MDEV-31067: selectivity_from_histogram >1.0 for a DOUBLE_PREC_HB histogrambb-10.4-mdev31067-variant2

Variant #2.

When Histogram::point_selectivity() sees that the point value of interest
falls into one bucket, it tries to guess whether the bucket has many
different (unpopular) values or a few popular values. (The number of
rows is fixed, as it's a Height-balanced histogram).
The basis for this guess is the "width" of the value range the bucket
covers. Buckets covering wider value ranges are assumed to contain
values with proportionally lower frequencies.

This is just a [brave] guesswork. For a very narrow bucket, it may
produce an estimate that's larger than total #rows in the bucket
or even in the whole table.

Remove the guesswork and replace it with basic logic: return
either the per-table average selectivity of col=const, or selectivity
of one bucket, whichever is lower.

5 files changed, 234 insertions, 53 deletions

diff --git a/mysql-test/main/selectivity.result b/mysql-test/main/selectivity.result
index 0b922609916..7d7343847cd 100644
--- a/mysql-test/main/selectivity.result
+++ b/mysql-test/main/selectivity.result
@@ -834,7 +834,7 @@ flush table t1;
 set optimizer_use_condition_selectivity=4;
 explain extended select * from t1 where a=0;
 id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
-1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	1025	0.39	Using where
+1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	1025	0.78	Using where
 Warnings:
 Note	1003	select `test`.`t1`.`a` AS `a` from `test`.`t1` where `test`.`t1`.`a` = 0
 drop table t1;
@@ -1649,7 +1649,7 @@ test.t1	analyze	status	Table is already up to date
 # Check what info the optimizer has about selectivities
 explain extended select * from t1 use index () where a in (17,51,5);
 id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
-1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	1000	3.90	Using where
+1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	1000	3.91	Using where
 Warnings:
 Note	1003	select `test`.`t1`.`a` AS `a`,`test`.`t1`.`b` AS `b` from `test`.`t1` USE INDEX () where `test`.`t1`.`a` in (17,51,5)
 explain extended select * from t1 use index () where b=2;
@@ -1935,9 +1935,78 @@ id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
 1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	5	25.00	Using where
 Warnings:
 Note	1003	select `test`.`t1`.`a` AS `a` from `test`.`t1` where `test`.`t1`.`a` = 2
+DROP TABLE t1;
+# End of 10.2 tests
+#
+# MDEV-31067: selectivity_from_histogram >1.0 for a DOUBLE_PREC_HB histogram
+#
+create table t0(a int);
+insert into t0 select 1 from seq_1_to_78;
+create table t1(a int);
+insert into t1 select 1 from seq_1_to_26;
+create table t10 (a int);
+insert into t10 select 0 from t0, seq_1_to_4;
+insert into t10 select 8693 from t1;
+insert into t10 select 8694 from t1;
+insert into t10 select 8695 from t1;
+insert into t10 select 34783 from t1;
+insert into t10 select 34784 from t1;
+insert into t10 select 34785 from t1;
+insert into t10 select 34785 from t0, seq_1_to_8;
+insert into t10 select 65214 from t1;
+insert into t10 select 65215 from t1;
+insert into t10 select 65216 from t1;
+insert into t10 select 65216 from t0, seq_1_to_52;
+insert into t10 select 65217 from t1;
+insert into t10 select 65218 from t1;
+insert into t10 select 65219 from t1;
+insert into t10 select 65219 from t0;
+insert into t10 select 73913 from t1;
+insert into t10 select 73914 from t1;
+insert into t10 select 73915 from t1;
+insert into t10 select 73915 from t0, seq_1_to_40;
+insert into t10 select 78257 from t1;
+insert into t10 select 78258 from t1;
+insert into t10 select 78259 from t1;
+insert into t10 select 91300 from t1;
+insert into t10 select 91301 from t1;
+insert into t10 select 91302 from t1;
+insert into t10 select 91302 from t0, seq_1_to_6;
+insert into t10 select 91303 from t1;
+insert into t10 select 91304 from t1;
+insert into t10 select 91305 from t1;
+insert into t10 select 91305 from t0, seq_1_to_8;
+insert into t10 select  99998 from t1;
+insert into t10 select  99999 from t1;
+insert into t10 select 100000 from t1;
+set use_stat_tables=preferably;
+analyze table t10 persistent for all;
+Table	Op	Msg_type	Msg_text
+test.t10	analyze	status	Engine-independent statistics collected
+test.t10	analyze	status	OK
+flush tables;
+set @tmp=@@optimizer_trace;
+set optimizer_trace=1;
+explain select * from t10  where a in (91303);
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	SIMPLE	t10	ALL	NULL	NULL	NULL	NULL	9984	Using where
+# Must have selectivity_from_histogram <= 1.0:
+select json_detailed(json_extract(trace, '$**.selectivity_for_columns')) 
+from information_schema.optimizer_trace;
+json_detailed(json_extract(trace, '$**.selectivity_for_columns'))
+[
+    [
+        {
+            "column_name": "a",
+            "ranges": 
+            ["91303 <= a <= 91303"],
+            "selectivity_from_histogram": 0.0357
+        }
+    ]
+]
+set optimizer_trace=@tmp;
+drop table t0,t1,t10;
 set optimizer_use_condition_selectivity= @save_optimizer_use_condition_selectivity;
 set histogram_size=@save_histogram_size;
 set use_stat_tables= @save_use_stat_tables;
-DROP TABLE t1;
-# End of 10.2 tests
 set @@global.histogram_size=@save_histogram_size;
diff --git a/mysql-test/main/selectivity.test b/mysql-test/main/selectivity.test
index 9c82a8d37a7..06a3e32da95 100644
--- a/mysql-test/main/selectivity.test
+++ b/mysql-test/main/selectivity.test
@@ -1319,14 +1319,93 @@ EXPLAIN EXTENDED SELECT * FROM t1 WHERE a=2;
 FLUSH TABLES;
 
