DECFLOAT (Firebird 4.0)

Function

DB2-compliant numeric type. DECFLOAT precisely (unlike FLOAT or DOUBLE PRECISION that provide binary approximation) stores decimal values being therefore ideal choice for business applications. Firebird according to IEEE standard has both 16- and 34-digit decimal float encodings. All intermediate calculations are performed with 34-digit values.

Author Alex Peshkoff <peshkoff@mail.ru>

Syntax rules

```    DECFLOAT
DECFLOAT(16)
DECFLOAT(34)
```

Storage

64-bit / 128-bit, format according to IEEE 754 Decimal64/Decimal128

Example(s)

```    1. DECLARE VARIABLE VAR1 DECFLOAT(34);
2. CREATE TABLE TABLE1 (FIELD1 DECFLOAT(16));
```

Note(s)

1. If no precision has been specified in the type declaration, the precision is 34.

2. A number of standard functions can be used with DECFLOAT datatype. It is:

``` ABS, CEILING, EXP, FLOOR, LN, LOG, LOG10, POWER, SIGN, SQRT.
```

Agregate functions SUM, AVG, MAX and MIN also work with DECFLOAT data. All statistics aggregates (like but not limited to STDDEV or CORR) work with DECFLOAT data.

3. Firebird supports four functions, specially designed to support DECFLOAT data:

• COMPARE_DECFLOAT - compares two DECFLOAT values to be equal, different or unordered. Returns SMALLINT value which can be as follows:
```                0 - values are equal
1 - first value is less than second
2 - first value is greater than second
3 - values unordered (i.e. one or both is NAN / SNAN)
```

Unlike comparison operators ('<', '=', '>', etc.) comparison is exact - i.e. COMPARE_DECFLOAT(2.17, 2.170) returns 2, not 0.

• NORMALIZE_DECFLOAT - has single DECFLOAT argument returned in it's simplest form. That means that for any nonzero value trailing zero are removed with appropriate correction of an exponent. For example NORMALIZE_DECFLOAT(12.00) returns 12 and NORMALIZE_DECFLOAT(120) returns 1.2E+2.
• QUANTIZE - has twoDECFLOAT arguments. The returned value is first argument scaled using second value as a pattern. For example QUANTIZE(1234, 9.999) returns 1234.000.
• TOTALORDER - compares two DECFLOAT values including any special value. The comparison is exact. Returns SMALLINT value which can be as follows:
```                -1 - first value is less than second
0 - values are equal
1 - first value is greater than second
```

DECFLOAT values are ordered as follows:

```                -nan < -snan < -inf < -0.1 < -0.10 < -0 < 0 < 0.10 < 0.1 < inf < snan < nan
```

4. Firebird supports new session control operator SET DECFLOAT. It has following forms:

• SET DECFLOAT ROUND <mode> - controls rounding mode used in operations with DECFLOAT values. Valid modes are: CEILING (towards +infinity), UP (away from 0), HALF_UP (to nearest, if equidistant - up), HALF_EVEN (to nearest, if equidistant - ensure last digit in the result to be even), HALF_DOWN (to nearest, if equidistant - down), DOWN (towards 0), FLOOR (towards -infinity), REROUND (up if digit to be rounded is 0 or 5, down in other cases). HALF_UP rounding is used by default.
• SET DECFLOAT TRAPS TO <comma-separated traps list - may be empty> - controls which exceptional conditions cause a trap. Valid traps are: Division_by_zero, Inexact, Invalid_operation, Overflow and Underflow. By default traps are set to: Division_by_zero, Invalid_operation, Overflow.
• SET DECFLOAT BIND <bind-type> - controls how are DECFLOAT values represented in outer world (i.e. in messages or in XSQLDA). Valid binding types are: NATIVE (use IEEE754 binary representation), CHAR/CHARACTER (use ASCII string), DOUBLE PRECISION (use 8-byte FP representation - same as used for DOUBLE PRECISION fields) or BIGINT with possible comma-separated SCALE clause (i.e. 'BIGINT, 3'). Various bindings are useful if one plans to use DECFLOAT values with some old client not supporting native format. One can choose between strings (ideal precision, but poor support for further processing), floating point values (ideal support for further processing but poor precision) or scaled integers (good support for further processing and required precision but range of values is very limited). When using in a tool like generic purporse GUI client choice of CHAR binding is OK in most cases. By default NATIVE binding is used.

5. The length of DECFLOAT literals are limited to 1024 characters. For longer values, you will need to use the scientific notation. For example, the 0.0<1020 zeroes>11 cannot be used as a literal, instead you can use the equivalent in scientific notation: 1.1E-1022. Similarly 10<1022 zeroes>0 can be presented as 1.0E1024.