MDEV-4362: {division by zero when lookup constant is outside the value table}

- Fix Histogram::point_selectivity() to work in the case where the 
  passed value_pos=0 (or 1) and the first (or the last) bucket in the 
  histogram has zero value-range (i.e one value).

mysql-test/r/selectivity.result

@@ -1356,6 +1356,37 @@ id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
 Warnings:
 Note	1003	select `test`.`t1`.`a` AS `a` from `test`.`t1` where (`test`.`t1`.`a` = <cache>(-(1)))
 drop table t0, t1;
+#
+# MDEV-4362: Selectivity estimates for IN (...) do not depend on whether the values are in range
+#
+create table t1 (col1 int);
+set @a=-1;
+create table t2 (a int)  select (@a:=@a+1) as a from information_schema.session_variables A limit 100;
+insert into t1 select A.a from t2 A, t2 B where A.a < 100 and B.a < 100;
+select min(col1), max(col1), count(*) from t1;
+min(col1)	max(col1)	count(*)
+0	99	10000
+set histogram_size=100;
+analyze table t1 persistent for all;
+Table	Op	Msg_type	Msg_text
+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
+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:
+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	3.00	Using where
+Warnings:
+Note	1003	select `test`.`t1`.`col1` AS `col1` from `test`.`t1` where (`test`.`t1`.`col1` in (<cache>(-(1)),<cache>(-(2)),<cache>(-(3))))
+explain extended select * from t1 where col1<=-1;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
+1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	10000	1.00	Using where
+Warnings:
+Note	1003	select `test`.`t1`.`col1` AS `col1` from `test`.`t1` where (`test`.`t1`.`col1` <= <cache>(-(1)))
+drop table t1, t2;
 set histogram_type=@save_histogram_type;
 set histogram_size=@save_histogram_size;
 set optimizer_use_condition_selectivity=@save_optimizer_use_condition_selectivity;

mysql-test/r/selectivity_innodb.result

@@ -1366,6 +1366,37 @@ id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
 Warnings:
 Note	1003	select `test`.`t1`.`a` AS `a` from `test`.`t1` where (`test`.`t1`.`a` = <cache>(-(1)))
 drop table t0, t1;
+#
+# MDEV-4362: Selectivity estimates for IN (...) do not depend on whether the values are in range
+#
+create table t1 (col1 int);
+set @a=-1;
+create table t2 (a int)  select (@a:=@a+1) as a from information_schema.session_variables A limit 100;
+insert into t1 select A.a from t2 A, t2 B where A.a < 100 and B.a < 100;
+select min(col1), max(col1), count(*) from t1;
+min(col1)	max(col1)	count(*)
+0	99	10000
+set histogram_size=100;
+analyze table t1 persistent for all;
+Table	Op	Msg_type	Msg_text
+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
+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:
+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	3.00	Using where
+Warnings:
+Note	1003	select `test`.`t1`.`col1` AS `col1` from `test`.`t1` where (`test`.`t1`.`col1` in (<cache>(-(1)),<cache>(-(2)),<cache>(-(3))))
+explain extended select * from t1 where col1<=-1;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
+1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	10000	1.00	Using where
+Warnings:
+Note	1003	select `test`.`t1`.`col1` AS `col1` from `test`.`t1` where (`test`.`t1`.`col1` <= <cache>(-(1)))
+drop table t1, t2;
 set histogram_type=@save_histogram_type;
 set histogram_size=@save_histogram_size;
 set optimizer_use_condition_selectivity=@save_optimizer_use_condition_selectivity;

mysql-test/t/selectivity.test

@@ -908,6 +908,22 @@ explain extended select * from t1 where a=-1;
 
 drop table t0, t1;
 
+--echo #
+--echo # MDEV-4362: Selectivity estimates for IN (...) do not depend on whether the values are in range
+--echo #
+create table t1 (col1 int);
+set @a=-1;
+create table t2 (a int)  select (@a:=@a+1) as a from information_schema.session_variables A limit 100;
+insert into t1 select A.a from t2 A, t2 B where A.a < 100 and B.a < 100;
+select min(col1), max(col1), count(*) from t1;
+set histogram_size=100;
+analyze table t1 persistent for all;
+explain extended select * from t1 where col1 in (1,2,3);
+--echo # Must not cause fp division by zero, or produce nonsense numbers:
+explain extended select * from t1 where col1 in (-1,-2,-3);
+explain extended select * from t1 where col1<=-1;
+drop table t1, t2;
+
 set histogram_type=@save_histogram_type;
 set histogram_size=@save_histogram_size;
 set optimizer_use_condition_selectivity=@save_optimizer_use_condition_selectivity;

sql/sql_statistics.h

@@ -302,16 +302,27 @@ public:
           (max + 1 == get_width() ?  1.0 : (get_value(max) * inv_prec_factor)) -
           (min == 0 ?  0.0 : (get_value(min-1) * inv_prec_factor));
 
-      /*
-        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.
-      */
-      DBUG_ASSERT(current_bucket_width);
-      sel= avg_sel * avg_bucket_width / current_bucket_width;
+      if (current_bucket_width < 1e-16)
+      {
+        /*
+          A special case: we are at the first (or the last) bucket in the
+          histogram, the bucket's value range is a singlepoint [x,x], and 
+          pos_value=0 (for the first bucket) or pos_value=1 (for the last).
+        */
+        sel= avg_sel;
+      }
+      else
+      {
+        /*
+          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