diff --git a/dbms/src/Functions/FunctionsConversion.h b/dbms/src/Functions/FunctionsConversion.h
index bd7cb6396ec..e7c4edcda5b 100644
--- a/dbms/src/Functions/FunctionsConversion.h
+++ b/dbms/src/Functions/FunctionsConversion.h
@@ -1138,8 +1138,7 @@ struct ToIntMonotonicity
 
     static IFunction::Monotonicity get(const IDataType & type, const Field & left, const Field & right)
     {
-        /// If type is string, the function is no monotonic
-        if (WhichDataType(type).isString())
+        if (!type.isValueRepresentedByNumber())
             return {};
 
         size_t size_of_type = type.getSizeOfValueInMemory();
@@ -1157,14 +1156,10 @@ struct ToIntMonotonicity
         }
 
         /// If type is same, too. (Enum has separate case, because it is different data type)
-        if (checkAndGetDataType<DataTypeNumber<T>>(&type) ||
+        if (checkAndGetDataType<DataTypeNumberBase<T>>(&type) ||
             checkAndGetDataType<DataTypeEnum<T>>(&type))
             return { true, true, true };
 
-        /// In other cases, if range is unbounded, we don't know, whether function is monotonic or not.
-        if (left.isNull() || right.isNull())
-            return {};
-
         /// If converting from float, for monotonicity, arguments must fit in range of result type.
         if (WhichDataType(type).isFloat())
         {
diff --git a/dbms/tests/queries/0_stateless/00653_monotonic_integer_cast.reference b/dbms/tests/queries/0_stateless/00653_monotonic_integer_cast.reference
index 6ed281c757a..d00491fd7e5 100644
--- a/dbms/tests/queries/0_stateless/00653_monotonic_integer_cast.reference
+++ b/dbms/tests/queries/0_stateless/00653_monotonic_integer_cast.reference
@@ -1,2 +1 @@
 1
-1
diff --git a/dbms/tests/queries/0_stateless/00653_monotonic_integer_cast.sql b/dbms/tests/queries/0_stateless/00653_monotonic_integer_cast.sql
index f681b024082..29a44a4aa22 100644
--- a/dbms/tests/queries/0_stateless/00653_monotonic_integer_cast.sql
+++ b/dbms/tests/queries/0_stateless/00653_monotonic_integer_cast.sql
@@ -1,10 +1,4 @@
-DROP TABLE IF EXISTS test.number_test_table;
-DROP TABLE IF EXISTS test.string_test_table;
-CREATE TABLE test.number_test_table (val Int32) ENGINE = MergeTree ORDER BY val;
-CREATE TABLE test.string_test_table (val String) ENGINE = MergeTree ORDER BY val;
-INSERT INTO test.number_test_table VALUES (-2), (0), (2);
-INSERT INTO test.string_test_table VALUES ('0'), ('2');
-SELECT count() FROM test.number_test_table WHERE toUInt64(val) == 0;
-SELECT count() FROM test.string_test_table WHERE toUInt64(val) == 0;
-DROP TABLE IF EXISTS test.number_test_table;
-DROP TABLE IF EXISTS test.string_test_table;
+drop table if exists test.table;
+create table test.table (val Int32) engine = MergeTree order by val;
+insert into test.table values (-2), (0), (2);
+select count() from test.table where toUInt64(val) == 0;
diff --git a/dbms/tests/queries/0_stateless/00653_verification_monotonic_data_load.reference b/dbms/tests/queries/0_stateless/00653_verification_monotonic_data_load.reference
new file mode 100644
index 00000000000..8900af059b8
--- /dev/null
+++ b/dbms/tests/queries/0_stateless/00653_verification_monotonic_data_load.reference
@@ -0,0 +1,26 @@
+no monotonic int case: String -> UInt64
+no monotonic int case: FixedString -> UInt64
+monotonic int case: Int32 -> Int64
+monotonic int case: Int32 -> UInt64
+monotonic int case: Int32 -> Int32
+monotonic int case: Int32 -> UInt32
+monotonic int case: Int32 -> Int16
+monotonic int case: Int32 -> UInt16
+monotonic int case: UInt32 -> Int64
+monotonic int case: UInt32 -> UInt64
+monotonic int case: UInt32 -> Int32
+monotonic int case: UInt32 -> UInt32
+monotonic int case: UInt32 -> Int16
+monotonic int case: UInt32 -> UInt16
+monotonic int case: Enum16 -> Int32
+monotonic int case: Enum16 -> UInt32
+monotonic int case: Enum16 -> Int16
+monotonic int case: Enum16 -> UInt16
+monotonic int case: Enum16 -> Int8
+monotonic int case: Enum16 -> UInt8
+monotonic int case: Date -> Int32
+monotonic int case: Date -> UInt32
+monotonic int case: Date -> Int16
+monotonic int case: Date -> UInt16
+monotonic int case: Date -> Int8
+monotonic int case: Date -> UInt8
diff --git a/dbms/tests/queries/0_stateless/00653_verification_monotonic_data_load.sh b/dbms/tests/queries/0_stateless/00653_verification_monotonic_data_load.sh
new file mode 100755
index 00000000000..325f19dc9ec
--- /dev/null
+++ b/dbms/tests/queries/0_stateless/00653_verification_monotonic_data_load.sh
@@ -0,0 +1,85 @@
+#!/usr/bin/env bash
+
+#--------------------------------------------
+# Description of test result:
+#   Test the correctness of the optimization
+#   by asserting read marks in the log.