 EXPLAIN EXTENDED SELECT * FROM t1 WHERE a=2;
-set optimizer_use_condition_selectivity= @save_optimizer_use_condition_selectivity;
-set histogram_size=@save_histogram_size;
-set use_stat_tables= @save_use_stat_tables;
 
 DROP TABLE t1;
 
 --echo # End of 10.2 tests
 
+--echo #
+--echo # MDEV-31067: selectivity_from_histogram >1.0 for a DOUBLE_PREC_HB histogram
+--echo #
+create table t0(a int);  # This holds how many rows we hold in a bucket.
+insert into t0 select 1 from seq_1_to_78;
+
+create table t1(a int);  # one-third of a bucket
+insert into t1 select 1 from seq_1_to_26;
+
+create table t10 (a int);
+insert into t10 select 0 from t0, seq_1_to_4;
+
+insert into t10 select 8693 from t1;
+insert into t10 select 8694 from t1;
+insert into t10 select 8695 from t1;
+
+
+insert into t10 select 34783 from t1;
+insert into t10 select 34784 from t1;
+insert into t10 select 34785 from t1;
+
+
+insert into t10 select 34785 from t0, seq_1_to_8;
+
+insert into t10 select 65214 from t1;
+insert into t10 select 65215 from t1;
+insert into t10 select 65216 from t1;
+
+insert into t10 select 65216 from t0, seq_1_to_52;
+
+insert into t10 select 65217 from t1;
+insert into t10 select 65218 from t1;
+insert into t10 select 65219 from t1;
+
+insert into t10 select 65219 from t0;
+
+
+insert into t10 select 73913 from t1;
+insert into t10 select 73914 from t1;
+insert into t10 select 73915 from t1;
+
+insert into t10 select 73915 from t0, seq_1_to_40;
+
+
+insert into t10 select 78257 from t1;
+insert into t10 select 78258 from t1;
+insert into t10 select 78259 from t1;
+
+insert into t10 select 91300 from t1;
+insert into t10 select 91301 from t1;
+insert into t10 select 91302 from t1;
+
+insert into t10 select 91302 from t0, seq_1_to_6;
+
+insert into t10 select 91303 from t1; # Only 1/3rd of bucket matches the search tuple
+insert into t10 select 91304 from t1;
+insert into t10 select 91305 from t1;
+
+insert into t10 select 91305 from t0, seq_1_to_8;
+
+insert into t10 select  99998 from t1;
+insert into t10 select  99999 from t1;
+insert into t10 select 100000 from t1;
+
+set use_stat_tables=preferably;
+analyze table t10 persistent for all;
+flush tables;
+
+set @tmp=@@optimizer_trace;
+set optimizer_trace=1;
+explain select * from t10  where a in (91303);
+
+--echo # Must have selectivity_from_histogram <= 1.0:
+select json_detailed(json_extract(trace, '$**.selectivity_for_columns')) 
+from information_schema.optimizer_trace;
+
+set optimizer_trace=@tmp;
+drop table t0,t1,t10;
+
+set optimizer_use_condition_selectivity= @save_optimizer_use_condition_selectivity;
+set histogram_size=@save_histogram_size;
+set use_stat_tables= @save_use_stat_tables;
 #
 # Clean up
 #
diff --git a/mysql-test/main/selectivity_innodb.result b/mysql-test/main/selectivity_innodb.result
index 4ee2da02ec6..dfba12f2b05 100644
--- a/mysql-test/main/selectivity_innodb.result
+++ b/mysql-test/main/selectivity_innodb.result
@@ -843,7 +843,7 @@ flush table t1;
 set optimizer_use_condition_selectivity=4;
 explain extended select * from t1 where a=0;
 id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
-1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	1025	0.39	Using where
+1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	1025	0.78	Using where
 Warnings:
 Note	1003	select `test`.`t1`.`a` AS `a` from `test`.`t1` where `test`.`t1`.`a` = 0
 drop table t1;
@@ -1659,7 +1659,7 @@ test.t1	analyze	status	OK
 # Check what info the optimizer has about selectivities
 explain extended select * from t1 use index () where a in (17,51,5);
 id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
-1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	1000	3.90	Using where
+1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	1000	3.91	Using where
 Warnings:
 Note	1003	select `test`.`t1`.`a` AS `a`,`test`.`t1`.`b` AS `b` from `test`.`t1` USE INDEX () where `test`.`t1`.`a` in (17,51,5)
 explain extended select * from t1 use index () where b=2;
@@ -1945,11 +1945,78 @@ id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
 1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	5	25.00	Using where
 Warnings:
 Note	1003	select `test`.`t1`.`a` AS `a` from `test`.`t1` where `test`.`t1`.`a` = 2
+DROP TABLE t1;
+# End of 10.2 tests
+#
+# MDEV-31067: selectivity_from_histogram >1.0 for a DOUBLE_PREC_HB histogram
+#
+create table t0(a int);
+insert into t0 select 1 from seq_1_to_78;
+create table t1(a int);
+insert into t1 select 1 from seq_1_to_26;
+create table t10 (a int);
+insert into t10 select 0 from t0, seq_1_to_4;
