MySQL 8.0 Reference Manual Including MySQL NDB Cluster 8.0

This section provides some examples that show precision math query results in MySQL. These examples demonstrate the principles described in Section 12.25.3, “Expression Handling”, and Section 12.25.4, “Rounding Behavior”.

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

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

For floating-point values, results are inexact:

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

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`

`S1`

`S2`

`S1`

+ `S2`

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

**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. A value with a fractional part of .5 or greater is rounded away from zero to the nearest integer, as shown here:mysql>

+------------+-------------+ | ROUND(2.5) | ROUND(-2.5) | +------------+-------------+ | 3 | -3 | +------------+-------------+`SELECT ROUND(2.5), ROUND(-2.5);`

Rounding for floating-point values uses the C library, which on many systems uses the “round to nearest even” rule. A value with a fractional part exactly half way between two integers is rounded to the nearest even integer:

mysql>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

mysql>Query OK, 0 rows affected (0.00 sec) 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);`

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

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

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

Approximate-value literals are evaluated using floating point, but
exact-value literals are handled as
`DECIMAL`

:

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

+-------+-----------------------+------+-----+---------+-------+ | 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)`DESCRIBE t;`

**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>mysql>`CREATE TABLE t (i INT, d DECIMAL, f FLOAT);`

mysql>`INSERT INTO t VALUES(1,1,1);`

`CREATE TABLE y SELECT AVG(i), AVG(d), AVG(f) FROM t;`

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

mysql>+--------+---------------+------+-----+---------+-------+ | 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 | | +--------+---------------+------+-----+---------+-------+`DESCRIBE y;`

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