﻿Chapter 21. Precision Math

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## Chapter 21. Precision Math

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 Section 5.2.6, “SQL Modes”.

## 21.1. Types of Numeric Values

The scope of precision math for exact-value operations includes the exact-value data types (`DECIMAL` and integer types) and exact-value numeric literals. Approximate-value data types and numeric literals still are handled as floating-point numbers.

Exact-value numeric literals have an integer part or fractional part, or both. They may be signed. Examples: `1`, `.2`, `3.4`, `-5`, `-6.78`, `+9.10`.

Approximate-value numeric literals are represented in scientific notation with a mantissa and exponent. Either or both parts may be signed. Examples: `1.2E3`, `1.2E-3`, `-1.2E3`, `-1.2E-3`.

Two numbers that look similar need not be both exact-value or both approximate-value. For example, `2.34` is an exact-value (fixed-point) number, whereas `2.34E0` is an approximate-value (floating-point) number.

The `DECIMAL` data type is a fixed-point type and calculations are exact. In MySQL, the `DECIMAL` type has several synonyms: `NUMERIC`, `DEC`, `FIXED`. The integer types also are exact-value types.

The `FLOAT` and `DOUBLE` data types are floating-point types and calculations are approximate. In MySQL, types that are synonymous with `FLOAT` or `DOUBLE` are `DOUBLE PRECISION` and `REAL`.