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ABAP Keyword Documentation → ABAP − Reference → Processing Internal Data → Numeric Calculations → Numerical Functions →round, rescale - Rounding Functions
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.
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. |
Example
For a demonstration of the rounding types, see Rounding Function round.
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.
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 |