diff --git a/mysql-test/r/mysqld--help.result b/mysql-test/r/mysqld--help.result
index 74faa205981..d7074d140b3 100644
--- a/mysql-test/r/mysqld--help.result
+++ b/mysql-test/r/mysqld--help.result
@@ -495,6 +495,9 @@ The following options may be given as the first argument:
  optimizer will switch to the original find_best search.
  NOTE: The value 63 and its associated behaviour is
  deprecated
+ --optimizer-selectivity-sampling-limit=# 
+ Controls number of record samples to check condition
+ selectivity
  --optimizer-switch=name 
  optimizer_switch=option=val[,option=val...], where option
  is one of {derived_merge, derived_with_keys, firstmatch,
@@ -523,7 +526,9 @@ The following options may be given as the first argument:
  any index to calculate the cardinality of a partial join,
  4 - use histograms to calculate selectivity of range
  conditions that are not backed by any index to calculate
- the cardinality of a partial join.
+ the cardinality of a partial join.5 - additionally use
+ selectivity of certain non-range predicates calculated on
+ record samples
  --performance-schema 
  Enable the performance schema.
  --performance-schema-accounts-size=# 
@@ -1126,6 +1131,7 @@ old-passwords FALSE
 old-style-user-limits FALSE
 optimizer-prune-level 1
 optimizer-search-depth 62
+optimizer-selectivity-sampling-limit 100
 optimizer-switch index_merge=on,index_merge_union=on,index_merge_sort_union=on,index_merge_intersection=on,index_merge_sort_intersection=off,engine_condition_pushdown=off,index_condition_pushdown=on,derived_merge=on,derived_with_keys=on,firstmatch=on,loosescan=on,materialization=on,in_to_exists=on,semijoin=on,partial_match_rowid_merge=on,partial_match_table_scan=on,subquery_cache=on,mrr=off,mrr_cost_based=off,mrr_sort_keys=off,outer_join_with_cache=on,semijoin_with_cache=on,join_cache_incremental=on,join_cache_hashed=on,join_cache_bka=on,optimize_join_buffer_size=off,table_elimination=on
 optimizer-use-condition-selectivity 1
 performance-schema FALSE
diff --git a/mysql-test/r/selectivity.result b/mysql-test/r/selectivity.result
index 79ff506d603..e59f4310431 100644
--- a/mysql-test/r/selectivity.result
+++ b/mysql-test/r/selectivity.result
@@ -37,6 +37,89 @@ set optimizer_use_condition_selectivity=@save_optimizer_use_condition_selectivit
 DROP DATABASE IF EXISTS dbt3_s001;
 CREATE DATABASE dbt3_s001;
 use dbt3_s001;
+=== Q2 ===
+set optimizer_use_condition_selectivity=5;
+explain extended
+select
+s_acctbal, s_name, n_name, p_partkey, p_mfgr, s_address, s_phone, s_comment
+from
+part, supplier, partsupp, nation, region
+where
+p_partkey = ps_partkey
+and s_suppkey = ps_suppkey
+and p_size = 9
+and p_type like '%TIN'
+	and s_nationkey = n_nationkey
+and n_regionkey = r_regionkey
+and r_name = 'ASIA'
+	and ps_supplycost = (
+select
+min(ps_supplycost)
+from
+partsupp, supplier, nation, region
+where
+p_partkey = ps_partkey
+and s_suppkey = ps_suppkey
+and s_nationkey = n_nationkey
+and n_regionkey = r_regionkey
+and r_name = 'ASIA'
+	)
+order by
+s_acctbal desc, n_name, s_name, p_partkey;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
+1	PRIMARY	part	ALL	PRIMARY	NULL	NULL	NULL	200	0.31	Using where; Using temporary; Using filesort
+1	PRIMARY	region	ALL	PRIMARY	NULL	NULL	NULL	5	20.00	Using where; Using join buffer (flat, BNL join)
+1	PRIMARY	partsupp	ref	PRIMARY,i_ps_partkey,i_ps_suppkey	PRIMARY	4	dbt3_s001.part.p_partkey	3	100.00	Using where
+1	PRIMARY	supplier	ALL	PRIMARY,i_s_nationkey	NULL	NULL	NULL	10	80.00	Using where; Using join buffer (flat, BNL join)
+1	PRIMARY	nation	eq_ref	PRIMARY,i_n_regionkey	PRIMARY	4	dbt3_s001.supplier.s_nationkey	1	100.00	Using where
+2	DEPENDENT SUBQUERY	region	ALL	PRIMARY	NULL	NULL	NULL	5	20.00	Using where
+2	DEPENDENT SUBQUERY	partsupp	ref	PRIMARY,i_ps_partkey,i_ps_suppkey	PRIMARY	4	dbt3_s001.part.p_partkey	3	100.00	
+2	DEPENDENT SUBQUERY	supplier	eq_ref	PRIMARY,i_s_nationkey	PRIMARY	4	dbt3_s001.partsupp.ps_suppkey	1	100.00	Using where
+2	DEPENDENT SUBQUERY	nation	eq_ref	PRIMARY,i_n_regionkey	PRIMARY	4	dbt3_s001.supplier.s_nationkey	1	100.00	Using where
+Warnings:
+Note	1276	Field or reference 'dbt3_s001.part.p_partkey' of SELECT #2 was resolved in SELECT #1
+Note	1003	select `dbt3_s001`.`supplier`.`s_acctbal` AS `s_acctbal`,`dbt3_s001`.`supplier`.`s_name` AS `s_name`,`dbt3_s001`.`nation`.`n_name` AS `n_name`,`dbt3_s001`.`part`.`p_partkey` AS `p_partkey`,`dbt3_s001`.`part`.`p_mfgr` AS `p_mfgr`,`dbt3_s001`.`supplier`.`s_address` AS `s_address`,`dbt3_s001`.`supplier`.`s_phone` AS `s_phone`,`dbt3_s001`.`supplier`.`s_comment` AS `s_comment` from `dbt3_s001`.`part` join `dbt3_s001`.`supplier` join `dbt3_s001`.`partsupp` join `dbt3_s001`.`nation` join `dbt3_s001`.`region` where ((`dbt3_s001`.`partsupp`.`ps_partkey` = `dbt3_s001`.`part`.`p_partkey`) and (`dbt3_s001`.`supplier`.`s_suppkey` = `dbt3_s001`.`partsupp`.`ps_suppkey`) and (`dbt3_s001`.`part`.`p_size` = 9) and (`dbt3_s001`.`nation`.`n_nationkey` = `dbt3_s001`.`supplier`.`s_nationkey`) and (`dbt3_s001`.`nation`.`n_regionkey` = `dbt3_s001`.`region`.`r_regionkey`) and (`dbt3_s001`.`region`.`r_name` = 'ASIA') and (`dbt3_s001`.`part`.`p_type` like '%TIN') and (`dbt3_s001`.`partsupp`.`ps_supplycost` = <expr_cache><`dbt3_s001`.`part`.`p_partkey`>((select min(`dbt3_s001`.`partsupp`.`ps_supplycost`) from `dbt3_s001`.`partsupp` join `dbt3_s001`.`supplier` join `dbt3_s001`.`nation` join `dbt3_s001`.`region` where ((`dbt3_s001`.`supplier`.`s_suppkey` = `dbt3_s001`.`partsupp`.`ps_suppkey`) and (`dbt3_s001`.`nation`.`n_nationkey` = `dbt3_s001`.`supplier`.`s_nationkey`) and (`dbt3_s001`.`nation`.`n_regionkey` = `dbt3_s001`.`region`.`r_regionkey`) and (`dbt3_s001`.`region`.`r_name` = 'ASIA') and (`dbt3_s001`.`part`.`p_partkey` = `dbt3_s001`.`partsupp`.`ps_partkey`)))))) order by `dbt3_s001`.`supplier`.`s_acctbal` desc,`dbt3_s001`.`nation`.`n_name`,`dbt3_s001`.`supplier`.`s_name`,`dbt3_s001`.`part`.`p_partkey`
+set optimizer_use_condition_selectivity=4;
+explain extended
+select
+s_acctbal, s_name, n_name, p_partkey, p_mfgr, s_address, s_phone, s_comment
+from
+part, supplier, partsupp, nation, region
+where
+p_partkey = ps_partkey
+and s_suppkey = ps_suppkey
+and p_size = 9
+and p_type like '%TIN'
+	and s_nationkey = n_nationkey
+and n_regionkey = r_regionkey
+and r_name = 'ASIA'
+	and ps_supplycost = (
+select
+min(ps_supplycost)
+from
+partsupp, supplier, nation, region
+where
+p_partkey = ps_partkey
+and s_suppkey = ps_suppkey
+and s_nationkey = n_nationkey
+and n_regionkey = r_regionkey
+and r_name = 'ASIA'
+	)
+order by
+s_acctbal desc, n_name, s_name, p_partkey;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
+1	PRIMARY	region	ALL	PRIMARY	NULL	NULL	NULL	5	20.00	Using where; Using temporary; Using filesort
+1	PRIMARY	part	ALL	PRIMARY	NULL	NULL	NULL	200	2.08	Using where; Using join buffer (flat, BNL join)
+1	PRIMARY	partsupp	ref	PRIMARY,i_ps_partkey,i_ps_suppkey	PRIMARY	4	dbt3_s001.part.p_partkey	3	100.00	Using where
+1	PRIMARY	supplier	ALL	PRIMARY,i_s_nationkey	NULL	NULL	NULL	10	80.00	Using where; Using join buffer (flat, BNL join)
+1	PRIMARY	nation	eq_ref	PRIMARY,i_n_regionkey	PRIMARY	4	dbt3_s001.supplier.s_nationkey	1	100.00	Using where
+2	DEPENDENT SUBQUERY	region	ALL	PRIMARY	NULL	NULL	NULL	5	20.00	Using where
+2	DEPENDENT SUBQUERY	partsupp	ref	PRIMARY,i_ps_partkey,i_ps_suppkey	PRIMARY	4	dbt3_s001.part.p_partkey	3	100.00	
+2	DEPENDENT SUBQUERY	supplier	eq_ref	PRIMARY,i_s_nationkey	PRIMARY	4	dbt3_s001.partsupp.ps_suppkey	1	100.00	Using where
+2	DEPENDENT SUBQUERY	nation	eq_ref	PRIMARY,i_n_regionkey	PRIMARY	4	dbt3_s001.supplier.s_nationkey	1	100.00	Using where
+Warnings:
+Note	1276	Field or reference 'dbt3_s001.part.p_partkey' of SELECT #2 was resolved in SELECT #1
+Note	1003	select `dbt3_s001`.`supplier`.`s_acctbal` AS `s_acctbal`,`dbt3_s001`.`supplier`.`s_name` AS `s_name`,`dbt3_s001`.`nation`.`n_name` AS `n_name`,`dbt3_s001`.`part`.`p_partkey` AS `p_partkey`,`dbt3_s001`.`part`.`p_mfgr` AS `p_mfgr`,`dbt3_s001`.`supplier`.`s_address` AS `s_address`,`dbt3_s001`.`supplier`.`s_phone` AS `s_phone`,`dbt3_s001`.`supplier`.`s_comment` AS `s_comment` from `dbt3_s001`.`part` join `dbt3_s001`.`supplier` join `dbt3_s001`.`partsupp` join `dbt3_s001`.`nation` join `dbt3_s001`.`region` where ((`dbt3_s001`.`partsupp`.`ps_partkey` = `dbt3_s001`.`part`.`p_partkey`) and (`dbt3_s001`.`supplier`.`s_suppkey` = `dbt3_s001`.`partsupp`.`ps_suppkey`) and (`dbt3_s001`.`part`.`p_size` = 9) and (`dbt3_s001`.`nation`.`n_nationkey` = `dbt3_s001`.`supplier`.`s_nationkey`) and (`dbt3_s001`.`nation`.`n_regionkey` = `dbt3_s001`.`region`.`r_regionkey`) and (`dbt3_s001`.`region`.`r_name` = 'ASIA') and (`dbt3_s001`.`part`.`p_type` like '%TIN') and (`dbt3_s001`.`partsupp`.`ps_supplycost` = <expr_cache><`dbt3_s001`.`part`.`p_partkey`>((select min(`dbt3_s001`.`partsupp`.`ps_supplycost`) from `dbt3_s001`.`partsupp` join `dbt3_s001`.`supplier` join `dbt3_s001`.`nation` join `dbt3_s001`.`region` where ((`dbt3_s001`.`supplier`.`s_suppkey` = `dbt3_s001`.`partsupp`.`ps_suppkey`) and (`dbt3_s001`.`nation`.`n_nationkey` = `dbt3_s001`.`supplier`.`s_nationkey`) and (`dbt3_s001`.`nation`.`n_regionkey` = `dbt3_s001`.`region`.`r_regionkey`) and (`dbt3_s001`.`region`.`r_name` = 'ASIA') and (`dbt3_s001`.`part`.`p_partkey` = `dbt3_s001`.`partsupp`.`ps_partkey`)))))) order by `dbt3_s001`.`supplier`.`s_acctbal` desc,`dbt3_s001`.`nation`.`n_name`,`dbt3_s001`.`supplier`.`s_name`,`dbt3_s001`.`part`.`p_partkey`
 === Q15 ===
 create view revenue0 (supplier_no, total_revenue) as
 select l_suppkey, sum(l_extendedprice * (1 - l_discount))
@@ -1011,4 +1094,38 @@ f1	f2	f2
 set optimizer_use_condition_selectivity=@save_optimizer_use_condition_selectivity;
 DROP TABLE t1,t2;
 set use_stat_tables=@save_use_stat_tables;
+#
+# Bug mdev-4406: range condition for non-nullable column   
+#                when optimizer_use_condition_selectivity=3
+#
+create table t1 (a int not null);
+insert into t1 values
+(7), (6), (4), (9), (1), (5), (2), (1), (3), (8);
+set use_stat_tables='preferably';
+analyze table t1;
+Table	Op	Msg_type	Msg_text
+test.t1	analyze	status	OK
+flush table t1;
+set optimizer_use_condition_selectivity=3;
+select count(*) from t1 where a between 5 and 7;
+count(*)
+3
+explain extended select * from t1 where a between 5 and 7;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
+1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	10	25.00	Using where
+Warnings:
+Note	1003	select `test`.`t1`.`a` AS `a` from `test`.`t1` where (`test`.`t1`.`a` between 5 and 7)
+alter table t1 change column a a int;
+analyze table t1;
+Table	Op	Msg_type	Msg_text
+test.t1	analyze	status	OK
+flush table t1;
+explain extended select * from t1 where a between 5 and 7;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
