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# round, rescale - Rounding Functions

Other versions:
7.31 | 7.40 | **7.54**

## Syntax

```
```

... round*|*rescale( val = arg ... ) ...

### Effect

The rounding functions expect a decimal
floating point number as a main argument `val`

and additional arguments
that describe how this floating point number is handled. The type of the return value of a rounding
function is always `decfloat34`

. Within an arithmetic expression, the argument
for the decimal floating point number can either be an arithmetic expression or a function. The other arguments must always be specified as numeric data objects.

Note

The class CL_ABAP_MATH includes the method NORMALIZE for normalizing a decimal floating point object. The mantissa does not have any closing zeros in a normalized floating point number.

## Rounding Function

The rounding function `round`

can be implemented in operand positions using the following syntax:

## Syntax

```
... round( val = arg
```*{*dec = n*}**|**{*prec = n*}* *[*mode = m*]* ) ...

### Effect

This function rounds a decimal floating point number declared as an argument for the parameter
val. A data object specified for `arg`

is converted to the data type `decfloat34`

before the function is executed, if necessary.

Either the parameter `dec`

or the parameter `prec`

must be given a value, and rounding must be to either a particular number of decimal places or
precision:

- If the parameter
`dec`

is given a value, the value entered is rounded to the number of decimal places specified in`n`

and returned.`n`

expects data objects of the type`i`

. The value of these data objects cannot be less than -6144. If a negative value is given, the relevant whole number place is rounded.

- If the parameter
`prec`

is given a value, the value entered is rounded to the precision specified in n and returned.`n`

expects data objects of the type`i`

. The value of these data objects must be greater than 0.

A rounding can reduce scaling and
precision but cannot increase
them. If `dec`

is specified, the mantissa of the return code does not contain
any zeroes after the place where the rounding applies. If `prec`

is specified,
the input value is returned without being changed, if the specified precision is greater than or equal to the input value.

The parameter `mode`

(optional) can be used to set the rounding type. For
m it is only possible to specify values that exist as ROUND_... constants in class CL_ABAP_MATH.
The following table shows the possible rounding rules. If `mode`

is not given a value, commercial rounding is used.

Constant | Rounding rule |
---|---|

ROUND_HALF_UP | The value is rounded down to the next round figure. If the value falls precisely halfway between two rounded values, it is rounded up away from zero (commercial rounding). |

ROUND_HALF_DOWN | The value is rounded down to the next round figure. If the value falls precisely halfway between two round values, it is rounded down towards zero. |

ROUND_HALF_EVEN | The value is rounded down to the next round figure. If the value falls precisely halfway between two rounded values, it is rounded to the value which has an even number in the last place. |

ROUND_UP | The value is always rounded away from zero/to the larger absolute value. |

ROUND_DOWN | The value is always rounded to zero/to the smaller absolute value. |

ROUND_CEILING | The value is always rounded in a positive direction/to the larger value. |

ROUND_FLOOR | The value is always rounded in a positive direction/to the larger value. |

Example

The following tables show the results of commercial rounding of the decimal floating point number 1234.56789
(scaling 5, precision 9) with various values for `dec`

and `prec`

.
The displayed results are generated by executing the program DEMO_ROUND_AND_RESCALE.

dec | Result | Scaling | Precision |
---|---|---|---|

-5 | 0E+5 | -5 | 1 |

-4 | 0E+4 | -4 | 1 |

-3 | 1E+3 | -3 | 1 |

-2 | 1.2E+3 | -2 | 2 |

-1 | 1.23E+3 | -1 | 3 |

0 | 1235 | 0 | 4 |

1 | 1234.6 | 1 | 5 |

2 | 1234.57 | 2 | 6 |

3 | 1234.568 | 3 | 7 |

4 | 1234.5679 | 4 | 8 |

5 | 1234.56789 | 5 | 9 |

6 | 1234.56789 | 5 | 9 |

prec | Result | Scaling | Precision |
---|---|---|---|

1 | 1E+3 | -3 | 1 |

2 | 1.2E+3 | -2 | 2 |

3 | 1.23E+3 | -1 | 3 |

4 | 1235 | 0 | 4 |

5 | 1234.6 | 1 | 5 |

6 | 1234.57 | 2 | 6 |

7 | 1234.568 | 3 | 7 |

8 | 1234.5679 | 4 | 8 |

9 | 1234.56789 | 5 | 9 |

10 | 1234.56789 | 5 | 9 |

### Executable Example

## Rescaling Function

The rescaling function `rescale`

can be implemented in operand positions using the following syntax:

## Syntax

```
... rescale( val = arg
```*{*dec = n*}**|**{*prec = n*}* *[*mode = m*]* ) ...

### Effect

This function changes the scaling
of a decimal floating point number declared as an argument for the parameter `val`

.
A data object specified for `arg`

is converted to the data type `decfloat34`

before the function is executed, if necessary.

Either the parameter `dec`

or the parameter `prec`

must be given a value, where either the
scaling or the precision is set:

- If the parameter
`dec`

is given a value, the value entered is rounded using the scaling specified in`n`

and returned.`n`

expects data objects of the type`i`

. The value of these data objects cannot be less than -6144. If the scaling produces more than 34 places in the mantissa of the return value, a handleable exception is raised.

- If the parameter
`prec`

is given a value, the value entered is returned with the precision specified in`n`

and appropriate scaling and returned.`n`

expects data objects of the type`i`

. The value of these data objects must be greater than 0 and less than 34.

A rescaling can both reduce and increase scaling and precision. An increase adds zeros on the right.

The input value is rounded if required. The optional parameter `mod`

can be
used to specify the rounding rule, as described under the function `round`

. The default is commercial rounding.

### Examples

The following tables show the results of rescaling of the decimal floating point number 1234.56789 (scaling
5, precision 9) with various values for `dec`

and `prec`

,
if commercial rounding is used. The displayed results are generated by executing the program DEMO_ROUND_AND_RESCALE.

dec | Result | Scaling | Precision |
---|---|---|---|

-5 | 0E+5 | -5 | 1 |

-4 | 0E+4 | -4 | 1 |

-3 | 1E+3 | -3 | 1 |

-2 | 1.2E+3 | -2 | 2 |

-1 | 1.23E+3 | -1 | 3 |

0 | 1235 | 0 | 4 |

1 | 1234.6 | 1 | 5 |

2 | 1234.57 | 2 | 6 |

3 | 1234.568 | 3 | 7 |

4 | 1234.5679 | 4 | 8 |

5 | 1234.56789 | 5 | 9 |

6 | 1234.567890 | 6 | 10 |

7 | 1234.5678900 | 7 | 11 |

8 | 1234.56789000 | 8 | 12 |

prec | Result | Scaling | Precision |
---|---|---|---|

1 | 1E+3 | -3 | 1 |

2 | 1.2E+3 | -2 | 2 |

3 | 1.23E+3 | -1 | 3 |

4 | 1235 | 0 | 4 |

5 | 1234.6 | 1 | 5 |

6 | 1234.57 | 2 | 6 |

7 | 1234.568 | 3 | 7 |

8 | 1234.5679 | 4 | 8 |

9 | 1234.56789 | 5 | 9 |

10 | 1234.567890 | 6 | 10 |

11 | 1234.5678900 | 7 | 11 |

12 | 1234.56789000 | 8 | 12 |