+# Relation of read marks and optimization:
+#   read marks =
+#       the number of monotonic marks filtered through predicates
+#       + no monotonic marks count
+#--------------------------------------------
+
+CURDIR=$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)
+. $CURDIR/../shell_config.sh
+
+${CLICKHOUSE_CLIENT} --query="SYSTEM STOP MERGES;"
+
+${CLICKHOUSE_CLIENT} --query="DROP TABLE IF EXISTS test.string_test_table;"
+${CLICKHOUSE_CLIENT} --query="DROP TABLE IF EXISTS test.fixed_string_test_table;"
+${CLICKHOUSE_CLIENT} --query="DROP TABLE IF EXISTS test.signed_integer_test_table;"
+${CLICKHOUSE_CLIENT} --query="DROP TABLE IF EXISTS test.unsigned_integer_test_table;"
+${CLICKHOUSE_CLIENT} --query="DROP TABLE IF EXISTS test.enum_test_table;"
+${CLICKHOUSE_CLIENT} --query="DROP TABLE IF EXISTS test.date_test_table;"
+
+${CLICKHOUSE_CLIENT} --query="CREATE TABLE test.string_test_table (val String) ENGINE = MergeTree ORDER BY val SETTINGS index_granularity = 1;"
+${CLICKHOUSE_CLIENT} --query="CREATE TABLE test.fixed_string_test_table (val FixedString(1)) ENGINE = MergeTree ORDER BY val SETTINGS index_granularity = 1;"
+${CLICKHOUSE_CLIENT} --query="CREATE TABLE test.signed_integer_test_table (val Int32) ENGINE = MergeTree ORDER BY val SETTINGS index_granularity = 1;"
+${CLICKHOUSE_CLIENT} --query="CREATE TABLE test.unsigned_integer_test_table (val UInt32) ENGINE = MergeTree ORDER BY val SETTINGS index_granularity = 1;"
+${CLICKHOUSE_CLIENT} --query="CREATE TABLE test.enum_test_table (val Enum16('hello' = 1, 'world' = 2, 'yandex' = 256, 'clickhouse' = 257)) ENGINE = MergeTree ORDER BY val SETTINGS index_granularity = 1;"
+${CLICKHOUSE_CLIENT} --query="CREATE TABLE test.date_test_table (val Date) ENGINE = MergeTree ORDER BY val SETTINGS index_granularity = 1;"
+
+
+${CLICKHOUSE_CLIENT} --query="INSERT INTO test.string_test_table VALUES ('0'), ('2'), ('2');"
+${CLICKHOUSE_CLIENT} --query="INSERT INTO test.fixed_string_test_table VALUES ('0'), ('2'), ('2');"
+# 131072 -> 17 bit is 1
+${CLICKHOUSE_CLIENT} --query="INSERT INTO test.signed_integer_test_table VALUES (-2), (0), (2), (2), (131072), (131073), (131073);"
+${CLICKHOUSE_CLIENT} --query="INSERT INTO test.unsigned_integer_test_table VALUES (0), (2), (2), (131072), (131073), (131073);"
+${CLICKHOUSE_CLIENT} --query="INSERT INTO test.enum_test_table VALUES ('hello'), ('world'), ('world'), ('yandex'), ('clickhouse'), ('clickhouse');"
+${CLICKHOUSE_CLIENT} --query="INSERT INTO test.date_test_table VALUES (1), (2), (2), (256), (257), (257);"
+
+export CLICKHOUSE_CLIENT=`echo ${CLICKHOUSE_CLIENT} |sed 's/'"${CLICKHOUSE_CLIENT_SERVER_LOGS_LEVEL}"'/debug/g'`
+
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.string_test_table WHERE toUInt64(val) == 0;" 2>&1 |grep -q "3 marks to read from 1 ranges" && echo "no monotonic int case: String -> UInt64"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.fixed_string_test_table WHERE toUInt64(val) == 0;" 2>&1 |grep -q "3 marks to read from 1 ranges" && echo "no monotonic int case: FixedString -> UInt64"
+
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.signed_integer_test_table WHERE toInt64(val) == 0;" 2>&1 |grep -q "2 marks to read from" && echo "monotonic int case: Int32 -> Int64"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.signed_integer_test_table WHERE toUInt64(val) == 0;" 2>&1 |grep -q "2 marks to read from" && echo "monotonic int case: Int32 -> UInt64"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.signed_integer_test_table WHERE toInt32(val) == 0;" 2>&1 |grep -q "2 marks to read from" && echo "monotonic int case: Int32 -> Int32"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.signed_integer_test_table WHERE toUInt32(val) == 0;" 2>&1 |grep -q "2 marks to read from" && echo "monotonic int case: Int32 -> UInt32"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.signed_integer_test_table WHERE toInt16(val) == 0;" 2>&1 |grep -q "5 marks to read from" && echo "monotonic int case: Int32 -> Int16"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.signed_integer_test_table WHERE toUInt16(val) == 0;" 2>&1 |grep -q "5 marks to read from" && echo "monotonic int case: Int32 -> UInt16"
