Arithmetic expressions <expr>
The usual calculation rules apply to handling arithmetic expressions:
- order-of-operations rule
- the parenthesis rule, whereby square brackets "[ ]" must be used. Round parenthesis "(...)” are for comments.
Parameters are often used in arithmetic expressions. The notation of parameters is:
- P followed by an integer, e.g. P12.
Example of an arithmetic expression:
P5 = [[sin[R1*30.00] + P2] / P5]
Macros (strings) may be assigned to arithmetical expressions and parts of them.
A macro name leads to a macro content which is analysed. Recursive handling is also possible.
Macro names must be placed in quotation marks. When decoded, the notation is case-sensitive (uppercase/lowercase).
Nested strings are identified by a preceding '\' before the double quotation marks. Make sure that complete nesting levels are always grouped in a macro, i.e. adding ´[´ at the start and ´]´ at the end of macro content should have no effect on the result of the mathematical expression.
Programming Example
Nested macros
Macros defined in the NC program are valid program global.
Section "Macroprogramming (# INIT MACRO TAB) “ describes how to program macros outside mathematical expressions.
Overview of all available calculation operations:
Basic types of calculation:
Addition | + | P1 = P2 + P3 + 0.357 |
Subtraction | - | P1 = P2 - 0.031 |
Multiplication | * | P1 = P2 * [P3 + 0.5] |
Division | / | P1 = P2 * P3 / [P5 + P6] |
Exponential calculation | ** | P1 = 2**P3 (2 to the power P3) |
Modulo calculation | MOD | P1 = 11 MOD 3 (-> 2) |
Numerical functions:
Absolute value formation | ABS [..] | P1 = ABS [P2 - P4] |
Squaring | SQR [..] | P1 = SQR [P2] + SQR [P3] |
Square root | SQRT [..] | P1 = SQRT [SQR[P2]+SQR[P3]] |
e function | EXP [..] | P1 = EXP [P2 * P4] |
Natural logarithm | LN [..] | P1 = LN [P2] + LN [P3] |
To the power of ten | DEXP [..] | P1 = DEXP [P2] |
Common logarithm | LOG [..] | P1 = LOG [P2] |
Notice | |
In the case of LN, LOG and SQRT the argument must always be greater than 0! |
Bit operators:
AND operation | & | P1 = P2 & P3 |
OR operation | | | P1 = P2 | P3 |
Exclusive OR | ^ | P1 = P2 ^ P3 |
Complement | INV[..] | P1 = INV[P2] |
Notice | |
The operands may be any positive mathematical expression or number within the range 0 ... 2^32-1 (UNS32). Negative expressions or numerals are not allowed. Floating point numbers are converted into integers. The result of a bit operation is always within the range of 0... 2^32-1 (UNS32). |
Logic operators:
AND operation | && / AND | P1 = P2 && P3 P1 = P2 AND P3 |
OR operation | || / OR | P1 = P2 || P3 P1 = P2 OR P3 |
Exclusive OR operation | XOR | P1 = P2 XOR P3 |
NOT operation | NOT[..] | P1 = NOT[P2] P1 = NOT[1] (P1 = 0) P1 = NOT[0.5] (P1 = 0) P1 = NOT[0.49] (P1 = 1) P1 = NOT[0] (P1 = 1) |
Notice | |
Operands may be any positive mathematical expression or numeral. Negative expressions or numerals are not allowed. A floating point numeral is evaluated as TRUE (1) if its value is > or = 0.5. |
Comparison operators:
Loops (Section Statements for influencing NC program flow) require comparison expressions. Verification can be conducted as follows:
Equality | == | $IF P1 == 10 |
Inequality | != | $IF P1 != 10 |
Greater than or equal to | >= | $IF P1 >= 10 |
Less than or equal to | <= | $IF P1 <= 10 |
Less than | < | $IF P1 < 10 |
Greater than | > | $IF P1 > 10 |
Operator priorities:
The priorities of available operators are listed in descending order. 10 is the highest and 1 is the lowest priority.
Priority | Operator | Description |
10 | ** | Power |
9 | *, / | Multiplication, division |
8 | +, - | Addition, subtraction |
7 | & | Bitwise AND |
6 | ^ | Bitwise exclusive OR |
5 | | | Bitwise OR |
4 | <=, >=, ==, <, >, != | Comparison operators |
3 | &&, AND | Logic AND |
2 | XOR | Logic exclusive OR |
1 | ||, OR | Logic OR |
Possible truth values are:
True | TRUE | $IF V.A.MERF.X == TRUE |
Not true | FALSE | $WHILE V.G.WZ[2].OK == FALSE |
Notice | |
Processing truth values: For TRUE, the value 1 is used in the controller. For FALSE, the value 0 is used in the controller. |
Trigonometric functions (angles specified in degrees):
Sine | SIN [..] | P1 = SIN [P2] |
Cosine | COS [..] | P1 = COS [P2] |
Tangent | TAN [..] | P1 = TAN [P2] |
Cotangent | COT [..] | P1 = COT [P2] |
Arcsine | ASIN [..] | P1 = ASIN [P2] |
Arccosine | ACOS [..] | P1 = ACOS [P2] |
Arctangent | ATAN [..] | P1 = ATAN [P2] |
Arctangent with | ATAN2 [y,x] | P1 = ATAN2[100,100] (-> result is 45°) |
Arc cotangent | ACOT [..] | P1 = ACOT [P2] |
Notice | |
With the numerical functions ASIN and ACOS, the argument must always be between -1 and +1. For the numerical function TAN, the argument should not assume the values... -90, 90, 270 ... degrees. For the numerical function COT, the argument should not assume the values... -180, 0, 180 ... degrees. The numerical function ATAN2 results in x!=0 for the angle of a position relative to the X axis in the correct quadrant. Special case: For ATAN2[0.0] (x = 0 and y = 0), the result is always 0. |
Transformation functions:
Remove | INT [..] | P1 = INT [123,567] (P1 = 123) |
Remove | FRACT [..] | P1 = FRACT [123,567] (P1 = 0,567) |
Round up to integer | ROUND [..] | P1 = ROUND [77.5] (P1 = 78) P1 = ROUND [45.4] (P1 = 45) |
Round up | CEIL [..] | P1 = CEIL [8.3] (P1 = 9) |
Round down | FLOOR [..] | P1 = FLOOR [8.7] (P1 = 8) |
Constants:
3.141592654 (π) | PI | P2 = 2*PI (P2 = 6.283185307) |
Special functions:
Check for existence of variables (V.P., V.L., V.S., V.E.) / parameters / M/H functions / macros |
EXIST [<Variable/ Parameter/ M function/ H function/ macro_name>] | $IF EXIST[V.P.MYVAR] == TRUE $IF EXIST[V.L.MYARRAY[0]] == TRUE * $IF EXIST[P1] != TRUE $IF EXIST[M55] == TRUE $IF EXIST[H20] == TRUE $IF EXIST["Macro1"] == TRUE *For arrays with valid indices! |
Determining the size of an array dimension of variables (V.P., V.L., V.S., V.E.) / parameters |
SIZEOF [<Array_name>, <Dimension>]
or for 1. Dim. SIZEOF [<Array_name>] | #VAR P99[3][4]= [1,2,3,4, 5,6,7,8, 11,12,13,14] #ENDVAR (P12 and P13 for 1st dimension) P12 = SIZEOF[P99] (P12 = 3) P13 = SIZEOF[P99,1] (P13 ==P12 =3) (P14 for 2nd dimension) P14 = SIZEOF[P99,2] (P14 = 4) (P15 for 3rd dimension that does not exist) P15 = SIZEOF[P99,3] (P15= -1) SIZEOF always results in -1 for non-existent array dimensions and for variables that are not arrays. |
Determine greater value | MIN [x,y] | P1 = MIN [P2, P3] |
Determine greater value | MAX [x,y] | P1 = MAX [P2, P3] |
Determine sign | SIGN [..] | P1 = SIGN [P2] results in positive values: 1 negative values: -1 Zero: 0 |
Determining the string length of a macro content. [as of V2.11.2841.00] | MACRO_LENGTH [<macro_name>] | "Macro53" = "G53 X0 Y0 Z0" "Empty" = "" P1 = MACRO_LENGTH["Macro53"] (P1 = 12) P1 = MACRO_LENGTH["Empty"] (P1 = 0) MACRO_LENGTH always results in -1 for non-existent macros. |
Reading and resolving a macro content. The return value is a string. [as of V3.1.3081.4] | <MACRO_CONTENT[<macro_name>] | "MACRO_1" = "1 + 2" "MACRO_2" = "SIN[\"MACRO_1\"]" MACRO_CONTENT["MACRO_1"] returns "1 + 2" MACRO_CONTENT["MACRO_2"] returns "SIN[1 + 2]" |
Encryption function:
This function is used to encrypt strings. The related key is user-definable. Strings may contain important data that require protection by encryption.
Encrypted data can then be saved to file with #MSG SAVE, for example, or supplied to the PLC by V.E. variables.
Encrypt string | ENCRYPT ["key", "string"] |
 | Due to an EU export regulation, the decryption function is no longer available. |
The product of ENCRYPT is assigned to a string-type variable. In this case, note the following:
- The string variable must at least be double the length of the encrypted string.
Programming Example
Encrypt string and save to file