MySQL 5.1 Reference Manual  /  ...  /  Precision Math Examples

### 12.18.5 Precision Math Examples

This section provides some examples that show precision math query results in MySQL 5.1. These examples demonstrate the principles described in Section 12.18.3, “Expression Handling”, and Section 12.18.4, “Rounding Behavior”.

Example 1. Numbers are used with their exact value as given when possible:

```mysql> `SELECT (.1 + .2) = .3;`
+----------------+
| (.1 + .2) = .3 |
+----------------+
|              1 |
+----------------+
```

For floating-point values, results are inexact:

```mysql> `SELECT (.1E0 + .2E0) = .3E0;`
+----------------------+
| (.1E0 + .2E0) = .3E0 |
+----------------------+
|                    0 |
+----------------------+
```

Another way to see the difference in exact and approximate value handling is to add a small number to a sum many times. Consider the following stored procedure, which adds `.0001` to a variable 1,000 times.

```CREATE PROCEDURE p ()
BEGIN
DECLARE i INT DEFAULT 0;
DECLARE d DECIMAL(10,4) DEFAULT 0;
DECLARE f FLOAT DEFAULT 0;
WHILE i < 10000 DO
SET d = d + .0001;
SET f = f + .0001E0;
SET i = i + 1;
END WHILE;
SELECT d, f;
END;
```

The sum for both `d` and `f` logically should be 1, but that is true only for the decimal calculation. The floating-point calculation introduces small errors:

```+--------+------------------+
| d      | f                |
+--------+------------------+
| 1.0000 | 0.99999999999991 |
+--------+------------------+
```

Example 2. Multiplication is performed with the scale required by standard SQL. That is, for two numbers `X1` and `X2` that have scale `S1` and `S2`, the scale of the result is ```S1 + S2```:

```mysql> `SELECT .01 * .01;`
+-----------+
| .01 * .01 |
+-----------+
| 0.0001    |
+-----------+
```

Example 3. Rounding behavior for exact-value numbers is well-defined:

Rounding behavior (for example, with the `ROUND()` function) is independent of the implementation of the underlying C library, which means that results are consistent from platform to platform.

• Rounding for exact-value columns (`DECIMAL` and integer) and exact-valued numbers uses the round half away from zero rule. Values with a fractional part of .5 or greater are rounded away from zero to the nearest integer, as shown here:

```mysql> `SELECT ROUND(2.5), ROUND(-2.5);`
+------------+-------------+
| ROUND(2.5) | ROUND(-2.5) |
+------------+-------------+
| 3          | -3          |
+------------+-------------+
```
• Rounding for floating-point values uses the C library, which on many systems uses the round to nearest even rule. Values with any fractional part on such systems are rounded to the nearest even integer:

```mysql> `SELECT ROUND(2.5E0), ROUND(-2.5E0);`
+--------------+---------------+
| ROUND(2.5E0) | ROUND(-2.5E0) |
+--------------+---------------+
|            2 |            -2 |
+--------------+---------------+
```

Example 4. In strict mode, inserting a value that is out of range for a column causes an error, rather than truncation to a legal value.

When MySQL is not running in strict mode, truncation to a legal value occurs:

```mysql> `SET sql_mode='';`
Query OK, 0 rows affected (0.00 sec)

mysql> `CREATE TABLE t (i TINYINT);`
Query OK, 0 rows affected (0.01 sec)

mysql> `INSERT INTO t SET i = 128;`
Query OK, 1 row affected, 1 warning (0.00 sec)

mysql> `SELECT i FROM t;`
+------+
| i    |
+------+
|  127 |
+------+
1 row in set (0.00 sec)
```

However, an error occurs if strict mode is in effect:

```mysql> `SET sql_mode='STRICT_ALL_TABLES';`
Query OK, 0 rows affected (0.00 sec)

mysql> `CREATE TABLE t (i TINYINT);`
Query OK, 0 rows affected (0.00 sec)

mysql> `INSERT INTO t SET i = 128;`
ERROR 1264 (22003): Out of range value adjusted for column 'i' at row 1

mysql> `SELECT i FROM t;`
Empty set (0.00 sec)
```

Example 5: In strict mode and with `ERROR_FOR_DIVISION_BY_ZERO` set, division by zero causes an error, not a result of `NULL`.