+1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	10	25.00	Using where
+Warnings:
+Note	1003	select `test`.`t1`.`a` AS `a` from `test`.`t1` where (`test`.`t1`.`a` between 5 and 7)
+set optimizer_use_condition_selectivity=@save_optimizer_use_condition_selectivity;
+drop table t1;
+set use_stat_tables=@save_use_stat_tables;
 set use_stat_tables=@save_use_stat_tables;
diff --git a/mysql-test/r/selectivity_innodb.result b/mysql-test/r/selectivity_innodb.result
index e32eea8827d..20efb16914b 100644
--- a/mysql-test/r/selectivity_innodb.result
+++ b/mysql-test/r/selectivity_innodb.result
@@ -40,6 +40,89 @@ set optimizer_use_condition_selectivity=@save_optimizer_use_condition_selectivit
 DROP DATABASE IF EXISTS dbt3_s001;
 CREATE DATABASE dbt3_s001;
 use dbt3_s001;
+=== Q2 ===
+set optimizer_use_condition_selectivity=5;
+explain extended
+select
+s_acctbal, s_name, n_name, p_partkey, p_mfgr, s_address, s_phone, s_comment
+from
+part, supplier, partsupp, nation, region
+where
+p_partkey = ps_partkey
+and s_suppkey = ps_suppkey
+and p_size = 9
+and p_type like '%TIN'
+	and s_nationkey = n_nationkey
+and n_regionkey = r_regionkey
+and r_name = 'ASIA'
+	and ps_supplycost = (
+select
+min(ps_supplycost)
+from
+partsupp, supplier, nation, region
+where
+p_partkey = ps_partkey
+and s_suppkey = ps_suppkey
+and s_nationkey = n_nationkey
+and n_regionkey = r_regionkey
+and r_name = 'ASIA'
+	)
+order by
+s_acctbal desc, n_name, s_name, p_partkey;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
+1	PRIMARY	part	ALL	PRIMARY	NULL	NULL	NULL	200	0.31	Using where; Using temporary; Using filesort
+1	PRIMARY	region	ALL	PRIMARY	NULL	NULL	NULL	5	20.00	Using where; Using join buffer (flat, BNL join)
+1	PRIMARY	partsupp	ref	PRIMARY,i_ps_partkey,i_ps_suppkey	PRIMARY	4	dbt3_s001.part.p_partkey	3	100.00	Using where
+1	PRIMARY	supplier	ALL	PRIMARY,i_s_nationkey	NULL	NULL	NULL	10	80.00	Using where; Using join buffer (flat, BNL join)
+1	PRIMARY	nation	eq_ref	PRIMARY,i_n_regionkey	PRIMARY	4	dbt3_s001.supplier.s_nationkey	1	100.00	Using where
+2	DEPENDENT SUBQUERY	region	ALL	PRIMARY	NULL	NULL	NULL	5	20.00	Using where
+2	DEPENDENT SUBQUERY	partsupp	ref	PRIMARY,i_ps_partkey,i_ps_suppkey	PRIMARY	4	dbt3_s001.part.p_partkey	3	100.00	
+2	DEPENDENT SUBQUERY	supplier	eq_ref	PRIMARY,i_s_nationkey	PRIMARY	4	dbt3_s001.partsupp.ps_suppkey	1	100.00	Using where
+2	DEPENDENT SUBQUERY	nation	eq_ref	PRIMARY,i_n_regionkey	PRIMARY	4	dbt3_s001.supplier.s_nationkey	1	100.00	Using where
+Warnings:
+Note	1276	Field or reference 'dbt3_s001.part.p_partkey' of SELECT #2 was resolved in SELECT #1
+Note	1003	select `dbt3_s001`.`supplier`.`s_acctbal` AS `s_acctbal`,`dbt3_s001`.`supplier`.`s_name` AS `s_name`,`dbt3_s001`.`nation`.`n_name` AS `n_name`,`dbt3_s001`.`part`.`p_partkey` AS `p_partkey`,`dbt3_s001`.`part`.`p_mfgr` AS `p_mfgr`,`dbt3_s001`.`supplier`.`s_address` AS `s_address`,`dbt3_s001`.`supplier`.`s_phone` AS `s_phone`,`dbt3_s001`.`supplier`.`s_comment` AS `s_comment` from `dbt3_s001`.`part` join `dbt3_s001`.`supplier` join `dbt3_s001`.`partsupp` join `dbt3_s001`.`nation` join `dbt3_s001`.`region` where ((`dbt3_s001`.`partsupp`.`ps_partkey` = `dbt3_s001`.`part`.`p_partkey`) and (`dbt3_s001`.`supplier`.`s_suppkey` = `dbt3_s001`.`partsupp`.`ps_suppkey`) and (`dbt3_s001`.`part`.`p_size` = 9) and (`dbt3_s001`.`nation`.`n_nationkey` = `dbt3_s001`.`supplier`.`s_nationkey`) and (`dbt3_s001`.`nation`.`n_regionkey` = `dbt3_s001`.`region`.`r_regionkey`) and (`dbt3_s001`.`region`.`r_name` = 'ASIA') and (`dbt3_s001`.`part`.`p_type` like '%TIN') and (`dbt3_s001`.`partsupp`.`ps_supplycost` = <expr_cache><`dbt3_s001`.`part`.`p_partkey`>((select min(`dbt3_s001`.`partsupp`.`ps_supplycost`) from `dbt3_s001`.`partsupp` join `dbt3_s001`.`supplier` join `dbt3_s001`.`nation` join `dbt3_s001`.`region` where ((`dbt3_s001`.`supplier`.`s_suppkey` = `dbt3_s001`.`partsupp`.`ps_suppkey`) and (`dbt3_s001`.`nation`.`n_nationkey` = `dbt3_s001`.`supplier`.`s_nationkey`) and (`dbt3_s001`.`nation`.`n_regionkey` = `dbt3_s001`.`region`.`r_regionkey`) and (`dbt3_s001`.`region`.`r_name` = 'ASIA') and (`dbt3_s001`.`part`.`p_partkey` = `dbt3_s001`.`partsupp`.`ps_partkey`)))))) order by `dbt3_s001`.`supplier`.`s_acctbal` desc,`dbt3_s001`.`nation`.`n_name`,`dbt3_s001`.`supplier`.`s_name`,`dbt3_s001`.`part`.`p_partkey`
+set optimizer_use_condition_selectivity=4;
+explain extended
+select
+s_acctbal, s_name, n_name, p_partkey, p_mfgr, s_address, s_phone, s_comment
+from
+part, supplier, partsupp, nation, region
+where
+p_partkey = ps_partkey
+and s_suppkey = ps_suppkey
+and p_size = 9
+and p_type like '%TIN'
+	and s_nationkey = n_nationkey
+and n_regionkey = r_regionkey
+and r_name = 'ASIA'
+	and ps_supplycost = (
+select
+min(ps_supplycost)
+from
+partsupp, supplier, nation, region
+where
+p_partkey = ps_partkey
+and s_suppkey = ps_suppkey
+and s_nationkey = n_nationkey
+and n_regionkey = r_regionkey
+and r_name = 'ASIA'
+	)
+order by
+s_acctbal desc, n_name, s_name, p_partkey;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
+1	PRIMARY	region	ALL	PRIMARY	NULL	NULL	NULL	5	20.00	Using where; Using temporary; Using filesort
+1	PRIMARY	part	ALL	PRIMARY	NULL	NULL	NULL	200	2.08	Using where; Using join buffer (flat, BNL join)
+1	PRIMARY	partsupp	ref	PRIMARY,i_ps_partkey,i_ps_suppkey	PRIMARY	4	dbt3_s001.part.p_partkey	3	100.00	Using where
+1	PRIMARY	supplier	ALL	PRIMARY,i_s_nationkey	NULL	NULL	NULL	10	80.00	Using where; Using join buffer (flat, BNL join)
+1	PRIMARY	nation	eq_ref	PRIMARY,i_n_regionkey	PRIMARY	4	dbt3_s001.supplier.s_nationkey	1	100.00	Using where
+2	DEPENDENT SUBQUERY	region	ALL	PRIMARY	NULL	NULL	NULL	5	20.00	Using where
+2	DEPENDENT SUBQUERY	partsupp	ref	PRIMARY,i_ps_partkey,i_ps_suppkey	PRIMARY	4	dbt3_s001.part.p_partkey	3	100.00	
+2	DEPENDENT SUBQUERY	supplier	eq_ref	PRIMARY,i_s_nationkey	PRIMARY	4	dbt3_s001.partsupp.ps_suppkey	1	100.00	Using where
+2	DEPENDENT SUBQUERY	nation	eq_ref	PRIMARY,i_n_regionkey	PRIMARY	4	dbt3_s001.supplier.s_nationkey	1	100.00	Using where
+Warnings:
+Note	1276	Field or reference 'dbt3_s001.part.p_partkey' of SELECT #2 was resolved in SELECT #1
+Note	1003	select `dbt3_s001`.`supplier`.`s_acctbal` AS `s_acctbal`,`dbt3_s001`.`supplier`.`s_name` AS `s_name`,`dbt3_s001`.`nation`.`n_name` AS `n_name`,`dbt3_s001`.`part`.`p_partkey` AS `p_partkey`,`dbt3_s001`.`part`.`p_mfgr` AS `p_mfgr`,`dbt3_s001`.`supplier`.`s_address` AS `s_address`,`dbt3_s001`.`supplier`.`s_phone` AS `s_phone`,`dbt3_s001`.`supplier`.`s_comment` AS `s_comment` from `dbt3_s001`.`part` join `dbt3_s001`.`supplier` join `dbt3_s001`.`partsupp` join `dbt3_s001`.`nation` join `dbt3_s001`.`region` where ((`dbt3_s001`.`partsupp`.`ps_partkey` = `dbt3_s001`.`part`.`p_partkey`) and (`dbt3_s001`.`supplier`.`s_suppkey` = `dbt3_s001`.`partsupp`.`ps_suppkey`) and (`dbt3_s001`.`part`.`p_size` = 9) and (`dbt3_s001`.`nation`.`n_nationkey` = `dbt3_s001`.`supplier`.`s_nationkey`) and (`dbt3_s001`.`nation`.`n_regionkey` = `dbt3_s001`.`region`.`r_regionkey`) and (`dbt3_s001`.`region`.`r_name` = 'ASIA') and (`dbt3_s001`.`part`.`p_type` like '%TIN') and (`dbt3_s001`.`partsupp`.`ps_supplycost` = <expr_cache><`dbt3_s001`.`part`.`p_partkey`>((select min(`dbt3_s001`.`partsupp`.`ps_supplycost`) from `dbt3_s001`.`partsupp` join `dbt3_s001`.`supplier` join `dbt3_s001`.`nation` join `dbt3_s001`.`region` where ((`dbt3_s001`.`supplier`.`s_suppkey` = `dbt3_s001`.`partsupp`.`ps_suppkey`) and (`dbt3_s001`.`nation`.`n_nationkey` = `dbt3_s001`.`supplier`.`s_nationkey`) and (`dbt3_s001`.`nation`.`n_regionkey` = `dbt3_s001`.`region`.`r_regionkey`) and (`dbt3_s001`.`region`.`r_name` = 'ASIA') and (`dbt3_s001`.`part`.`p_partkey` = `dbt3_s001`.`partsupp`.`ps_partkey`)))))) order by `dbt3_s001`.`supplier`.`s_acctbal` desc,`dbt3_s001`.`nation`.`n_name`,`dbt3_s001`.`supplier`.`s_name`,`dbt3_s001`.`part`.`p_partkey`
 === Q15 ===
 create view revenue0 (supplier_no, total_revenue) as
 select l_suppkey, sum(l_extendedprice * (1 - l_discount))
@@ -1019,6 +1102,40 @@ f1	f2	f2
 set optimizer_use_condition_selectivity=@save_optimizer_use_condition_selectivity;
 DROP TABLE t1,t2;
 set use_stat_tables=@save_use_stat_tables;
+#
+# Bug mdev-4406: range condition for non-nullable column   
+#                when optimizer_use_condition_selectivity=3
+#
+create table t1 (a int not null);
+insert into t1 values
+(7), (6), (4), (9), (1), (5), (2), (1), (3), (8);
+set use_stat_tables='preferably';
+analyze table t1;
+Table	Op	Msg_type	Msg_text
+test.t1	analyze	status	OK
+flush table t1;
+set optimizer_use_condition_selectivity=3;
+select count(*) from t1 where a between 5 and 7;
+count(*)
+3
+explain extended select * from t1 where a between 5 and 7;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
+1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	10	25.00	Using where
+Warnings:
+Note	1003	select `test`.`t1`.`a` AS `a` from `test`.`t1` where (`test`.`t1`.`a` between 5 and 7)
+alter table t1 change column a a int;
+analyze table t1;
+Table	Op	Msg_type	Msg_text
+test.t1	analyze	status	OK
+flush table t1;
+explain extended select * from t1 where a between 5 and 7;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	filtered	Extra
+1	SIMPLE	t1	ALL	NULL	NULL	NULL	NULL	10	25.00	Using where
+Warnings:
+Note	1003	select `test`.`t1`.`a` AS `a` from `test`.`t1` where (`test`.`t1`.`a` between 5 and 7)
+set optimizer_use_condition_selectivity=@save_optimizer_use_condition_selectivity;
+drop table t1;
+set use_stat_tables=@save_use_stat_tables;
 set use_stat_tables=@save_use_stat_tables;
 set optimizer_switch=@save_optimizer_switch_for_selectivity_test;
 SET SESSION STORAGE_ENGINE=DEFAULT;
diff --git a/mysql-test/r/statistics.result b/mysql-test/r/statistics.result
index 20469c01a2e..640a2f649d6 100644
--- a/mysql-test/r/statistics.result
+++ b/mysql-test/r/statistics.result
@@ -1416,6 +1416,43 @@ WORLD_INNODB	CITY	Country	1	17.5819
 WORLD_INNODB	COUNTRYLANGUAGE	PRIMARY	1	4.2232
 WORLD_INNODB	COUNTRYLANGUAGE	PRIMARY	2	1.0000
 WORLD_INNODB	COUNTRYLANGUAGE	Percentage	1	2.7640
+use world;
+set use_stat_tables='preferably';
+set histogram_size=100;
+set histogram_type='SINGLE_PREC_HB';
+ANALYZE TABLE CountryLanguage;
+set histogram_size=254;
+set histogram_type='DOUBLE_PREC_HB';
+ANALYZE TABLE City;
+FLUSH TABLES;
+select UPPER(db_name),UPPER(table_name),UPPER(column_name),min_value,max_value,nulls_ratio,avg_length,avg_frequency,hist_size,hist_type,hex(histogram),decode_histogram(histogram,hist_type) from mysql.column_stats where UPPER(db_name)='WORLD' and UPPER(table_name)='COUNTRYLANGUAGE' and UPPER(column_name) = 'PERCENTAGE';;
+UPPER(db_name)	WORLD
+UPPER(table_name)	COUNTRYLANGUAGE
