MDEV-16695: Estimate for rows of derived tables is very high when we are using index_merge union

For index merge union[or sort union], the estimates are not taken into account while calculating the selectivity of
a condition. So instead of showing the estimates of the index merge union[or sort union], it shows estimates equal to
all the records of the table.
The fix for the issue is to include the selectivity of index merge
union[or sort union] while calculating the selectivity of a condition.

mysql-test/r/index_merge_myisam.result

@@ -1712,3 +1712,53 @@ id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
 1	SIMPLE	t1	ALL	PRIMARY,c1,i,c2	NULL	NULL	NULL	69	Using where
 DROP TABLE t1;
 set optimizer_switch= @optimizer_switch_save;
+#
+# MDEV-16695: Estimate for rows of derived tables is very high when we are using index_merge union
+#
+create table t0
+(
+key1 int not null,
+INDEX i1(key1)
+);
+insert into t0 values (1),(2),(3),(4),(5),(6),(7),(8);
+set @d=8;
+insert into t0 select key1+ @d from t0;
+set @d=@d*2;
+insert into t0 select key1+ @d from t0;
+set @d=@d*2;
+insert into t0 select key1+ @d from t0;
+set @d=@d*2;
+insert into t0 select key1+ @d from t0;
+set @d=@d*2;
+insert into t0 select key1+ @d from t0;
+set @d=@d*2;
+insert into t0 select key1+ @d from t0;
+set @d=@d*2;
+insert into t0 select key1+ @d from t0;
+set @d=@d*2;
+alter table t0 add key2 int not null, add index i2(key2);
+alter table t0 add key3 int not null, add index i3(key3);
+alter table t0 add key8 int not null, add index i8(key8);
+update t0 set key2=key1,key3=key1,key8=1024-key1;
+analyze table t0;
+Table	Op	Msg_type	Msg_text
+test.t0	analyze	status	OK
+set @optimizer_switch_save=@@optimizer_switch;
+set optimizer_switch='derived_merge=off,derived_with_keys=off';
+explain select * from (select * from t0 where key1 = 3 or key2 =3) as Z where Z.key8 > 5;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	PRIMARY	<derived2>	ALL	NULL	NULL	NULL	NULL	2	Using where
+2	DERIVED	t0	index_merge	i1,i2	i1,i2	4,4	NULL	2	Using union(i1,i2); Using where
+select * from (select * from t0 where key1 = 3 or key2 =3) as Z where Z.key8 > 5;
+key1	key2	key3	key8
+3	3	3	1021
+set optimizer_use_condition_selectivity=2;
+explain select * from (select * from t0 where key1 = 3 or key2 =3) as Z where Z.key8 > 5;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	PRIMARY	<derived2>	ALL	NULL	NULL	NULL	NULL	2	Using where
+2	DERIVED	t0	index_merge	i1,i2	i1,i2	4,4	NULL	2	Using union(i1,i2); Using where
+select * from (select * from t0 where key1 = 3 or key2 =3) as Z where Z.key8 > 5;
+key1	key2	key3	key8
+3	3	3	1021
+set @@optimizer_switch= @optimizer_switch_save;
+drop table t0;

mysql-test/t/index_merge_myisam.test

@@ -243,3 +243,38 @@ DROP TABLE t1;
 
 set optimizer_switch= @optimizer_switch_save;
 
+--echo #
+--echo # MDEV-16695: Estimate for rows of derived tables is very high when we are using index_merge union
+--echo #
+
+create table t0
+(
+  key1 int not null,
+  INDEX i1(key1)
+);
+
+insert into t0 values (1),(2),(3),(4),(5),(6),(7),(8);
+let $1=7;
+set @d=8;
+while ($1)
+{
+  eval insert into t0 select key1+ @d from t0;
+  eval set @d=@d*2;
+  dec $1;
+}
+alter table t0 add key2 int not null, add index i2(key2);
+alter table t0 add key3 int not null, add index i3(key3);
+alter table t0 add key8 int not null, add index i8(key8);
+
+update t0 set key2=key1,key3=key1,key8=1024-key1;
+analyze table t0;
+
+set @optimizer_switch_save=@@optimizer_switch;
+set optimizer_switch='derived_merge=off,derived_with_keys=off';
+explain select * from (select * from t0 where key1 = 3 or key2 =3) as Z where Z.key8 > 5;
+select * from (select * from t0 where key1 = 3 or key2 =3) as Z where Z.key8 > 5;
+set optimizer_use_condition_selectivity=2;
+explain select * from (select * from t0 where key1 = 3 or key2 =3) as Z where Z.key8 > 5;
+select * from (select * from t0 where key1 = 3 or key2 =3) as Z where Z.key8 > 5;
+set @@optimizer_switch= @optimizer_switch_save;
+drop table t0;

sql/opt_range.cc

@@ -3725,6 +3725,12 @@ bool calculate_cond_selectivity_for_table(THD *thd, TABLE *table, Item *cond)
 
   }
 
+  if (quick && (quick->get_type() == QUICK_SELECT_I::QS_TYPE_ROR_UNION || 
+     quick->get_type() == QUICK_SELECT_I::QS_TYPE_INDEX_MERGE))
+  {
+    table->cond_selectivity*= (quick->records/table_records);
+  }
+
   bitmap_union(used_fields, &handled_columns);
 
   /* Check if we can improve selectivity estimates by using sampling */