Arithmetical expressions <expr>
In the handling of arithmetical expressions, the general computing rules are used:
- point before dash calculation
- the parenthesis rule, whereby square parentheses "[ ]" are to be used
In arithmetical expressions, parameters are often used; the notation of parameters is:
- P followed by an integer, for instance P12.
Example for an arithmetical expression:
P5 = [[sin[R1*30.00] + P2] / P5]
Symbolic character sets can be assigned to arithmetical expressions and to parts thereof.
Such a string leads to the default string, which is analyzed in place of the character string. A recursive handling is also possible.
The character strings must be within quotation marks. During their decoding a differentiation is made between the upper-case and lower case letters. The nesting of strings is displayed through a pre-set '\'-character before the limiting quotation mark. Attention must be paid to the fact that always complete nesting levels are to be grouped in one string, i.e. the adding of ´[´ at the beginning and ´]´ at the end of the replacement text should not have any effect on the result of the mathematical expression.
Programming example
Correct:
N10 "STRING1" = "COS[\"STRING2\"]"
N20 "STRING2" = "5 * 12"
N30 "STRING3" = "SIN[89.5 + \"STRING1\"]"
N40 X[-2 * "STRING1" + "STRING2" + "STRING3"] (Traverse after X60)
M30
Wrong: Only complete nesting levels should be put together in the string
N10 "STRING1" = "COS["
N20 "STRING2" = "90]"
N30 "STRING3" = "\"STRING1\" \"STRING2\" "
The character sets defined in the NC-program are valid program-globally.
The programming of symbol character sets outside the mathematical expressions is described in the separate programming manual symbolic character sets.
Survey 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 exponent 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 extraction | SQRT [..] | P1 = SQRT [SQR[P2]+SQR[P3]] |
e - function | EXP [..] | P1 = EXP [P2 * P4] |
Natural logarithm | LN [..] | P1 = LN [P2] + LN [P3] |
Tens - exponential | 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 arguments can be any positive mathematical expressions or numbers. Negative expressions or numbers are not allowed. Floating point arguments are converted to integer. |
Logical operators :
logic AND operation | && / AND | $IF P1 >= P2 && P3 != P4 respectively $IF P1 >= P2 AND P3 != P4 |
logic OR operation | || / OR | $IF P1 >= P2 || P3 != P4 respectively $IF P1 >= P2 OR P3 !=P4 |
Comparison operators:
In loop constructions (see paragraph 10: "Program branches) comparison operations will be necessary. Verifications can be done as follows:
Equality | == | $IF P1 == 5 |
Inequality | != | $IF P1 != 5 |
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 |
Possible truth values are:
TRUE | true | $IF V.A.MERF.X == TRUE |
FALSE | not true | $WHILE V.G.WZ[2].OK == FALSE |
Notice | |
Use of the truth values:For TRUE control internally the value 1 is used.For FALSE control internally the value 0 is used. |
Trigonometric functions (specification of angles in degrees):
Sine | SIN [..] | P1 = SIN [P2 * 30 +10] |
Cosine | COS [..] | P1 = COS [P2 * 30 +10] |
Tangent | TAN [..] | P1 = TAN [P2 * 30 +10] |
Arc sine | ASIN [..] | P1 = ASIN [P2 * 10] |
Arc cosine | ACOS [..] | P1 = ACOS [P2 * 10] |
Arc tangent | ATAN [..] | P1 = ATAN [P2 * 10] |
Arc tangent with 2 arguments | ATAN2 [y,x] | P1 = ATAN2[100,100] (-> Result |
Notice | |
In the case of the trigonometric functions ASIN and ACOS the argument must always be between -1 and +1.For the function TAN, the argument should not assume the values ... -90, 90, 270 ... degrees.The function ATAN2 calculates for x != 0 the angle of a position to the X axis in the correct quadrant.Exception: For ATAN2[0,0] (x = y = 0) the result is always 0. |
Transformation functions:
Integer | INT [..] | cuts off the digits after the decimal point |
Float | FRACT [..] | removes integer |
Rounding Off | ROUND [..] | rounds off to integer |
Special functions:
Check for existence of variables/ parameters/ M/H functions | EXIST [ <variable/parameter/ M function/ H function>] | $IF EXIST[V.P.MY_VAR] == TRUE $IF EXIST[P1] != TRUE $IF EXIST[M55] == TRUE $IF EXIST[H20] == TRUE | |
Determine the size of an array dimension | SIZEOF [<array_name>, <dimension>] oder SIZEOF [<array_name>] (für 1. Dim.) | $IF [V.P.MY_ARRAY,2] P1 = | |