+UPPER(column_name)	PERCENTAGE
+min_value	0.0
+max_value	99.9
+nulls_ratio	0.0000
+avg_length	4.0000
+avg_frequency	2.7640
+hist_size	100
+hist_type	SINGLE_PREC_HB
+hex(histogram)	0000000000000000000000000101010101010101010202020303030304040404050505050606070707080809090A0A0B0C0D0D0E0E0F10111213131415161718191B1C1E202224292A2E33373B4850575F6A76818C9AA7B9C4CFDADFE5EBF0F4F8FAFCFF
+decode_histogram(histogram,hist_type)	0.000,0.000,0.000,0.000,0.000,0.000,0.000,0.000,0.000,0.000,0.000,0.000,0.004,0.000,0.000,0.000,0.000,0.000,0.000,0.000,0.000,0.004,0.000,0.000,0.004,0.000,0.000,0.000,0.004,0.000,0.000,0.000,0.004,0.000,0.000,0.000,0.004,0.000,0.004,0.000,0.000,0.004,0.000,0.004,0.000,0.004,0.000,0.004,0.004,0.004,0.000,0.004,0.000,0.004,0.004,0.004,0.004,0.004,0.000,0.004,0.004,0.004,0.004,0.004,0.004,0.008,0.004,0.008,0.008,0.008,0.008,0.020,0.004,0.016,0.020,0.016,0.016,0.051,0.031,0.027,0.031,0.043,0.047,0.043,0.043,0.055,0.051,0.071,0.043,0.043,0.043,0.020,0.024,0.024,0.020,0.016,0.016,0.008,0.008,0.012,0.000
+select UPPER(db_name),UPPER(table_name),UPPER(column_name),min_value,max_value,nulls_ratio,avg_length,avg_frequency,hist_size,hist_type,hex(histogram),decode_histogram(histogram,hist_type) from mysql.column_stats where UPPER(db_name)='WORLD' and UPPER(table_name)='CITY' and UPPER(column_name) = 'POPULATION';;
+UPPER(db_name)	WORLD
+UPPER(table_name)	CITY
+UPPER(column_name)	POPULATION
+min_value	42
+max_value	10500000
+nulls_ratio	0.0000
+avg_length	4.0000
+avg_frequency	1.0467
+hist_size	254
+hist_type	DOUBLE_PREC_HB
+hex(histogram)	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
+decode_histogram(histogram,hist_type)	0.00047,0.00198,0.00601,0.00008,0.00008,0.00005,0.00011,0.00006,0.00009,0.00008,0.00006,0.00009,0.00008,0.00009,0.00008,0.00009,0.00006,0.00006,0.00008,0.00008,0.00008,0.00011,0.00009,0.00008,0.00009,0.00006,0.00011,0.00006,0.00012,0.00012,0.00012,0.00012,0.00011,0.00011,0.00014,0.00011,0.00011,0.00011,0.00014,0.00006,0.00011,0.00009,0.00011,0.00009,0.00015,0.00015,0.00015,0.00009,0.00018,0.00015,0.00015,0.00015,0.00017,0.00018,0.00018,0.00015,0.00018,0.00020,0.00024,0.00021,0.00023,0.00027,0.00024,0.00024,0.00027,0.00023,0.00020,0.00029,0.00020,0.00027,0.00020,0.00027,0.00026,0.00034,0.00024,0.00034,0.00031,0.00037,0.00043,0.00038,0.00038,0.00035,0.00047,0.00056,0.00058,0.00041,0.00047,0.00056,0.00072,0.00044,0.00060,0.00072,0.00061,0.00072,0.00066,0.00085,0.00075,0.00078,0.00082,0.00073,0.00108,0.00089,0.00105,0.00105,0.00151,0.00150,0.00110,0.00145,0.00163,0.00160,0.00165,0.00232,0.00201,0.00371,0.00365,0.00383,0.00459,0.00583,0.00662,0.00984,0.00969,0.01080,0.01379,0.02063,0.04308,0.05960,0.15816,0.59464
+set histogram_type=default;
+set histogram_size=default;
 use test;
 DROP DATABASE world;
 SELECT UPPER(db_name), UPPER(table_name), cardinality
diff --git a/mysql-test/suite/sys_vars/r/optimizer_selectivity_sampling_limit_basic.result b/mysql-test/suite/sys_vars/r/optimizer_selectivity_sampling_limit_basic.result
new file mode 100644
index 00000000000..4df024b9cec
--- /dev/null
+++ b/mysql-test/suite/sys_vars/r/optimizer_selectivity_sampling_limit_basic.result
@@ -0,0 +1,141 @@
+SET @start_global_value = @@global.optimizer_selectivity_sampling_limit;
+SELECT @start_global_value;
+@start_global_value
+100
+SET @start_session_value = @@session.optimizer_selectivity_sampling_limit;
+SELECT @start_session_value;
+@start_session_value
+100
+'#--------------------FN_DYNVARS_115_01-------------------------#'
+SET @@global.optimizer_selectivity_sampling_limit = DEFAULT;
+SELECT @@global.optimizer_selectivity_sampling_limit;
+@@global.optimizer_selectivity_sampling_limit
+100
+SET @@session.optimizer_selectivity_sampling_limit = DEFAULT;
+SELECT @@session.optimizer_selectivity_sampling_limit;
+@@session.optimizer_selectivity_sampling_limit
+100
+'#--------------------FN_DYNVARS_115_02-------------------------#'
+SET @@global.optimizer_selectivity_sampling_limit = DEFAULT;
+SELECT @@global.optimizer_selectivity_sampling_limit = 100;
+@@global.optimizer_selectivity_sampling_limit = 100
+1
+SET @@session.optimizer_selectivity_sampling_limit = DEFAULT;
+SELECT @@session.optimizer_selectivity_sampling_limit = 100;
+@@session.optimizer_selectivity_sampling_limit = 100
+1
+'#--------------------FN_DYNVARS_115_03-------------------------#'
+SELECT @@global.optimizer_selectivity_sampling_limit;
+@@global.optimizer_selectivity_sampling_limit
+100
+SET @@global.optimizer_selectivity_sampling_limit = 9;
+Warnings:
+Warning	1292	Truncated incorrect optimizer_selectivity_sampling_l value: '9'
+SELECT @@global.optimizer_selectivity_sampling_limit;
+@@global.optimizer_selectivity_sampling_limit
+10
+SET @@global.optimizer_selectivity_sampling_limit = 10;
+SELECT @@global.optimizer_selectivity_sampling_limit;
+@@global.optimizer_selectivity_sampling_limit
+10
+SET @@global.optimizer_selectivity_sampling_limit = 11;
+SELECT @@global.optimizer_selectivity_sampling_limit;
+@@global.optimizer_selectivity_sampling_limit
+11
+SET @@global.optimizer_selectivity_sampling_limit = 7777;
+SELECT @@global.optimizer_selectivity_sampling_limit;
+@@global.optimizer_selectivity_sampling_limit
+7777
+SET @@global.optimizer_selectivity_sampling_limit = 4294967294;
+SELECT @@global.optimizer_selectivity_sampling_limit;
+@@global.optimizer_selectivity_sampling_limit
+4294967294
+SET @@global.optimizer_selectivity_sampling_limit = 4294967295;
+SELECT @@global.optimizer_selectivity_sampling_limit;
+@@global.optimizer_selectivity_sampling_limit
+4294967295
+SET @@global.optimizer_selectivity_sampling_limit = 4294967296;
+Warnings:
+Warning	1292	Truncated incorrect optimizer_selectivity_sampling_l value: '4294967296'
+SELECT @@global.optimizer_selectivity_sampling_limit;
+@@global.optimizer_selectivity_sampling_limit
+4294967295
+'#--------------------FN_DYNVARS_115_04-------------------------#'
+SELECT @@session.optimizer_selectivity_sampling_limit;
+@@session.optimizer_selectivity_sampling_limit
+100
+SET @@session.optimizer_selectivity_sampling_limit = 9;
+Warnings:
+Warning	1292	Truncated incorrect optimizer_selectivity_sampling_l value: '9'
+SELECT @@session.optimizer_selectivity_sampling_limit;
+@@session.optimizer_selectivity_sampling_limit
+10
+SET @@session.optimizer_selectivity_sampling_limit = 10;
+SELECT @@session.optimizer_selectivity_sampling_limit;
+@@session.optimizer_selectivity_sampling_limit
+10
+SET @@session.optimizer_selectivity_sampling_limit = 11;
+SELECT @@session.optimizer_selectivity_sampling_limit;
+@@session.optimizer_selectivity_sampling_limit
+11
+SET @@session.optimizer_selectivity_sampling_limit = 7777;
+SELECT @@session.optimizer_selectivity_sampling_limit;
+@@session.optimizer_selectivity_sampling_limit
+7777
+SET @@session.optimizer_selectivity_sampling_limit = 4294967294;
+SELECT @@session.optimizer_selectivity_sampling_limit;
+@@session.optimizer_selectivity_sampling_limit
+4294967294
+SET @@session.optimizer_selectivity_sampling_limit = 4294967295;
+SELECT @@session.optimizer_selectivity_sampling_limit;
+@@session.optimizer_selectivity_sampling_limit
+4294967295
+SET @@session.optimizer_selectivity_sampling_limit = 4294967296;
+Warnings:
+Warning	1292	Truncated incorrect optimizer_selectivity_sampling_l value: '4294967296'
+SELECT @@session.optimizer_selectivity_sampling_limit;
+@@session.optimizer_selectivity_sampling_limit
+4294967295
+'#------------------FN_DYNVARS_115_05-----------------------#'
+SET @@global.optimizer_selectivity_sampling_limit = ON;
+ERROR 42000: Incorrect argument type to variable 'optimizer_selectivity_sampling_limit'
+SET @@global.optimizer_selectivity_sampling_limit = OFF;
+ERROR 42000: Incorrect argument type to variable 'optimizer_selectivity_sampling_limit'
+SET @@session.optimizer_selectivity_sampling_limit = 65530.34;
+ERROR 42000: Incorrect argument type to variable 'optimizer_selectivity_sampling_limit'
+SET @@session.optimizer_selectivity_sampling_limit = test;
+ERROR 42000: Incorrect argument type to variable 'optimizer_selectivity_sampling_limit'
+'#------------------FN_DYNVARS_115_06-----------------------#'
+SELECT @@global.optimizer_selectivity_sampling_limit = VARIABLE_VALUE 
+FROM INFORMATION_SCHEMA.GLOBAL_VARIABLES 
+WHERE VARIABLE_NAME='optimizer_selectivity_sampling_limit';
+@@global.optimizer_selectivity_sampling_limit = VARIABLE_VALUE
+1
+'#------------------FN_DYNVARS_115_07-----------------------#'
+SELECT @@session.optimizer_selectivity_sampling_limit = VARIABLE_VALUE
+FROM INFORMATION_SCHEMA.SESSION_VARIABLES 
+WHERE VARIABLE_NAME='optimizer_selectivity_sampling_limit';
+@@session.optimizer_selectivity_sampling_limit = VARIABLE_VALUE
+1
+'#---------------------FN_DYNVARS_115_08----------------------#'
+SET @@optimizer_selectivity_sampling_limit = 10;
+SET @@global.optimizer_selectivity_sampling_limit = 30;
+SELECT @@optimizer_selectivity_sampling_limit = @@global.optimizer_selectivity_sampling_limit;
+@@optimizer_selectivity_sampling_limit = @@global.optimizer_selectivity_sampling_limit
+0
+'#---------------------FN_DYNVARS_115_09----------------------#'
+SET @@optimizer_selectivity_sampling_limit = 20;
+SELECT @@optimizer_selectivity_sampling_limit = @@local.optimizer_selectivity_sampling_limit;
+@@optimizer_selectivity_sampling_limit = @@local.optimizer_selectivity_sampling_limit
+1
+SELECT @@local.optimizer_selectivity_sampling_limit = @@session.optimizer_selectivity_sampling_limit;
+@@local.optimizer_selectivity_sampling_limit = @@session.optimizer_selectivity_sampling_limit
+1
+SET @@global.optimizer_selectivity_sampling_limit = @start_global_value;
+SELECT @@global.optimizer_selectivity_sampling_limit;
+@@global.optimizer_selectivity_sampling_limit
+100
+SET @@session.optimizer_selectivity_sampling_limit = @start_session_value;
+SELECT @@session.optimizer_selectivity_sampling_limit;
+@@session.optimizer_selectivity_sampling_limit
+100
diff --git a/mysql-test/suite/sys_vars/r/optimizer_use_condition_selectivity_basic.result b/mysql-test/suite/sys_vars/r/optimizer_use_condition_selectivity_basic.result
index 418c221b5aa..a030bae3750 100644
--- a/mysql-test/suite/sys_vars/r/optimizer_use_condition_selectivity_basic.result
+++ b/mysql-test/suite/sys_vars/r/optimizer_use_condition_selectivity_basic.result
@@ -28,6 +28,12 @@ SELECT @@session.optimizer_use_condition_selectivity = 1;
 SELECT @@global.optimizer_use_condition_selectivity;
 @@global.optimizer_use_condition_selectivity
 1
+SET @@global.optimizer_use_condition_selectivity = 0;
+Warnings:
+Warning	1292	Truncated incorrect optimizer_use_condition_selectiv value: '0'
+SELECT @@global.optimizer_use_condition_selectivity;
+@@global.optimizer_use_condition_selectivity
+1
