ABAP Keyword Documentation → ABAP - Reference → Processing Internal Data → Numeric Calculations → Numerical Functions
round, rescale - Rounding Functions
Other versions: 7.31 | 7.40 | 7.54
Syntax Forms
... 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 trailing 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.
- If the parameter
decis given a value, the value entered is rounded to the number of decimal places specified innand returned. Data objects of typeiis expected forn. 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
precis given a value, the value entered is rounded to the precision specified in n and returned. Data objects of typeiare expected forn. 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 zeros after the position 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 up 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 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 decimal 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. |
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.
- If the parameter
decis given a value, the value entered is rounded using the scaling specified innand returned. Data objects of typeiis expected forn. The value of these data objects cannot be less than -6144. The value of these data objects cannot be less than -6144. If the scaling results in more than 34 decimal places in the mantissa of the return value, an exception that can be handled is raised.
- If the parameter
precis given a value, the value entered is returned with the precision specified innand appropriate scaling and returned. Data objects of typeiare expected forn. 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 table shows the results of commercial rounding of the decimal floating point number 1234.56789 (scaling 5, precision 9) with various values for dec.
| dec | String Representation | Internal Representation | Scaling | Precision |
|---|---|---|---|---|
| -5 | 0E+5 | 0...0000000000E+5 | -5 | 1 |
| -4 | 0E+4 | 0...0000000000E+4 | -4 | 1 |
| -3 | 1E+3 | 0...0000000001E+3 | -3 | 1 |
| -2 | 1.2E+3 | 0...0000000012E+2 | -2 | 2 |
| -1 | 1.23E+3 | 0...0000000123E+1 | -1 | 3 |
| 0 | 1235 | 0...0000001235E+0 | 0 | 4 |
| 1 | 1234.6 | 0...0000012346E-1 | 1 | 5 |
| 2 | 1234.57 | 0...0000123457E-2 | 2 | 6 |
| 3 | 1234.568 | 0...0001234568E-3 | 3 | 7 |
| 4 | 1234.5679 | 0...0012345679E-4 | 4 | 8 |
| 5 | 1234.56789 | 0...0123456789E-5 | 5 | 9 |
| 6 | 1234.56789 | 0...0123456789E-5 | 5 | 9 |
The following table shows the results of commercial rounding of the decimal floating point number 1234.56789 (scaling 5, precision 9) with various values for prec.
| prec | String Representation | Internal Representation | Scaling | Precision |
|---|---|---|---|---|
| 1 | 1E+3 | 0...0000000001E+3 | -3 | 1 |
| 2 | 1.2E+3 | 0...0000000012E+2 | -2 | 2 |
| 3 | 1.23E+3 | 0...0000000123E+1 | -1 | 3 |
| 4 | 1235 | 0...0000001235E+0 | 0 | 4 |
| 5 | 1234.6 | 0...0000012346E-1 | 1 | 5 |
| 6 | 1234.57 | 0...0000123457E-2 | 2 | 6 |
| 7 | 1234.568 | 0...0001234568E-3 | 3 | 7 |
| 8 | 1234.5679 | 0...0012345679E-4 | 4 | 8 |
| 9 | 1234.56789 | 0...0123456789E-5 | 5 | 9 |
| 10 | 1234.56789 | 0...0123456789E-5 | 5 | 9 |
The following table shows the results of rescaling of the decimal floating point number 1234.56789 (scaling 5, precision 9) with various values for dec, if commercial rounding is used.
| dec | String Representation | Internal Representation | Scaling | Precision |
|---|---|---|---|---|
| -5 | 0E+5 | 0...0000000000000E+5 | -5 | 1 |
| -4 | 0E+4 | 0...0000000000000E+4 | -4 | 1 |
| -3 | 1E+3 | 0...0000000000001E+3 | -3 | 1 |
| -2 | 1.2E+3 | 0...0000000000012E+2 | -2 | 2 |
| -1 | 1.23E+3 | 0...0000000000123E+1 | -1 | 3 |
| 0 | 1235 | 0...0000000001235E+0 | 0 | 4 |
| 1 | 1234.6 | 0...0000000012346E-1 | 1 | 5 |
| 2 | 1234.57 | 0...0000000123457E-2 | 2 | 6 |
| 3 | 1234.568 | 0...0000001234568E-3 | 3 | 7 |
| 4 | 1234.5679 | 0...0000012345679E-4 | 4 | 8 |
| 5 | 1234.56789 | 0...0000123456789E-5 | 5 | 9 |
| 6 | 1234.567890 | 0...0001234567890E-6 | 6 | 10 |
| 7 | 1234.5678900 | 0...0012345678900E-7 | 7 | 11 |
| 8 | 1234.56789000 | 0...0123456789000E-8 | 8 | 12 |
The following table shows the results of rescaling of the decimal floating point number 1234.56789 (scaling 5, precision 9) with various values for prec, if commercial rounding is used.
| prec | String Representation | Internal Representation | Scaling | Precision |
|---|---|---|---|---|
| 1 | 1E+3 | 0...0000000000001E+3 | -3 | 1 |
| 2 | 1.2E+3 | 0...0000000000012E+2 | -2 | 2 |
| 3 | 1.23E+3 | 0...0000000000123E+1 | -1 | 3 |
| 4 | 1235 | 0...00000000001235+0 | 0 | 4 |
| 5 | 1234.6 | 0...0000000012346E-1 | 1 | 5 |
| 6 | 1234.57 | 0...0000000123457E-2 | 2 | 6 |
| 7 | 1234.568 | 0...0000001234568E-3 | 3 | 7 |
| 8 | 1234.5679 | 0...0000012345679E-4 | 4 | 8 |
| 9 | 1234.56789 | 0...0000123456789E-5 | 5 | 9 |
| 10 | 1234.567890 | 0...0001234567890E-6 | 6 | 10 |
| 11 | 1234.5678900 | 0...0012345678900E-7 | 7 | 11 |
| 12 | 1234.56789000 | 0...0123456789000E-8 | 8 | 12 |