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# (mysql.info) precision-math

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21 Precision Math
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### Menu

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* precision-math-numbers       Types of Numeric Values
* precision-math-decimal-changes  `DECIMAL' Data Type Changes
* precision-math-expressions   Expression Handling
* precision-math-rounding      Rounding Behavior
* precision-math-examples      Precision Math Examples

MySQL 5.0 introduces precision math: numeric value handling that
results in more accurate results and more control over invalid values
than in earlier versions of MySQL. Precision math is based on two
implementation changes:

* The introduction of SQL modes in MySQL 5.0 that control how strict
the server is about accepting or rejecting invalid data.

* The introduction in MySQL 5.0.3 of a library for fixed-point
arithmetic.

These changes have several implications for numeric operations:

* *More precise calculations*: For exact-value numbers, calculations
do not introduce floating-point errors. Instead, exact precision
is used. For example, a number such as `.0001' is treated as an
exact value rather than as an approximation, and summing it 10,000
times produces a result of exactly `1', not a value that merely
`close' to 1.

* *Well-defined rounding behavior*: For exact-value numbers, the
result of `ROUND()' depends on its argument, not on environmental
factors such as how the underlying C library works.

* *Improved platform independence*: Operations on exact numeric
values are the same across different platforms such as Windows and
Unix.

* *Control over handling of invalid values*: Overflow and division
by zero are detectable and can be treated as errors. For example,
you can treat a value that is too large for a column as an error
rather than having the value truncated to lie within the range of
the column's data type. Similarly, you can treat division by zero
as an error rather than as an operation that produces a result of
`NULL'. The choice of which approach to take is determined by the
setting of the `sql_mode' system variable.

An important result of these changes is that MySQL provides improved
compliance with standard SQL.

The following discussion covers several aspects of how precision math
works (including possible incompatibilities with older applications).
At the end, some examples are given that demonstrate how MySQL 5.0
handles numeric operations precisely. For information about using the
`sql_mode' system variable to control the SQL mode, see
server-sql-mode.

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