+insert into t10 select 8693 from t1;
+insert into t10 select 8694 from t1;
+insert into t10 select 8695 from t1;
+insert into t10 select 34783 from t1;
+insert into t10 select 34784 from t1;
+insert into t10 select 34785 from t1;
+insert into t10 select 34785 from t0, seq_1_to_8;
+insert into t10 select 65214 from t1;
+insert into t10 select 65215 from t1;
+insert into t10 select 65216 from t1;
+insert into t10 select 65216 from t0, seq_1_to_52;
+insert into t10 select 65217 from t1;
+insert into t10 select 65218 from t1;
+insert into t10 select 65219 from t1;
+insert into t10 select 65219 from t0;
+insert into t10 select 73913 from t1;
+insert into t10 select 73914 from t1;
+insert into t10 select 73915 from t1;
+insert into t10 select 73915 from t0, seq_1_to_40;
+insert into t10 select 78257 from t1;
+insert into t10 select 78258 from t1;
+insert into t10 select 78259 from t1;
+insert into t10 select 91300 from t1;
+insert into t10 select 91301 from t1;
+insert into t10 select 91302 from t1;
+insert into t10 select 91302 from t0, seq_1_to_6;
+insert into t10 select 91303 from t1;
+insert into t10 select 91304 from t1;
+insert into t10 select 91305 from t1;
+insert into t10 select 91305 from t0, seq_1_to_8;
+insert into t10 select  99998 from t1;
+insert into t10 select  99999 from t1;
+insert into t10 select 100000 from t1;
+set use_stat_tables=preferably;
+analyze table t10 persistent for all;
+Table	Op	Msg_type	Msg_text
+test.t10	analyze	status	Engine-independent statistics collected
+test.t10	analyze	status	OK
+flush tables;
+set statement optimizer_trace=1 for
+explain select * from t10  where a in (91303);
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	SIMPLE	t10	ALL	NULL	NULL	NULL	NULL	9984	Using where
+# Must have selectivity_from_histogram <= 1.0:
+select json_detailed(json_extract(trace, '$**.selectivity_for_columns')) 
+from information_schema.optimizer_trace;
+json_detailed(json_extract(trace, '$**.selectivity_for_columns'))
+[
+    [
+        {
+            "column_name": "a",
+            "ranges": 
+            ["91303 <= a <= 91303"],
+            "selectivity_from_histogram": 0.035714283
+        }
+    ]
+]
+drop table t0,t1,t10;
 set optimizer_use_condition_selectivity= @save_optimizer_use_condition_selectivity;
 set histogram_size=@save_histogram_size;
 set use_stat_tables= @save_use_stat_tables;
-DROP TABLE t1;
-# End of 10.2 tests
 set @@global.histogram_size=@save_histogram_size;
 set optimizer_switch=@save_optimizer_switch_for_selectivity_test;
 set @tmp_ust= @@use_stat_tables;
diff --git a/mysql-test/main/selectivity_no_engine.result b/mysql-test/main/selectivity_no_engine.result
index b6830e91f61..9ecf2eea23a 100644
--- a/mysql-test/main/selectivity_no_engine.result
+++ b/mysql-test/main/selectivity_no_engine.result
@@ -36,12 +36,12 @@ test.t2	analyze	status	OK
 # The following two must have the same in 'Extra' column:
 explain extended select * from t2 where col1 IN (20, 180);
 id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
-1	SIMPLE	t2	ALL	NULL	NULL	NULL	NULL	1100	1.35	Using where
+1	SIMPLE	t2	ALL	NULL	NULL	NULL	NULL	1100	1.00	Using where
 Warnings:
 Note	1003	select `test`.`t2`.`col1` AS `col1` from `test`.`t2` where `test`.`t2`.`col1` in (20,180)
 explain extended select * from t2 where col1 IN (180, 20);
 id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
-1	SIMPLE	t2	ALL	NULL	NULL	NULL	NULL	1100	1.35	Using where
+1	SIMPLE	t2	ALL	NULL	NULL	NULL	NULL	1100	1.00	Using where
 Warnings:
 Note	1003	select `test`.`t2`.`col1` AS `col1` from `test`.`t2` where `test`.`t2`.`col1` in (180,20)
 drop table t1, t2;
@@ -102,7 +102,7 @@ test.t1	analyze	status	Engine-independent statistics collected
 test.t1	analyze	status	OK
 explain extended select * from t1 where col1 in (1,2,3);
 id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
-1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	10000	3.37	Using where
+1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	10000	2.97	Using where
 Warnings:
 Note	1003	select `test`.`t1`.`col1` AS `col1` from `test`.`t1` where `test`.`t1`.`col1` in (1,2,3)
 # Must not cause fp division by zero, or produce nonsense numbers:
diff --git a/sql/sql_statistics.cc b/sql/sql_statistics.cc
index c7f6d2ff489..f27da375562 100644
--- a/sql/sql_statistics.cc
+++ b/sql/sql_statistics.cc
@@ -3902,50 +3902,16 @@ double Histogram::point_selectivity(double pos, double avg_sel)
   }
   else
   {
-    /* 
+    /*
       The value 'pos' fits within one single histogram bucket.
 
