MySQL本身對於位運算有與或非的專屬符號 & | ^
在MySQL中提供了bit_and、bit_or、bit_xor的分組函式。

此外MySQL還提供了bit_count函式用以統計二進位制中含有1的個數。
mysql> select bit_count(10);
+---------------+
| bit_count(10) |
+---------------+
|             2 |
+---------------+
1 row in set (0.00 sec)

mysql> select bit_count(b'1010');
+--------------------+
| bit_count(b'1010') |
+--------------------+
|                  2 |
+--------------------+
1 row in set (0.00 sec)



bit_or：二進位制數按位或，bit_and:二進位制數按位與，bit_count:統計二進位制數1個個數。

應用統計：
mysql> create table visituser(id bigint unsigned not  null auto_increment primary key,userid int,brokerid int,y int,m int(2) unsigned zerofill,d int(2) unsigned zerofill);
Query OK, 0 rows affected (0.04 sec)

mysql> insert into visituser(userid,brokerid,y,m,d)values(1000,1,2018,8,1),(1000,2,2018,8,15),(1000,2,2018,8,21),(1002,1,2018,9,1),(1002,1,2018,9,16),(1000,2,2018,9,20),(1000,2,2018,9,25),(1000,2,2018,9,25);
Query OK, 7 rows affected (0.02 sec)
Records: 7  Duplicates: 0  Warnings: 0


select y,m,count(distinct d) days from visit  group by y,m;

select y,m,bit_count(bit_or(1<<d)) days from visit  group by y,m;
select y,m,userid,brokerid,bit_count(bit_or(1<<d)) days from visituser  group by y,m,userid,brokerid;


mysql> select y,m,userid,brokerid,bit_count(bit_or(1<<d)) days from visituser  group by y,m,userid,brokerid;
+------+------+--------+----------+------+
| y    | m    | userid | brokerid | days |
+------+------+--------+----------+------+
| 2018 |   08 |   1000 |        1 |    1 |
| 2018 |   08 |   1000 |        2 |    2 |
| 2018 |   09 |   1002 |        1 |    2 |
| 2018 |   09 |   1000 |        2 |    2 |
+------+------+--------+----------+------+
4 rows in set (0.01 sec)

count(distinct d)
mysql> select y,m,userid,brokerid,count(distinct d) days from visituser  group by y,m,userid,brokerid;


mysql> select y,m,userid,brokerid,count(distinct d) days from visituser  group by y,m,userid,brokerid;
+------+------+--------+----------+------+
| y    | m    | userid | brokerid | days |
+------+------+--------+----------+------+
| 2018 |   08 |   1000 |        1 |    1 |
| 2018 |   08 |   1000 |        2 |    2 |
| 2018 |   09 |   1000 |        2 |    2 |
| 2018 |   09 |   1002 |        1 |    2 |
+------+------+--------+----------+------+
4 rows in set (0.03 sec)


解釋：
此處針對1<<d 進行解釋：這裡的計數採取的是點陣圖法，每天有訪問就用1表示，02天表示100，23表示1000..(23個0）。
最後經過bit_or按位或後變成10000..(20個0)100,然後用bit_count統計二進位制1的個數，非常巧妙。