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# abs, sign, ceil, floor, trunc, frac - Numerical Functions

The following table shows the general numerical functions for a single unnamed argument with any numerical data type. These functions are overloaded with the effect that the return value can have different numerical types.

Other versions: 7.31 | 7.40 | 7.54

## Syntax

``````
... func( arg ) ...
``````

### Effect

The argument of a general numerical function must be an individual data object outside an arithmetic expression, and can itself be a numeric expression within an arithmetic expression.

Effect of the general numerical functions.

Function func Return Value
`abs` Absolute value of argument `arg`
`sign` Sign of argument `arg`: -1, if the value of `arg`is negative; 0, if the value of `arg` is 0; 1, if the value of `arg` is positive
`ceil` Smallest integer that is not less than the value of the argument `arg` is
`floor` Largest integer that is not greater than the value of the argument `arg` is
`trunc` Value of the integer part of the argument `arg`
`frac` Value of the decimal places of the argument` arg`

The following applies with regard to the data type of the return value:

• With the exception of an arithmetic expression, the data type of the argument determines the data type of the return value.
• Within an arithmetic expression, the argument of the function contributes to the calculation type of the entire expression and the function is calculated using the calculation type. If the argument itself is an arithmetic expression, its operands contribute to the entire calculation type and the argument is also calculated with this type.

If the argument of a numerical function outside of an arithmetic expression has no numerical data type, `i`, `p`, `decfloat16`, `decfloat34`, or `f` its data type determines the type of return value as follows:

• `d` and `t` give` i`
• `c`, `n` and `string` give` p`
• `x` and `xstring` give`i`

Before the calculation of the function, the argument is converted into the respective type..

Note

The functions described here are some of the functions that can be used in the obsolete extended functional operand positions, even if their argument is a single data object.

Example

For a demonstration of the numeric functions, see Numeric Functions.