# DECIMAL(p,s)

The `DECIMAL`

data type is provided to handle large numeric
values with exact decimal storage.

## Syntax

`DECIMAL ``[`

( `precision``[`

,`scale``]`

) `]`

`precision`defines the number of significant digits (limit is 32, default is 16).`scale`defines the number of digits to the right of the decimal point.- When no
`scale`is specified, the data type defines a floating point number. - When no (
`precision`,`scale`) is specified, it defaults to`DECIMAL(16)`

.

## Usage

Use the `DECIMAL`

data type when you need to store values that have
a fixed number of digits on the right and left of the decimal point (`DECIMAL(p,s)`

),
or to store a floating point decimal with an exact number of significant digits
(`DECIMAL(p)`

).

`DEC`

, `DECIMAL`

and `NUMERIC`

are
synonyms.

`DECIMAL`

variables are initialized to `NULL`

in
functions, modules and globals.

When using `DECIMAL(p,s)`

with a precision and scale, you define a decimal for
fixed point arithmetic, with p significant digits and s digits on the right of the decimal point.
For example, `DECIMAL(8,2)`

can hold the value 123456.78 (8 (p) = 6 digits on the
left + 2 (s) digits on the right of the decimal point).

When using `DECIMAL(p)`

with a precision but no scale, you define a floating-point
number with p significant digits. For example, `DECIMAL(8)`

can store 12345678, as
well as 0.12345678.

In most database implementations, the decimal data type always has a fixed number of decimal
digits. Use `DECIMAL`

types with precision and scale to implement portable code, and
avoid mistakes if default sizes apply when precisions and/or scale are omitted in SQL statements.
For example, with Oracle®, a
`NUMBER(p)`

is equivalent to a `DECIMAL(p,0)`

in BDL, not
`DECIMAL(p)`

.

When using `DECIMAL`

without a precision and scale, it defaults to
`DECIMAL(16)`

, a floating-point number with a precision of 16 digits.

```
MAIN
DEFINE d1 DECIMAL(10,4)
DEFINE d2 DECIMAL(10,3)
LET d1 = 1234.4567
LET d2 = d1 / 3 -- Rounds decimals to 3 digits
DISPLAY d1, d2
END MAIN
```

`DECIMAL`

values can be converted to strings based on the DBFORMAT (or DBMONEY) environment variable
(defines the decimal separator) setting.

## Value ranges

The largest absolute value that a `DECIMAL(p,s)`

can store without errors is
10^{p-s} - 10^{s}. The stored value can have up to 30 significant decimal
digits in its fractional part, or up to 32 digits to the left of the decimal point.

When using `DECIMAL(p,s)`

the range of values is defined by the p, the
number of significant digits. For example, a variable defined as
`DECIMAL(5,3)`

can store values in the range -99.999 to 99.999. The
smallest positive non zero value is 0.001.

When using `DECIMAL(p)`

the magnitude can range from -N*10^{-124} to
N*10^{124}, where N can have up to p significant digits and be 0<N<10. For
example, a variable defined as `DECIMAL(5)`

can store values in the range
-9.9999e-124 to 9.9999e+124. The smallest positive non zero value is 9.9999e-130.

## Exceptions

When the default exception handler is used, if you try to assign a value larger than the
decimal definition (for example, 12345.45 into `DECIMAL(4,2)`

), no
out of range error occurs, and the variable is assigned with `NULL`

.
If `WHENEVER ANY ERROR`

is used, it raises error -1226. If you do not
use `WHENEVER ANY ERROR`

, the status variable is not set to -1226.

Data type conversion can be controlled by catching the runtime exceptions. For more details, see Handling type conversion errors.

## Computation and rounding rules

When computing or converting decimal values, the "round half away from zero" rule will apply: If the fraction of the value v is exactly 0.5, then r = v + 0.5 if v is positive, and r = v - 0.5 if v is negative. For example, when the result must be rounded to a whole number, 23.5 gets rounded to 24, and -23.5 gets rounded to -24.

In the next example, the division result of 11 / 3 gives the infinite decimal value
3.666666... (with an infinite decimal part). However, this value cannot be stored in a fixed
point decimal type. When stored in a `DECIMAL(10,2)`

, the value will be
rounded to 3.67, and when multiplying 3.67 by 3, the result will be 11.01, instead of 11:

```
MAIN
DEFINE v DECIMAL(10,2)
LET v = 11 / 3
DISPLAY "1. v = ", v USING "---&.&&&&&&&&"
LET v = v * 3
DISPLAY "2. v = ", v USING "---&.&&&&&&&&"
END MAIN
```

```
1. v = 3.67000000
2. v = 11.01000000
```

## High-precision math functions

A couple of precision math functions are available, to be used with DECIMAL values.
These functions have a higher precision as the standard C library functions based on C
double data type, which is equivalent to `FLOAT`

: