3.2. Floating-Point Data Types

Firebird supports two types of floating-point data types:

  1. Approximate or binary floating-point data types (FLOAT and DOUBLE PRECISION)

  2. Decimal floating-point types (DECFLOAT)

3.2.1. Approximate Floating-Point Data Types

Approximate floating-point values are stored in an IEEE 754 binary format that comprises sign, exponent and mantissa. Precision is dynamic, corresponding to the physical storage format of the value, which is 4 bytes for the FLOAT type and 8 bytes for DOUBLE PRECISION.

Considering the peculiarities of floating-point numbers, these data types are not recommended for storing monetary data. For the same reasons, columns of a floating-point type are not recommended for use as primary or unique keys.

For testing data in columns with floating-point data types, expressions should check using a range, e.g. using BETWEEN, rather than searching for exact matches.

When using these data types in expressions, extreme care is advised regarding the rounding of evaluation results.

3.2.1.1. FLOAT

Data Type Declaration Format 

FLOAT [(bin_prec)]

Table 3.2. FLOAT Type Parameters
ParameterDescription

bin_prec

Precision in binary digits, default is 24 (32-bit single precision)

1 - 24

32-bit single precision

25 - 53

64-bit double precision

The FLOAT data type defaults to a 32-bit single precision floating-point type with an approximate precision of 7 decimal digits (24 binary digits).

The syntax FLOAT(bin_prec) behaves as follows:

  • 1 <= bin_prec <= 23: 32-bit single precision (synonym for FLOAT)

  • 25 <= bin_prec <= 53: 64-bit double precision (synonym for DOUBLE PRECISION)

The behaviour of FLOAT (without explicit precision) behaves as the SQL standard type Section 3.2.1.2, “REAL”.

Compatibility Notes

  • For bin_prec in FLOAT(bin_prec), the values 1 <= bin_prec <= 24 are all treated as bin_prec = 24, values 25 <= bin_prec <= 53 are all handled as bin_prec = 53.

  • Most Firebird tools will report FLOAT(1) — FLOAT(24) as FLOAT, and FLOAT(25) — FLOAT(53) as DOUBLE PRECISION.

3.2.1.2. REAL

Data Type Declaration Format 

REAL

The data type REAL is a synonym for FLOAT, and is provided for syntax compatibility. When used to define a column or parameter, it’s indistinguishable from using FLOAT or FLOAT(1) — FLOAT(24).

Compatibility Notes

  • Most Firebird tools will report FLOAT instead of REAL.

3.2.1.3. DOUBLE PRECISION

Data Type Declaration Format 

DOUBLE PRECISION

The DOUBLE PRECISION data type is stored with an approximate precision of 15 decimal digits (53 binary digits).

Compatibility Notes

  • Firebird also has the — previously undocumented — synonyms for DOUBLE PRECISION: LONG FLOAT and LONG FLOAT(bin_prec), with 1 <= bin_prec <= 53.

    These non-standard type names are deprecated and may be removed in a future Firebird version.

3.2.2. Decimal Floating-Point Types

Decimal floating-point values are stored in an IEEE 754 decimal format that comprises sign, exponent and coefficient. Contrary to the approximate floating-point data types, precision is either 16 or 34 decimal digits.

3.2.2.1. DECFLOAT

Data Type Declaration Format 

DECFLOAT [(dec_prec)]

Table 3.3. DECFLOAT Type Parameters
ParameterDescription

dec_prec

Precision in decimal digits, either 16 or 34. Default is 34.

DECFLOAT is a SQL standard numeric type that stores a floating-point number precisely, unlike FLOAT or DOUBLE PRECISION that provide a binary approximation of the purported precision.

The type is stored and transmitted as IEEE 754 standard types Decimal64 (DECFLOAT(16)) or Decimal128 (DECFLOAT(34)).

All intermediate calculations are performed with 34-digit values.

16-digit and 34-digit

The 16 and 34 refer to the maximum precision in Base-10 digits. See https://en.wikipedia.org/wiki/iEEE_754#Basic_and_interchange_formats for a comprehensive table.

Table 3.4. Range of Values
TypeMaximum precisionMinimum ExponentMaximum ExponentSmallest valueLargest value

DECFLOAT(16)

16

-383

+384

1E-398

9.9..9E+384

DECFLOAT(34)

34

-6143

+6144

1E-6176

9.9..9E+6144

Observe that although the smallest exponent for DECFLOAT(16) is -383, the smallest value has an exponent of -398, but 15 fewer digits. And similar for DECFLOAT(34), smallest exponent is -6143, but the smallest value has an exponent of -6176, but 33 fewer digits. The reason is that precision was sacrificed to be able to store a smaller value.

This is a result of how the value is stored: as a decimal value of 16 or 34 digits and an exponent. For example, 1.234567890123456e-383 is stored as coefficient 1234567890123456 and exponent -398, while 1E-398 is stored as coefficient 1, exponent -398.

3.2.2.1.1. Behaviour of DECFLOAT Operations

The behaviour of DECFLOAT operations in a session, specifically rounding and error behaviour, can be configured using the SET DECFLOAT management statement, and the isc_dpb_decfloat_round and isc_dpb_decfloat_traps DPB items.

3.2.2.1.2. Length of DECFLOAT Literals

It is possible to express DECFLOAT(34) values in approximate numeric literals, but only for values with a mantissa of 20 or more digits, or an absolute exponent larger than 308. Scientific notation literals with fewer digits or a smaller absolute exponent are DOUBLE PRECISION literals. Exact numeric literals with 40 or more digits — actually 39 digits, when larger than the maximum INT128 value — are also handled as DECFLOAT(34).

Alternatively, use a string literal and explicitly cast to the desired DECFLOAT type.

The length of DECFLOAT literals cannot exceed 1024 characters. Scientific notation is required for greater values. For example, 0.0<1020 zeroes>11 cannot be used as a literal, but the equivalent in scientific notation, 1.1E-1022, is valid. Similarly, 10<1022 zeroes>0 can be presented as 1.0E1024. Literals with more than 34 significant digits are rounded using the DECFLOAT rounding mode of the session.

3.2.2.1.3. DECFLOAT and Functions
Use with Standard Functions

A number of standard scalar functions can be used with expressions and values of the DECFLOAT type. They are:

The aggregate functions SUM, AVG, MAX and MIN work with DECFLOAT data, as do all the statistical aggregates (including but not limited to STDDEV or CORR).

Special Functions for DECFLOAT

Firebird supports four functions, designed to support DECFLOAT data specifically:

COMPARE_DECFLOAT

compares two DECFLOAT values to be equal, different or unordered

NORMALIZE_DECFLOAT

takes a single DECFLOAT argument and returns it in its simplest form

QUANTIZE

takes two DECFLOAT arguments and returns the first argument scaled using the second value as a pattern

TOTALORDER

performs an exact comparison on two DECFLOAT values

Detailed descriptions are available in the Special Functions for DECFLOAT section of the Built-in Scalar Functions chapter.