# Mathematical System Functions

The following mathematical functions are supported in arithmetic processing statements (`ADD`, `COMPUTE`, `DIVIDE`, `MULTIPLY`, `SUBTRACT`) and in logical condition criteria:

Function Format/Length Explanation
`ABS(field)` same as `field` Absolute value of `field`.
`ATN(field)` F8 Arc tangent of `field`.
`COS(field)` F8

Cosine of field.

If the value of the field is equal to or greater than 1017, `COS(field)` will be "1".

`EXP(field)` F8 Exponentiation of exponent field to base e , that is, efield, where e is Euler's number.
`FRAC(field)` same as `field` Fractional part of `field`.
`INT(field)` same as `field` Integer part of `field`.
`LOG(field)` F8 Natural logarithm of `field`.
`SGN(field)` same as `field` Sign of `field` (-1, 0, +1).
`SIN(field)` F8

Sine of `field` .

If the value of the `field` is equal to or greater than 1017, `SIN(field)` will be "0".

`SQRT(field)` (*)

Square root of `field`.

A negative value in the argument field will be treated as positive.

`TAN(field)` F8

Tangent of `field`.

If the value of the `field` is equal to or greater than 1017, `TAN(field)` will be "0".

`VAL(field)` same as target field

Extract numeric value from an alphanumeric `field`. The content of the `field` must be the alphanumeric (code page or Unicode) character representation of a numeric value. Leading or trailing blanks in the `field` will be ignored; decimal point and leading sign character will be processed.

If the target field is not long enough, decimal digits will be truncated (see also Field Truncation and Field Rounding in the section Rules for Arithmetic Assignment of the Programming Guide).

* This function is evaluated as follows:

• If `field` has format/length F4, format/length of `SQRT(field)` will be F4.

• If `field` has format/length F8 or I, format/length of `SQRT(field)` will be F8.

• If `field` has format N or P, see Precision of Results of Arithmetic Operations for format/length of `SQRT(field)`.

A `field` to be used with a mathematical function - except `VAL` - may be a constant or a scalar; its format must be numeric (N), packed numeric (P), integer (I), or floating point (F).

A `field` to be used with the `VAL` function may be a constant, a scalar, or an array; its format must be alphanumeric.

#### Mathematical Functions Example:

```** Example 'MATHEX': Mathematical functions
************************************************************************
DEFINE DATA LOCAL
1 #A     (N2.1) INIT <10>
1 #B     (N2.1) INIT <-6.3>
1 #C     (N2.1) INIT <0>
1 #LOGA  (N2.6)
1 #SQRTA (N2.6)
1 #TANA  (N2.6)
1 #ABS   (N2.1)
1 #FRAC  (N2.1)
1 #INT   (N2.1)
1 #SGN   (N1)
END-DEFINE
*
COMPUTE #LOGA = LOG(#A)
WRITE NOTITLE '=' #A 5X 'LOG'         40T #LOGA
*
COMPUTE #SQRTA = SQRT(#A)
WRITE         '=' #A 5X 'SQUARE ROOT' 40T #SQRTA
*
COMPUTE #TANA  = TAN(#A)
WRITE         '=' #A 5X 'TANGENT'     40T #TANA
*
COMPUTE #ABS   = ABS(#B)
WRITE     //  '=' #B 5X 'ABSOLUTE'    40T #ABS
*
COMPUTE #FRAC  = FRAC(#B)
WRITE         '=' #B 5X 'FRACTIONAL'  40T #FRAC
*
COMPUTE #INT   = INT(#B)
WRITE         '=' #B 5X 'INTEGER'     40T #INT
*
COMPUTE #SGN   = SGN(#A)
WRITE      // '=' #A 5X 'SIGN'        40T #SGN
*
COMPUTE #SGN   = SGN(#B)
WRITE         '=' #B 5X 'SIGN'        40T #SGN
*
COMPUTE #SGN   = SGN(#C)
WRITE         '=' #C 5X 'SIGN'        40T #SGN
*
END                                        ```

Output of program `MATHEX`:

```#A:  10.0     LOG                        2.302585
#A:  10.0     SQUARE ROOT                3.162277
#A:  10.0     TANGENT                    0.648360

#B:  -6.3     ABSOLUTE                   6.3
#B:  -6.3     FRACTIONAL                -0.3
#B:  -6.3     INTEGER                   -6.0

#A:  10.0     SIGN                      1
#B:  -6.3     SIGN                     -1
#C:   0.0     SIGN                      0       ```