 SET @@global.optimizer_use_condition_selectivity = 1;
 SELECT @@global.optimizer_use_condition_selectivity;
 @@global.optimizer_use_condition_selectivity
@@ -44,10 +50,26 @@ SET @@global.optimizer_use_condition_selectivity = 4;
 SELECT @@global.optimizer_use_condition_selectivity;
 @@global.optimizer_use_condition_selectivity
 4
+SET @@global.optimizer_use_condition_selectivity = 5;
+SELECT @@global.optimizer_use_condition_selectivity;
+@@global.optimizer_use_condition_selectivity
+5
+SET @@global.optimizer_use_condition_selectivity = 6;
+Warnings:
+Warning	1292	Truncated incorrect optimizer_use_condition_selectiv value: '6'
+SELECT @@global.optimizer_use_condition_selectivity;
+@@global.optimizer_use_condition_selectivity
+5
 '#--------------------FN_DYNVARS_115_04-------------------------#'
 SELECT @@session.optimizer_use_condition_selectivity;
 @@session.optimizer_use_condition_selectivity
 1
+SET @@session.optimizer_use_condition_selectivity = 0;
+Warnings:
+Warning	1292	Truncated incorrect optimizer_use_condition_selectiv value: '0'
+SELECT @@session.optimizer_use_condition_selectivity;
+@@session.optimizer_use_condition_selectivity
+1
 SET @@session.optimizer_use_condition_selectivity = 1;
 SELECT @@session.optimizer_use_condition_selectivity;
 @@session.optimizer_use_condition_selectivity
@@ -64,6 +86,16 @@ SET @@session.optimizer_use_condition_selectivity = 4;
 SELECT @@session.optimizer_use_condition_selectivity;
 @@session.optimizer_use_condition_selectivity
 4
+SET @@session.optimizer_use_condition_selectivity = 5;
+SELECT @@session.optimizer_use_condition_selectivity;
+@@session.optimizer_use_condition_selectivity
+5
+SET @@session.optimizer_use_condition_selectivity = 6;
+Warnings:
+Warning	1292	Truncated incorrect optimizer_use_condition_selectiv value: '6'
+SELECT @@session.optimizer_use_condition_selectivity;
+@@session.optimizer_use_condition_selectivity
+5
 '#------------------FN_DYNVARS_115_05-----------------------#'
 SET @@global.optimizer_use_condition_selectivity = ON;
 ERROR 42000: Incorrect argument type to variable 'optimizer_use_condition_selectivity'
diff --git a/mysql-test/suite/sys_vars/t/optimizer_selectivity_sampling_limit_basic.test b/mysql-test/suite/sys_vars/t/optimizer_selectivity_sampling_limit_basic.test
new file mode 100644
index 00000000000..232ff99db74
--- /dev/null
+++ b/mysql-test/suite/sys_vars/t/optimizer_selectivity_sampling_limit_basic.test
@@ -0,0 +1,154 @@
+
+--source include/load_sysvars.inc
+
+#################################################################
+#      START OF optimizer_selectivity_sampling_limit TESTS       # 
+#################################################################
+
+
+#############################################################
+#                 Save initial value                        #
+#############################################################
+
+SET @start_global_value = @@global.optimizer_selectivity_sampling_limit;
+SELECT @start_global_value;
+SET @start_session_value = @@session.optimizer_selectivity_sampling_limit;
+SELECT @start_session_value;
+
+
+--echo '#--------------------FN_DYNVARS_115_01-------------------------#'
+#########################################################################
+#     Display the DEFAULT value of optimizer_selectivity_sampling_limit  #
+#########################################################################
+
+SET @@global.optimizer_selectivity_sampling_limit = DEFAULT;
+SELECT @@global.optimizer_selectivity_sampling_limit;
+
+SET @@session.optimizer_selectivity_sampling_limit = DEFAULT;
+SELECT @@session.optimizer_selectivity_sampling_limit;
+
+
+--echo '#--------------------FN_DYNVARS_115_02-------------------------#'
+#########################################################################
+#     Check the DEFAULT value of optimizer_selectivity_sampling_limit    #
+#########################################################################
+
+SET @@global.optimizer_selectivity_sampling_limit = DEFAULT;
+SELECT @@global.optimizer_selectivity_sampling_limit = 100;
+
+SET @@session.optimizer_selectivity_sampling_limit = DEFAULT;
+SELECT @@session.optimizer_selectivity_sampling_limit = 100;
+
+
+--echo '#--------------------FN_DYNVARS_115_03-------------------------#'
+#############################################################################################
+# Change the value of optimizer_selectivity_sampling_limit to a valid value for GLOBAL Scope #
+#############################################################################################
+
+SELECT @@global.optimizer_selectivity_sampling_limit;
+SET @@global.optimizer_selectivity_sampling_limit = 9;
+SELECT @@global.optimizer_selectivity_sampling_limit;
+SET @@global.optimizer_selectivity_sampling_limit = 10;
+SELECT @@global.optimizer_selectivity_sampling_limit;
+SET @@global.optimizer_selectivity_sampling_limit = 11;
+SELECT @@global.optimizer_selectivity_sampling_limit;
+SET @@global.optimizer_selectivity_sampling_limit = 7777;
+SELECT @@global.optimizer_selectivity_sampling_limit;
+SET @@global.optimizer_selectivity_sampling_limit = 4294967294;
+SELECT @@global.optimizer_selectivity_sampling_limit;
+SET @@global.optimizer_selectivity_sampling_limit = 4294967295;
+SELECT @@global.optimizer_selectivity_sampling_limit;
+SET @@global.optimizer_selectivity_sampling_limit = 4294967296;
+SELECT @@global.optimizer_selectivity_sampling_limit;
+
+
+--echo '#--------------------FN_DYNVARS_115_04-------------------------#'
+#############################################################################################
+# Change the value of optimizer_selectivity_sampling_limit to a valid value for SESSION Scope#
+#############################################################################################
+ 
+SELECT @@session.optimizer_selectivity_sampling_limit;
+SET @@session.optimizer_selectivity_sampling_limit = 9;
+SELECT @@session.optimizer_selectivity_sampling_limit;
+SET @@session.optimizer_selectivity_sampling_limit = 10;
+SELECT @@session.optimizer_selectivity_sampling_limit;
+SET @@session.optimizer_selectivity_sampling_limit = 11;
+SELECT @@session.optimizer_selectivity_sampling_limit;
+SET @@session.optimizer_selectivity_sampling_limit = 7777;
+SELECT @@session.optimizer_selectivity_sampling_limit;
+SET @@session.optimizer_selectivity_sampling_limit = 4294967294;
+SELECT @@session.optimizer_selectivity_sampling_limit;
+SET @@session.optimizer_selectivity_sampling_limit = 4294967295;
+SELECT @@session.optimizer_selectivity_sampling_limit;
+SET @@session.optimizer_selectivity_sampling_limit = 4294967296;
+SELECT @@session.optimizer_selectivity_sampling_limit;
+
+
+--echo '#------------------FN_DYNVARS_115_05-----------------------#'
+###############################################################################
+# Change the value of optimizer_selectivity_sampling_limit to an invalid value #
+##############################################################################
+
+--Error ER_WRONG_TYPE_FOR_VAR
+SET @@global.optimizer_selectivity_sampling_limit = ON;
+--Error ER_WRONG_TYPE_FOR_VAR
+SET @@global.optimizer_selectivity_sampling_limit = OFF;
+--Error ER_WRONG_TYPE_FOR_VAR
+SET @@session.optimizer_selectivity_sampling_limit = 65530.34;
+--Error ER_WRONG_TYPE_FOR_VAR
+SET @@session.optimizer_selectivity_sampling_limit = test;
+
+--echo '#------------------FN_DYNVARS_115_06-----------------------#'
+####################################################################
+#   Check if the value in GLOBAL Table matches value in variable   #
+####################################################################
+
+
+SELECT @@global.optimizer_selectivity_sampling_limit = VARIABLE_VALUE 
+FROM INFORMATION_SCHEMA.GLOBAL_VARIABLES 
+WHERE VARIABLE_NAME='optimizer_selectivity_sampling_limit';
+
+--echo '#------------------FN_DYNVARS_115_07-----------------------#'
+####################################################################
+#  Check if the value in SESSION Table matches value in variable   #
+####################################################################
+
+SELECT @@session.optimizer_selectivity_sampling_limit = VARIABLE_VALUE
+FROM INFORMATION_SCHEMA.SESSION_VARIABLES 
+WHERE VARIABLE_NAME='optimizer_selectivity_sampling_limit';
+
+
+--echo '#---------------------FN_DYNVARS_115_08----------------------#'
+###############################################################################
+#  Check if global and session variable are independent of each other         #
+###############################################################################
+
+SET @@optimizer_selectivity_sampling_limit = 10;
+SET @@global.optimizer_selectivity_sampling_limit = 30;
+SELECT @@optimizer_selectivity_sampling_limit = @@global.optimizer_selectivity_sampling_limit;
+
+
+--echo '#---------------------FN_DYNVARS_115_09----------------------#'
+###############################################################################
+#    Check if accessing variable with SESSION,LOCAL and without SCOPE points  #
+#    to same session variable                                                 #
+###############################################################################
+
+SET @@optimizer_selectivity_sampling_limit = 20;
+SELECT @@optimizer_selectivity_sampling_limit = @@local.optimizer_selectivity_sampling_limit;
+SELECT @@local.optimizer_selectivity_sampling_limit = @@session.optimizer_selectivity_sampling_limit;
+
+
+####################################
+#     Restore initial value        #
+####################################
+
+SET @@global.optimizer_selectivity_sampling_limit = @start_global_value;
+SELECT @@global.optimizer_selectivity_sampling_limit;
+SET @@session.optimizer_selectivity_sampling_limit = @start_session_value;
+SELECT @@session.optimizer_selectivity_sampling_limit;
+
+########################################################################
+#                END OF optimizer_selectivity_sampling_limit TESTS     #
+########################################################################
+
diff --git a/mysql-test/suite/sys_vars/t/optimizer_use_condition_selectivity_basic.test b/mysql-test/suite/sys_vars/t/optimizer_use_condition_selectivity_basic.test
index 58a1af4b975..c409abd0d1b 100644
--- a/mysql-test/suite/sys_vars/t/optimizer_use_condition_selectivity_basic.test
+++ b/mysql-test/suite/sys_vars/t/optimizer_use_condition_selectivity_basic.test
@@ -45,6 +45,8 @@ SELECT @@session.optimizer_use_condition_selectivity = 1;
 # Change the value of optimizer_use_condition_selectivity to a valid value for GLOBAL Scope #
 #############################################################################################
 