-      Histogram buckets have the same numbers of rows, but they cover
-      different ranges of values.
-
-      We assume that values are uniformly distributed across the [0..1] value
-      range.
-    */
-
-    /* 
-      If all buckets covered value ranges of the same size, the width of
-      value range would be:
+      We also have avg_sel which is per-table average selectivity of col=const.
+      If there are popular values, this may be larger than one bucket, so 
+      cap the returned number by the selectivity of one bucket.
     */
     double avg_bucket_width= 1.0 / (get_width() + 1);
-    
-    /*
-      Let's see what is the width of value range that our bucket is covering.
-        (min==max currently. they are kept in the formula just in case we 
-         will want to extend it to handle multi-bucket case)
-    */
-    double inv_prec_factor= (double) 1.0 / prec_factor(); 
-    double current_bucket_width= 
-        (max + 1 == get_width() ?  1.0 : (get_value(max) * inv_prec_factor)) -
-        (min == 0 ?  0.0 : (get_value(min-1) * inv_prec_factor));
-
-    DBUG_ASSERT(current_bucket_width); /* We shouldn't get a one zero-width bucket */
-
-    /*
-      So:
-      - each bucket has the same #rows 
-      - values are unformly distributed across the [min_value,max_value] domain.
 
-      If a bucket has value range that's N times bigger then average, than
-      each value will have to have N times fewer rows than average.
-    */
-    sel= avg_sel * avg_bucket_width / current_bucket_width;
-
-    /*
-      (Q: if we just follow this proportion we may end up in a situation
-      where number of different values we expect to find in this bucket
-      exceeds the number of rows that this histogram has in a bucket. Are 
-      we ok with this or we would want to have certain caps?)
-    */
+    sel= MY_MIN(avg_bucket_width, avg_sel);
   }
   return sel;
 }