt/selfuncs.c b/src/backend/utils/adt/selfuncs.c
index 5b35debc8ffd..fb4fb65b84e6 100644
--- a/src/backend/utils/adt/selfuncs.c
+++ b/src/backend/utils/adt/selfuncs.c
@@ -501,29 +501,44 @@ var_eq_non_const(VariableStatData *vardata, Oid oproid, Oid collation,
 
 		/*
 		 * Search is for a value that we do not know a priori, but we will
-		 * assume it is not NULL.  Estimate the selectivity as non-null
-		 * fraction divided by number of distinct values, so that we get a
-		 * result averaged over all possible values whether common or
-		 * uncommon.  (Essentially, we are assuming that the not-yet-known
-		 * comparison value is equally likely to be any of the possible
-		 * values, regardless of their frequency in the table.  Is that a good
-		 * idea?)
+		 * assume it is not NULL.  Estimate the selectivity as quadratic mean of
+		 * non-null fraction divided by number of distinct values and set of MCV
+		 * selectivities. Use quadratic mean because it includes the squared
+		 * deviation (error) as well and here it would be nice to compute upper
+		 * limit of estimation to prevent wrong choose of nested loop, for
+		 * example.
 		 */
 		selec = 1.0 - nullfrac;
 		ndistinct = get_variable_numdistinct(vardata, &isdefault);
 		if (ndistinct > 1)
 			selec /= ndistinct;
 
-		/*
-		 * Cross-check: selectivity should never be estimated as more than the
-		 * most common value's.
-		 */
 		if (get_attstatsslot(&sslot, vardata->statsTuple,
 							 STATISTIC_KIND_MCV, InvalidOid,
-							 ATTSTATSSLOT_NUMBERS))
+							 ATTSTATSSLOT_VALUES | ATTSTATSSLOT_NUMBERS))
 		{
-			if (sslot.nnumbers > 0 && selec > sslot.numbers[0])
-				selec = sslot.numbers[0];
+			int i;
+			double sum_selec = 0.0;
+
+			/*
+			 * Compute quadratic mean, walk on array in reverse direction to
+			 * do not lose accuracy. We don't bother about sslot.nnumbers
+			 * equality to zero, because in this case we just get the same
+			 * result. But equality to zero is unlikely.
+			 */
+			for(i=sslot.nnumbers - 1; i>=0; i--)
+				sum_selec += sslot.numbers[i] * sslot.numbers[i];
+
+			selec = sqrt((selec * selec + sum_selec) /
+						 ((double)sslot.nnumbers + 1.0));
+
+			/*
+			 * Cross-check: selectivity should never be estimated as
+			 * more than the most common value's.
+			 */
+			 if (sslot.nnumbers > 0 && selec > sslot.numbers[0])
+					selec = sslot.numbers[0];
+
 			free_attstatsslot(&sslot);
 		}
 	}