+SELECT @@global.optimizer_use_condition_selectivity;
+SET @@global.optimizer_use_condition_selectivity = 0;
 SELECT @@global.optimizer_use_condition_selectivity;
 SET @@global.optimizer_use_condition_selectivity = 1;
 SELECT @@global.optimizer_use_condition_selectivity;
@@ -54,6 +56,10 @@ SET @@global.optimizer_use_condition_selectivity = 3;
 SELECT @@global.optimizer_use_condition_selectivity;
 SET @@global.optimizer_use_condition_selectivity = 4;
 SELECT @@global.optimizer_use_condition_selectivity;
+SET @@global.optimizer_use_condition_selectivity = 5;
+SELECT @@global.optimizer_use_condition_selectivity;
+SET @@global.optimizer_use_condition_selectivity = 6;
+SELECT @@global.optimizer_use_condition_selectivity;
 
 
 --echo '#--------------------FN_DYNVARS_115_04-------------------------#'
@@ -61,6 +67,8 @@ SELECT @@global.optimizer_use_condition_selectivity;
 # Change the value of optimizer_use_condition_selectivity to a valid value for SESSION Scope#
 #############################################################################################
  
+SELECT @@session.optimizer_use_condition_selectivity;
+SET @@session.optimizer_use_condition_selectivity = 0;
 SELECT @@session.optimizer_use_condition_selectivity;
 SET @@session.optimizer_use_condition_selectivity = 1;
 SELECT @@session.optimizer_use_condition_selectivity;
@@ -70,6 +78,10 @@ SET @@session.optimizer_use_condition_selectivity = 3;
 SELECT @@session.optimizer_use_condition_selectivity;
 SET @@session.optimizer_use_condition_selectivity = 4;
 SELECT @@session.optimizer_use_condition_selectivity;
+SET @@session.optimizer_use_condition_selectivity = 5;
+SELECT @@session.optimizer_use_condition_selectivity;
+SET @@session.optimizer_use_condition_selectivity = 6;
+SELECT @@session.optimizer_use_condition_selectivity;
 
