3.3 Fixed-Point Data Types

Fixed-point data types ensure the predictability of multiplication and division operations, making them the choice for storing monetary values. Firebird implements two fixed-point data types: NUMERIC and DECIMAL. According to the standard, both types limit the stored number to the declared scale (the number of digits after the decimal point).

Different treatments limit precision for each type: precision for NUMERIC columns is exactly as declared, while DECIMAL columns accepts numbers whose precision is at least equal to what was declared.

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Note

The behaviour of NUMERIC and DECIMAL in Firebird is like the SQL-standard DECIMAL; the precision is at least equal to what was declared.

For instance, NUMERIC(4, 2) defines a number consisting altogether of four digits, including two digits after the decimal point; that is, it can have up to two digits before the point and no more than two digits after the point. If the number 3.1415 is written to a column with this data type definition, the value of 3.14 will be saved in the NUMERIC(4, 2) column.

The form of declaration for fixed-point data, for instance, NUMERIC(p, s), is common to both types. It is important to realise that the s argument in this template is scale, rather than a count of digits after the decimal point. Understanding the mechanism for storing and retrieving fixed-point data should help to visualise why: for storage, the number is multiplied by 10s (10 to the power of s), converting it to an integer; when read, the integer is converted back.

The method of storing fixed-point data in the database depends on several factors: declared precision, database dialect, declaration type.

Table 3.3.1 Method of Physical Storage for Fixed-Point Numbers
PrecisionData typeDialect 1Dialect 3

1 - 4

NUMERIC

SMALLINT

SMALLINT

1 - 4

DECIMAL

INTEGER

INTEGER

5 - 9

NUMERIC or DECIMAL

INTEGER

INTEGER

10 - 18

NUMERIC or DECIMAL

DOUBLE PRECISION

BIGINT

19 - 38

NUMERIC or DECIMAL

INT128

INT128

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Note

Numerics with precision less than 19 digits use SMALLINT, INTEGER, BIGINT or DOUBLE PRECISION as the base datatype, depending on the number of digits and SQL dialect. When precision is between 19 and 38 digits a 128-bit integer is used for internal storage, and the actual precision is always extended to the full 38 digits.

For complex calculations, those digits are cast internally to DECFLOAT(34). The result of various mathematical operations, such as LOG(), EXP() and so on, and aggregate functions using a high precision numeric argument, will be DECFLOAT(34).

3.3.1 NUMERIC

Data Type Declaration Format

  NUMERIC
| NUMERIC(precision)
| NUMERIC(precision, scale)

Table 3.3.1.1 NUMERIC Type Parameters
ParameterDescription

precision

Precision, between 1 and 38. Defaults to 9.

scale

Scale, between 0 and precision. Defaults to 0.

Storage ExamplesFurther to the explanation above, Firebird will store NUMERIC data according the declared precision and scale. Some more examples are:

NUMERIC(4) stored as      SMALLINT (exact data)
NUMERIC(4,2)              SMALLINT (data * 102)
NUMERIC(10,4) (Dialect 1) DOUBLE PRECISION
              (Dialect 3) BIGINT (data * 104)
NUMERIC(38,6)             INT128 (data * 106)
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Caution

Always keep in mind that the storage format depends on the precision. For instance, you define the column type as NUMERIC(2,2) presuming that its range of values will be -0.99…​0.99. However, the actual range of values for the column will be -327.68…​327.67, which is due to storing the NUMERIC(2,2) data type in the SMALLINT format. In storage, the NUMERIC(4,2), NUMERIC(3,2) and NUMERIC(2,2) data types are the same, in fact. It means that if you really want to store data in a column with the NUMERIC(2,2) data type and limit the range to -0.99…​0.99, you will have to create a constraint for it.

3.3.2 DECIMAL

Data Type Declaration Format

  DECIMAL
| DECIMAL(precision)
| DECIMAL(precision, scale)

Table 3.3.2.1 DECIMAL Type Parameters
ParameterDescription

precision

Precision, between 1 and 38. Defaults to 9.

scale

Scale, between 0 and precision. Defaults to 0.

Storage ExamplesThe storage format in the database for DECIMAL is very similar to NUMERIC, with some differences that are easier to observe with the help of some more examples:

DECIMAL(4) stored as      INTEGER (exact data)
DECIMAL(4,2)              INTEGER (data * 102)
DECIMAL(10,4) (Dialect 1) DOUBLE PRECISION
              (Dialect 3) BIGINT (data * 104)
DECIMAL(38,6)             INT128 (data * 106)