In nonstrict mode, division by zero has a result of `NULL`:

```mysql> `SET sql_mode='';`
Query OK, 0 rows affected (0.01 sec)

mysql> `CREATE TABLE t (i TINYINT);`
Query OK, 0 rows affected (0.00 sec)

mysql> `INSERT INTO t SET i = 1 / 0;`
Query OK, 1 row affected (0.00 sec)

mysql> `SELECT i FROM t;`
+------+
| i    |
+------+
| NULL |
+------+
1 row in set (0.03 sec)
```

However, division by zero is an error if the proper SQL modes are in effect:

```mysql> `SET sql_mode='STRICT_ALL_TABLES,ERROR_FOR_DIVISION_BY_ZERO';`
Query OK, 0 rows affected (0.00 sec)

mysql> `CREATE TABLE t (i TINYINT);`
Query OK, 0 rows affected (0.00 sec)

mysql> `INSERT INTO t SET i = 1 / 0;`
ERROR 1365 (22012): Division by 0

mysql> `SELECT i FROM t;`
Empty set (0.01 sec)
```

Example 6. Exact-value literals are evaluated as exact values.

Prior to MySQL 5.0.3, exact-value and approximate-value literals both are evaluated as double-precision floating-point values:

```mysql> `SELECT VERSION();`
+------------+
| VERSION()  |
+------------+
| 4.1.18-log |
+------------+
1 row in set (0.01 sec)

mysql> `CREATE TABLE t SELECT 2.5 AS a, 25E-1 AS b;`
Query OK, 1 row affected (0.07 sec)
Records: 1  Duplicates: 0  Warnings: 0

mysql> `DESCRIBE t;`
+-------+-------------+------+-----+---------+-------+
| Field | Type        | Null | Key | Default | Extra |
+-------+-------------+------+-----+---------+-------+
| a     | double(3,1) |      |     | 0.0     |       |
| b     | double      |      |     | 0       |       |
+-------+-------------+------+-----+---------+-------+
2 rows in set (0.04 sec)
```

As of MySQL 5.0.3, the approximate-value literal is evaluated using floating point, but the exact-value literal is handled as `DECIMAL`:

```mysql> `SELECT VERSION();`
+-----------------+
| VERSION()       |
+-----------------+
| 5.1.6-alpha-log |
+-----------------+
1 row in set (0.11 sec)

mysql> `CREATE TABLE t SELECT 2.5 AS a, 25E-1 AS b;`
Query OK, 1 row affected (0.01 sec)
Records: 1  Duplicates: 0  Warnings: 0

mysql> `DESCRIBE t;`
+-------+-----------------------+------+-----+---------+-------+
| Field | Type                  | Null | Key | Default | Extra |
+-------+-----------------------+------+-----+---------+-------+
| a     | decimal(2,1) unsigned | NO   |     | 0.0     |       |
| b     | double                | NO   |     | 0       |       |
+-------+-----------------------+------+-----+---------+-------+
2 rows in set (0.01 sec)
```

Example 7. If the argument to an aggregate function is an exact numeric type, the result is also an exact numeric type, with a scale at least that of the argument.

Consider these statements:

```mysql> `CREATE TABLE t (i INT, d DECIMAL, f FLOAT);`
mysql> `INSERT INTO t VALUES(1,1,1);`
mysql> `CREATE TABLE y SELECT AVG(i), AVG(d), AVG(f) FROM t;`
```

Before MySQL 5.0.3, the result is a double no matter the argument type:

```mysql> `DESCRIBE y;`
+--------+--------------+------+-----+---------+-------+
| Field  | Type         | Null | Key | Default | Extra |
+--------+--------------+------+-----+---------+-------+
| AVG(i) | double(17,4) | YES  |     | NULL    |       |
| AVG(d) | double(17,4) | YES  |     | NULL    |       |
| AVG(f) | double       | YES  |     | NULL    |       |
+--------+--------------+------+-----+---------+-------+
```

As of MySQL 5.0.3, the result is a double only for the floating-point argument. For exact type arguments, the result is also an exact type:

```mysql> `DESCRIBE y;`
+--------+---------------+------+-----+---------+-------+
| Field  | Type          | Null | Key | Default | Extra |
+--------+---------------+------+-----+---------+-------+
| AVG(i) | decimal(14,4) | YES  |     | NULL    |       |
| AVG(d) | decimal(14,4) | YES  |     | NULL    |       |
| AVG(f) | double        | YES  |     | NULL    |       |
+--------+---------------+------+-----+---------+-------+
```

The result is a double only for the floating-point argument. For exact type arguments, the result is also an exact type.