 
 --echo '#------------------FN_DYNVARS_115_05-----------------------#'
diff --git a/mysql-test/t/selectivity.test b/mysql-test/t/selectivity.test
index 56908e50c65..47f62365816 100644
--- a/mysql-test/t/selectivity.test
+++ b/mysql-test/t/selectivity.test
@@ -56,6 +56,64 @@ customer, lineitem, nation, orders, part, partsupp, region, supplier;
 --enable_result_log
 --enable_query_log
 
+--echo === Q2 ===
+
+set optimizer_use_condition_selectivity=5;
+explain extended
+select
+	s_acctbal, s_name, n_name, p_partkey, p_mfgr, s_address, s_phone, s_comment
+from
+	part, supplier, partsupp, nation, region
+where
+	p_partkey = ps_partkey
+	and s_suppkey = ps_suppkey
+	and p_size = 9
+	and p_type like '%TIN'
+	and s_nationkey = n_nationkey
+	and n_regionkey = r_regionkey
+	and r_name = 'ASIA'
+	and ps_supplycost = (
+		select
+			min(ps_supplycost)
+		from
+			partsupp, supplier, nation, region
+		where
+			p_partkey = ps_partkey
+			and s_suppkey = ps_suppkey
+			and s_nationkey = n_nationkey
+			and n_regionkey = r_regionkey
+			and r_name = 'ASIA'
+	)
+order by
+	s_acctbal desc, n_name, s_name, p_partkey;
+set optimizer_use_condition_selectivity=4;
+explain extended
+select
+	s_acctbal, s_name, n_name, p_partkey, p_mfgr, s_address, s_phone, s_comment
+from
+	part, supplier, partsupp, nation, region
+where
+	p_partkey = ps_partkey
+	and s_suppkey = ps_suppkey
+	and p_size = 9
+	and p_type like '%TIN'
+	and s_nationkey = n_nationkey
+	and n_regionkey = r_regionkey
+	and r_name = 'ASIA'
+	and ps_supplycost = (
+		select
+			min(ps_supplycost)
+		from
+			partsupp, supplier, nation, region
+		where
+			p_partkey = ps_partkey
+			and s_suppkey = ps_suppkey
+			and s_nationkey = n_nationkey
+			and n_regionkey = r_regionkey
+			and r_name = 'ASIA'
+	)
+order by
+	s_acctbal desc, n_name, s_name, p_partkey;
 
 --echo === Q15 ===
 
@@ -230,7 +288,6 @@ flush table nation;
 eval EXPLAIN EXTENDED $Q20;
 eval $Q20; 
 
-
 DROP DATABASE dbt3_s001;
 
 set histogram_type=@save_histogram_type;
@@ -619,5 +676,36 @@ DROP TABLE t1,t2;
 
 set use_stat_tables=@save_use_stat_tables;
 
+--echo #
+--echo # Bug mdev-4406: range condition for non-nullable column   
+--echo #                when optimizer_use_condition_selectivity=3
+--echo #
+
+create table t1 (a int not null);
+insert into t1 values
+  (7), (6), (4), (9), (1), (5), (2), (1), (3), (8);
+
+set use_stat_tables='preferably';
+
+analyze table t1;
+flush table t1;
+
+set optimizer_use_condition_selectivity=3;
+
+select count(*) from t1 where a between 5 and 7;
+explain extended select * from t1 where a between 5 and 7;
+
+alter table t1 change column a a int;
+analyze table t1;
+flush table t1;
+
+explain extended select * from t1 where a between 5 and 7;
+
+set optimizer_use_condition_selectivity=@save_optimizer_use_condition_selectivity;
+
+drop table t1;
+
+set use_stat_tables=@save_use_stat_tables;
+
 
 set use_stat_tables=@save_use_stat_tables;
diff --git a/mysql-test/t/statistics.test b/mysql-test/t/statistics.test
index b2a052fd3e8..a6ecffaaff2 100644
--- a/mysql-test/t/statistics.test
+++ b/mysql-test/t/statistics.test
@@ -564,9 +564,27 @@ SELECT UPPER(db_name), UPPER(table_name),
        index_name, prefix_arity, avg_frequency
   FROM mysql.index_stats;
 
-use test;
+use world;
+set use_stat_tables='preferably';
+--disable_result_log
+set histogram_size=100;
+set histogram_type='SINGLE_PREC_HB';
+ANALYZE TABLE CountryLanguage;
+set histogram_size=254;
+set histogram_type='DOUBLE_PREC_HB';
+ANALYZE TABLE City;
+FLUSH TABLES;
+--enable_result_log
 
+--query_vertical select UPPER(db_name),UPPER(table_name),UPPER(column_name),min_value,max_value,nulls_ratio,avg_length,avg_frequency,hist_size,hist_type,hex(histogram),decode_histogram(histogram,hist_type) from mysql.column_stats where UPPER(db_name)='WORLD' and UPPER(table_name)='COUNTRYLANGUAGE' and UPPER(column_name) = 'PERCENTAGE';
+--query_vertical select UPPER(db_name),UPPER(table_name),UPPER(column_name),min_value,max_value,nulls_ratio,avg_length,avg_frequency,hist_size,hist_type,hex(histogram),decode_histogram(histogram,hist_type) from mysql.column_stats where UPPER(db_name)='WORLD' and UPPER(table_name)='CITY' and UPPER(column_name) = 'POPULATION';
+
+set histogram_type=default;
+set histogram_size=default;
+
+use test;
 DROP DATABASE world;
+
 SELECT UPPER(db_name), UPPER(table_name), cardinality
   FROM mysql.table_stats;
 SELECT UPPER(db_name), UPPER(table_name), 
diff --git a/sql/item.h b/sql/item.h
index 6f1b6801669..b3d08011a39 100644
--- a/sql/item.h
+++ b/sql/item.h
@@ -548,6 +548,14 @@ typedef bool (Item::*Item_analyzer) (uchar **argp);
 typedef Item* (Item::*Item_transformer) (uchar *arg);
 typedef void (*Cond_traverser) (const Item *item, void *arg);
 
+struct st_cond_statistic;
+
+struct find_selective_predicates_list_processor_data
+{
+  TABLE *table;
+  List<st_cond_statistic> list;
+};
+
 class Item_equal;
 class COND_EQUAL;
 
@@ -1108,6 +1116,11 @@ public:
     return (this->*processor)(arg);
   }
 
+  virtual bool walk_top_and(Item_processor processor, uchar *arg)
+  {
+    return (this->*processor)(arg);
+  }
+
   virtual Item* transform(Item_transformer transformer, uchar *arg);
 
   /*
@@ -1174,6 +1187,8 @@ public:
     return FALSE;
   }
   virtual bool exists2in_processor(uchar *opt_arg) { return 0; }
+  virtual bool find_selective_predicates_list_processor(uchar *opt_arg)
+  { return 0; }
 
   /* To call bool function for all arguments */
   struct bool_func_call_args
diff --git a/sql/item_cmpfunc.cc b/sql/item_cmpfunc.cc
index b5b143a2448..7ca85a72cfa 100644
--- a/sql/item_cmpfunc.cc
+++ b/sql/item_cmpfunc.cc
@@ -4428,6 +4428,16 @@ bool Item_cond::walk(Item_processor processor, bool walk_subquery, uchar *arg)
   return Item_func::walk(processor, walk_subquery, arg);
 }
 
+bool Item_cond_and::walk_top_and(Item_processor processor, uchar *arg)
+{
+  List_iterator_fast<Item> li(list);
+  Item *item;
+  while ((item= li++))
+    if (item->walk_top_and(processor, arg))
+      return 1;
+  return Item_cond::walk_top_and(processor, arg);
+}
+
 
 /**
   Transform an Item_cond object with a transformer callback function.
@@ -4940,6 +4950,7 @@ bool Item_func_like::fix_fields(THD *thd, Item **ref)
         turboBM_compute_bad_character_shifts();
         DBUG_PRINT("info",("done"));
       }
+      use_sampling= ((*first == wild_many || *first == wild_one) && len > 2);
     }
   }
   return FALSE;
@@ -4951,6 +4962,28 @@ void Item_func_like::cleanup()
   Item_bool_func2::cleanup();
 }
 