+
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.unsigned_integer_test_table WHERE toInt64(val) == 0;" 2>&1 |grep -q "1 marks to read from" && echo "monotonic int case: UInt32 -> Int64"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.unsigned_integer_test_table WHERE toUInt64(val) == 0;" 2>&1 |grep -q "1 marks to read from" && echo "monotonic int case: UInt32 -> UInt64"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.unsigned_integer_test_table WHERE toInt32(val) == 0;" 2>&1 |grep -q "1 marks to read from" && echo "monotonic int case: UInt32 -> Int32"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.unsigned_integer_test_table WHERE toUInt32(val) == 0;" 2>&1 |grep -q "1 marks to read from" && echo "monotonic int case: UInt32 -> UInt32"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.unsigned_integer_test_table WHERE toInt16(val) == 0;" 2>&1 |grep -q "4 marks to read from" && echo "monotonic int case: UInt32 -> Int16"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.unsigned_integer_test_table WHERE toUInt16(val) == 0;" 2>&1 |grep -q "4 marks to read from" && echo "monotonic int case: UInt32 -> UInt16"
+
+
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.enum_test_table WHERE toInt32(val) == 1;" 2>&1 |grep -q "1 marks to read from" && echo "monotonic int case: Enum16 -> Int32"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.enum_test_table WHERE toUInt32(val) == 1;" 2>&1 |grep -q "1 marks to read from" && echo "monotonic int case: Enum16 -> UInt32"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.enum_test_table WHERE toInt16(val) == 1;" 2>&1 |grep -q "1 marks to read from" && echo "monotonic int case: Enum16 -> Int16"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.enum_test_table WHERE toUInt16(val) == 1;" 2>&1 |grep -q "1 marks to read from" && echo "monotonic int case: Enum16 -> UInt16"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.enum_test_table WHERE toInt8(val) == 1;" 2>&1 |grep -q "5 marks to read from" && echo "monotonic int case: Enum16 -> Int8"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.enum_test_table WHERE toUInt8(val) == 1;" 2>&1 |grep -q "5 marks to read from" && echo "monotonic int case: Enum16 -> UInt8"
+
+
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.date_test_table WHERE toInt32(val) == 1;" 2>&1 |grep -q "1 marks to read from" && echo "monotonic int case: Date -> Int32"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.date_test_table WHERE toUInt32(val) == 1;" 2>&1 |grep -q "1 marks to read from" && echo "monotonic int case: Date -> UInt32"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.date_test_table WHERE toInt16(val) == 1;" 2>&1 |grep -q "1 marks to read from" && echo "monotonic int case: Date -> Int16"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.date_test_table WHERE toUInt16(val) == 1;" 2>&1 |grep -q "1 marks to read from" && echo "monotonic int case: Date -> UInt16"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.date_test_table WHERE toInt8(val) == 1;" 2>&1 |grep -q "5 marks to read from" && echo "monotonic int case: Date -> Int8"
+${CLICKHOUSE_CLIENT} --query="SELECT count() FROM test.date_test_table WHERE toUInt8(val) == 1;" 2>&1 |grep -q "5 marks to read from" && echo "monotonic int case: Date -> UInt8"
+
+export CLICKHOUSE_CLIENT=`echo ${CLICKHOUSE_CLIENT} |sed 's/debug/'"${CLICKHOUSE_CLIENT_SERVER_LOGS_LEVEL}"'/g'`
+
+${CLICKHOUSE_CLIENT} --query="DROP TABLE IF EXISTS test.string_test_table;"
+${CLICKHOUSE_CLIENT} --query="DROP TABLE IF EXISTS test.fixed_string_test_table;"
+${CLICKHOUSE_CLIENT} --query="DROP TABLE IF EXISTS test.signed_integer_test_table;"
+${CLICKHOUSE_CLIENT} --query="DROP TABLE IF EXISTS test.unsigned_integer_test_table;"
+${CLICKHOUSE_CLIENT} --query="DROP TABLE IF EXISTS test.enum_test_table;"
+${CLICKHOUSE_CLIENT} --query="DROP TABLE IF EXISTS test.date_test_table;"
+
+${CLICKHOUSE_CLIENT} --query="SYSTEM START MERGES;"