+
+bool Item_func_like::find_selective_predicates_list_processor(uchar *arg)
+{
+  find_selective_predicates_list_processor_data *data=
+    (find_selective_predicates_list_processor_data *) arg;
+  if (use_sampling && used_tables() == data->table->map)
+  {
+    COND_STATISTIC *stat= (COND_STATISTIC *)sql_alloc(sizeof(COND_STATISTIC));
+    if (!stat)
+      return TRUE;
+    stat->cond= this;
+    Item *arg0= args[0]->real_item();
+    if (args[1]->const_item() && arg0->type() == FIELD_ITEM)
+      stat->field_arg= ((Item_field *)arg0)->field;
+    else
+      stat->field_arg= NULL;
+    data->list.push_back(stat);
+  }
+  return FALSE;
+}
+
+
 /**
   @brief Compile regular expression.
 
diff --git a/sql/item_cmpfunc.h b/sql/item_cmpfunc.h
index 81598ba96c8..ab4219564fe 100644
--- a/sql/item_cmpfunc.h
+++ b/sql/item_cmpfunc.h
@@ -1487,8 +1487,9 @@ class Item_func_like :public Item_bool_func2
   enum { alphabet_size = 256 };
 
   Item *escape_item;
-  
+
   bool escape_used_in_parsing;
+  bool use_sampling;
 
 public:
   int escape;
@@ -1496,7 +1497,7 @@ public:
   Item_func_like(Item *a,Item *b, Item *escape_arg, bool escape_used)
     :Item_bool_func2(a,b), canDoTurboBM(FALSE), pattern(0), pattern_len(0), 
      bmGs(0), bmBc(0), escape_item(escape_arg),
-     escape_used_in_parsing(escape_used) {}
+     escape_used_in_parsing(escape_used), use_sampling(0) {}
   longlong val_int();
   enum Functype functype() const { return LIKE_FUNC; }
   optimize_type select_optimize() const;
@@ -1504,6 +1505,8 @@ public:
   const char *func_name() const { return "like"; }
   bool fix_fields(THD *thd, Item **ref);
   void cleanup();
+
+  bool find_selective_predicates_list_processor(uchar *arg);
 };
 
 
@@ -1914,6 +1917,7 @@ public:
   Item *neg_transformer(THD *thd);
   void mark_as_condition_AND_part(TABLE_LIST *embedding);
   virtual uint exists2in_reserved_items() { return list.elements; };
+  bool walk_top_and(Item_processor processor, uchar *arg);
 };
 
 inline bool is_cond_and(Item *item)
diff --git a/sql/item_create.cc b/sql/item_create.cc
index c1cefed6f8b..ce4dc7ced8f 100644
--- a/sql/item_create.cc
+++ b/sql/item_create.cc
@@ -614,6 +614,19 @@ protected:
 };
 
 
+class Create_func_decode_histogram : public Create_func_arg2
+{
+public:
+  Item *create_2_arg(THD *thd, Item *arg1, Item *arg2);
+
+  static Create_func_decode_histogram s_singleton;
+
+protected:
+  Create_func_decode_histogram() {}
+  virtual ~Create_func_decode_histogram() {}
+};
+
+
 class Create_func_concat_ws : public Create_native_func
 {
 public:
@@ -3231,6 +3244,13 @@ Create_func_concat::create_native(THD *thd, LEX_STRING name,
   return new (thd->mem_root) Item_func_concat(*item_list);
 }
 
+Create_func_decode_histogram Create_func_decode_histogram::s_singleton;
+
+Item *
+Create_func_decode_histogram::create_2_arg(THD *thd, Item *arg1, Item *arg2)
+{
+  return new (thd->mem_root) Item_func_decode_histogram(arg1, arg2);
+}
 
 Create_func_concat_ws Create_func_concat_ws::s_singleton;
 
@@ -5377,6 +5397,7 @@ static Native_func_registry func_array[] =
   { { C_STRING_WITH_LEN("DAYOFYEAR") }, BUILDER(Create_func_dayofyear)},
   { { C_STRING_WITH_LEN("DECODE") }, BUILDER(Create_func_decode)},
   { { C_STRING_WITH_LEN("DEGREES") }, BUILDER(Create_func_degrees)},
+  { { C_STRING_WITH_LEN("DECODE_HISTOGRAM") }, BUILDER(Create_func_decode_histogram)},
   { { C_STRING_WITH_LEN("DES_DECRYPT") }, BUILDER(Create_func_des_decrypt)},
   { { C_STRING_WITH_LEN("DES_ENCRYPT") }, BUILDER(Create_func_des_encrypt)},
   { { C_STRING_WITH_LEN("DIMENSION") }, GEOM_BUILDER(Create_func_dimension)},
diff --git a/sql/item_strfunc.cc b/sql/item_strfunc.cc
index 532c6d7ff08..e5c3c48b3bb 100644
--- a/sql/item_strfunc.cc
+++ b/sql/item_strfunc.cc
@@ -60,6 +60,7 @@ C_MODE_START
 C_MODE_END
 #include "sql_show.h"                           // append_identifier
 #include <sql_repl.h>
+#include "sql_statistics.h"
 
 /**
    @todo Remove this. It is not safe to use a shared String object.
@@ -471,6 +472,82 @@ void Item_func_aes_decrypt::fix_length_and_dec()
    set_persist_maybe_null(1);
 }
 
+///////////////////////////////////////////////////////////////////////////////
+
+
+const char *histogram_types[] =
+           {"SINGLE_PREC_HB", "DOUBLE_PREC_HB", 0};
+static TYPELIB hystorgam_types_typelib=
+  { array_elements(histogram_types),
+    "histogram_types",
+    histogram_types, NULL};
+const char *representation_by_type[]= {"%.3f", "%.5f"};
+
+String *Item_func_decode_histogram::val_str(String *str)
+{
+  DBUG_ASSERT(fixed == 1);
+  char buff[STRING_BUFFER_USUAL_SIZE];
+  String *res, tmp(buff, sizeof(buff), &my_charset_bin);
+  int type;
+
+  tmp.length(0);
+  if (!(res= args[1]->val_str(&tmp)) ||
+      (type= find_type(res->c_ptr_safe(),
+                       &hystorgam_types_typelib, MYF(0))) <= 0)
+  {
+    null_value= 1;
+    return 0;
+  }
+  type--;
+
+  tmp.length(0);
+  if (!(res= args[0]->val_str(&tmp)))
+  {
+    null_value= 1;
+    return 0;
+  }
+  if (type == DOUBLE_PREC_HB && res->length() % 2 != 0)
+    res->length(res->length() - 1); // one byte is unused
+
+  double prev= 0.0;
+  uint i;
+  str->length(0);
+  char numbuf[32];
+  const uchar *p= (uchar*)res->c_ptr();
+  for (i= 0; i < res->length(); i++)
+  {
+    double val;
+    switch (type)
+    {
+    case SINGLE_PREC_HB:
+      val= p[i] / ((double)((1 << 8) - 1));
+      break;
+    case DOUBLE_PREC_HB:
+      val= ((uint16 *)(p + i))[0] / ((double)((1 << 16) - 1));
+      i++;
+      break;
+    default:
+      val= 0;
+      DBUG_ASSERT(0);
+    }
+    /* show delta with previous value */
+    int size= my_snprintf(numbuf, sizeof(numbuf),
+                          representation_by_type[type], val - prev);
+    str->append(numbuf, size);
+    str->append(",");
+    prev= val;
+  }
+  /* show delta with max */
+  int size= my_snprintf(numbuf, sizeof(numbuf),
+                        representation_by_type[type], 1.0 - prev);
+  str->append(numbuf, size);
+
+  null_value=0;
+  return str;
+}
+
+
+///////////////////////////////////////////////////////////////////////////////
 
 /**
   Concatenate args with the following premises:
diff --git a/sql/item_strfunc.h b/sql/item_strfunc.h
index 89d7fa67f6b..169da25e826 100644
--- a/sql/item_strfunc.h
+++ b/sql/item_strfunc.h
@@ -143,6 +143,22 @@ public:
   const char *func_name() const { return "concat"; }
 };
 
+class Item_func_decode_histogram :public Item_str_func
+{
+  String tmp_value;
+public:
+  Item_func_decode_histogram(Item *a, Item *b)
+    :Item_str_func(a, b) {}
+  String *val_str(String *);
+  void fix_length_and_dec()
+  {
+    collation.set(system_charset_info);
+    max_length= MAX_BLOB_WIDTH;
+    set_persist_maybe_null(1);
+  }
+  const char *func_name() const { return "decode_histogram"; }
+};
+
 class Item_func_concat_ws :public Item_str_func
 {
   String tmp_value;
diff --git a/sql/opt_range.cc b/sql/opt_range.cc
index 0087e73072c..f20e3ed7739 100644
--- a/sql/opt_range.cc
+++ b/sql/opt_range.cc
@@ -3530,7 +3530,74 @@ bool calculate_cond_selectivity_for_table(THD *thd, TABLE *table, Item *cond)
         }
       } 
     }
-  } 
+  }
+
+  /* Calculate selectivity of probably highly selective predicates */
+  ulong check_rows=
+    min(thd->variables.optimizer_selectivity_sampling_limit,
+        (ulong) (table_records * SELECTIVITY_SAMPLING_SHARE));
+  if (cond && check_rows > SELECTIVITY_SAMPLING_THRESHOLD &&
+      thd->variables.optimizer_use_condition_selectivity > 4)
+  {
+    find_selective_predicates_list_processor_data *dt=
+      (find_selective_predicates_list_processor_data *)
+      alloc_root(thd->mem_root,
+                 sizeof(find_selective_predicates_list_processor_data));
+    if (!dt)
+      DBUG_RETURN(TRUE);
+    dt->list.empty();
+    dt->table= table;
+    if (cond->walk(&Item::find_selective_predicates_list_processor, 0,
+                    (uchar*) dt))
+      DBUG_RETURN(TRUE);
+    if (dt->list.elements > 0)
+    {
+      check_rows= check_selectivity(thd, check_rows, table, &dt->list);
+      if (check_rows > SELECTIVITY_SAMPLING_THRESHOLD)
+      {
+        COND_STATISTIC *stat;
+        List_iterator_fast<COND_STATISTIC> it(dt->list);
+        double examined_rows= check_rows;
+        while ((stat= it++))
+        {
+          if (!stat->positive)
+          {
+            DBUG_PRINT("info", ("To avoid 0 assigned 1 to the counter"));
+            stat->positive= 1; // avoid 0
+          }
+          DBUG_PRINT("info", ("The predicate selectivity : %g",
+                              (double)stat->positive / examined_rows));
+          double selectivity= ((double)stat->positive) / examined_rows;
+          table->cond_selectivity*= selectivity;
+          /*
+            If a field is involved then we register its selectivity in case
+            there in an equality with the field.
+            For example in case
+            t1.a LIKE "%bla%" and t1.a = t2.b
+            the selectivity we have found could be used also for t2.
+          */
+          if (stat->field_arg)
+          {
+            stat->field_arg->cond_selectivity*= selectivity;
+
+            if (stat->field_arg->next_equal_field)
+            {
+              for (Field *next_field= stat->field_arg->next_equal_field;
+                   next_field != stat->field_arg;
+                   next_field= next_field->next_equal_field)
+              {
+                next_field->cond_selectivity*= selectivity;
+                next_field->table->cond_selectivity*= selectivity;
+              }
+            }
+          }
+        }
+
+      }
+      /* This list and its elements put to mem_root so should not be freed */
+      table->cond_selectivity_sampling_explain= &dt->list;
+    }
+  }
 
   DBUG_RETURN(FALSE);
 }
diff --git a/sql/opt_range.h b/sql/opt_range.h
index d98bf1186e8..ddaa5c5e59a 100644
--- a/sql/opt_range.h
+++ b/sql/opt_range.h
@@ -1051,4 +1051,11 @@ void store_key_image_to_rec(Field *field, uchar *ptr, uint len);
 
 extern String null_string;
 
+/* check this number of rows (default value) */
+#define SELECTIVITY_SAMPLING_LIMIT 100
+/* but no more then this part of table (10%) */
+#define SELECTIVITY_SAMPLING_SHARE 0.10
+/* do not check if we are going check less then this number of records */
+#define SELECTIVITY_SAMPLING_THRESHOLD 10
+
 #endif
diff --git a/sql/sql_class.h b/sql/sql_class.h
index fc931820dcd..5ae777fe817 100644
--- a/sql/sql_class.h
+++ b/sql/sql_class.h
@@ -517,6 +517,7 @@ typedef struct system_variables
   ulong net_write_timeout;
   ulong optimizer_prune_level;
   ulong optimizer_search_depth;
+  ulong optimizer_selectivity_sampling_limit;
   ulong optimizer_use_condition_selectivity;
   ulong use_stat_tables;
   ulong histogram_size;
diff --git a/sql/sql_select.cc b/sql/sql_select.cc
index 9f9442a624c..c19c7aa95a7 100644
--- a/sql/sql_select.cc
+++ b/sql/sql_select.cc
@@ -23935,6 +23935,78 @@ uint get_index_for_order(ORDER *order, TABLE *table, SQL_SELECT *select,
   return MAX_KEY;
 }
 
+/*
+  Count how much times conditions are true for several first rows of the table
+
+  @param thd             thread handle
+  @param rows_to_read    how much rows to check
+  @param table           table which should be checked
+  @conds conds           list of conditions and countars for them
+
+  @return number of really checked rows or 0 in case of error or empty table
+*/
+
+ulong check_selectivity(THD *thd,
+                        ulong rows_to_read,
+                        TABLE *table,
+                        List<COND_STATISTIC> *conds)
+{
+  ulong count= 0;
+  COND_STATISTIC *cond;
+  List_iterator_fast<COND_STATISTIC> it(*conds);
+  handler *file= table->file;
+  uchar *record= table->record[0];
+  int error= 0;
+  DBUG_ENTER("check_selectivity");
+
+  DBUG_ASSERT(rows_to_read > 0);
+  while ((cond= it++))
+  {
+    DBUG_ASSERT(cond->cond);
+    DBUG_ASSERT(cond->cond->used_tables() == table->map);
+    cond->positive= 0;
+  }
+  it.rewind();
+
+  if (file->ha_rnd_init_with_error(1))
+    DBUG_RETURN(0);
+  do
+  {
+    error= file->ha_rnd_next(record);
+
+    if (thd->killed)
+    {
+      thd->send_kill_message();
+      count= 0;
+      goto err;
+    }
+    if (error)
+    {
+      if (error == HA_ERR_RECORD_DELETED)
+        continue;
+      if (error == HA_ERR_END_OF_FILE)
+	break;
+      goto err;
+    }
+
+    count++;
+    while ((cond= it++))
+    {
+      if (cond->cond->val_bool())
+        cond->positive++;
+    }
+    it.rewind();
+
+  } while (count < rows_to_read);
+
+  file->ha_rnd_end();
+  DBUG_RETURN(count);
+
+err:
+  DBUG_PRINT("error", ("error %d", error));
+  file->ha_rnd_end();
+  DBUG_RETURN(0);
+}
 
 /**
   @} (end of group Query_Optimizer)
diff --git a/sql/sql_select.h b/sql/sql_select.h
index 22880a251aa..d1f11b8ae71 100644
--- a/sql/sql_select.h
+++ b/sql/sql_select.h
@@ -1846,4 +1846,17 @@ void setup_tmp_table_column_bitmaps(TABLE *table, uchar *bitmaps);
 double prev_record_reads(POSITION *positions, uint idx, table_map found_ref);
 void fix_list_after_tbl_changes(SELECT_LEX *new_parent, List<TABLE_LIST> *tlist);
 
+struct st_cond_statistic
+{
+  Item *cond;
+  Field *field_arg;
+  ulong positive;
+};
+typedef struct st_cond_statistic COND_STATISTIC;
+
+ulong check_selectivity(THD *thd,
+                        ulong rows_to_read,
+                        TABLE *table,
+                        List<COND_STATISTIC> *conds);
+
 #endif /* SQL_SELECT_INCLUDED */
diff --git a/sql/sql_statistics.cc b/sql/sql_statistics.cc
index 4df4b4d257d..f355f2c7760 100644
--- a/sql/sql_statistics.cc
+++ b/sql/sql_statistics.cc
@@ -3520,7 +3520,7 @@ double get_column_range_cardinality(Field *field,
     {
       double sel, min_mp_pos, max_mp_pos;
 
-      if (min_endp && !min_endp->key[0])
+      if (min_endp && !(field->null_ptr && min_endp->key[0]))
       {
         store_key_image_to_rec(field, (uchar *) min_endp->key,
                                min_endp->length);
diff --git a/sql/sys_vars.cc b/sql/sys_vars.cc
index ae7f4fa7335..8c5a6c92a6b 100644
--- a/sql/sys_vars.cc
+++ b/sql/sys_vars.cc
@@ -59,6 +59,7 @@
 #endif /* WITH_PERFSCHEMA_STORAGE_ENGINE */
 #include "threadpool.h"
 #include "sql_repl.h"
+#include "opt_range.h"
 
 /*
   The rule for this file: everything should be 'static'. When a sys_var
@@ -1663,6 +1664,14 @@ static Sys_var_ulong Sys_optimizer_prune_level(
        SESSION_VAR(optimizer_prune_level), CMD_LINE(REQUIRED_ARG),
        VALID_RANGE(0, 1), DEFAULT(1), BLOCK_SIZE(1));
 
+static Sys_var_ulong Sys_optimizer_selectivity_sampling_limit(
+       "optimizer_selectivity_sampling_limit",
+       "Controls number of record samples to check condition selectivity",
+       SESSION_VAR(optimizer_selectivity_sampling_limit),
+       CMD_LINE(REQUIRED_ARG),
+       VALID_RANGE(SELECTIVITY_SAMPLING_THRESHOLD, UINT_MAX),
+       DEFAULT(SELECTIVITY_SAMPLING_LIMIT), BLOCK_SIZE(1));
+
 static Sys_var_ulong Sys_optimizer_use_condition_selectivity(
        "optimizer_use_condition_selectivity",
        "Controls selectivity of which conditions the optimizer takes into "
@@ -1678,9 +1687,11 @@ static Sys_var_ulong Sys_optimizer_use_condition_selectivity(
        "not backed by any index to calculate the cardinality of a partial join, "
        "4 - use histograms to calculate selectivity of range conditions that "
        "are not backed by any index to calculate the cardinality of "
-       "a partial join.",
+       "a partial join."
+       "5 - additionally use selectivity of certain non-range predicates "
+       "calculated on record samples",
        SESSION_VAR(optimizer_use_condition_selectivity), CMD_LINE(REQUIRED_ARG),
-       VALID_RANGE(1, 4), DEFAULT(1), BLOCK_SIZE(1));
+       VALID_RANGE(1, 5), DEFAULT(1), BLOCK_SIZE(1));
 
 /** Warns about deprecated value 63 */
 static bool fix_optimizer_search_depth(sys_var *self, THD *thd,
@@ -4138,8 +4149,7 @@ static Sys_var_ulong Sys_histogram_size(
        SESSION_VAR(histogram_size), CMD_LINE(REQUIRED_ARG),
        VALID_RANGE(0, 255), DEFAULT(0), BLOCK_SIZE(1));
 
-const char *histogram_types[] =
-           {"SINGLE_PREC_HB", "DOUBLE_PREC_HB", 0};
+extern const char *histogram_types[];
 static Sys_var_enum Sys_histogram_type(
        "histogram_type",
        "Specifies type of the histograms created by ANALYZE. "
diff --git a/sql/table.cc b/sql/table.cc
index 6ee21eb22d8..2f867eb7dc4 100644
--- a/sql/table.cc
+++ b/sql/table.cc
@@ -3891,6 +3891,7 @@ void TABLE::init(THD *thd, TABLE_LIST *tl)
   reginfo.impossible_range= 0;
   created= TRUE;
   cond_selectivity= 1.0;
+  cond_selectivity_sampling_explain= NULL;
 
   /* Catch wrong handling of the auto_increment_field_not_null. */
   DBUG_ASSERT(!auto_increment_field_not_null);
diff --git a/sql/table.h b/sql/table.h
index e721d60f892..af79bffd437 100644
--- a/sql/table.h
+++ b/sql/table.h
@@ -1038,6 +1038,8 @@ enum index_hint_type
   INDEX_HINT_FORCE
 };
 
+struct st_cond_statistic;
+
 #define      CHECK_ROW_FOR_NULLS_TO_REJECT   (1 << 0)
 #define      REJECT_ROW_DUE_TO_NULL_FIELDS   (1 << 1)
 
@@ -1163,6 +1165,7 @@ public:
   ha_rows       quick_condition_rows;
 
   double cond_selectivity;
+  List<st_cond_statistic> *cond_selectivity_sampling_explain;
 
   table_map	map;                    /* ID bit of table (1,2,4,8,16...) */