# String arithmetic functions The string arithmetic functions and pre-compiler are the last method of using AccuMath in your applications. These functions are compatible with the Ultimate string math functions. Using the pre-compiler, source code compatibility with programs using Ultimate's string arithmetic functions can be maintained. Only SADD(), SSUB(), SMUL(), SDIV() and SCMP() are defined as string arithmetic functions. These functions will accept either two or three arguments. The first two arguments are the two operands supplied to the function. The third, optional operand, is an explicit precision for the function. These functions behave exactly like the explicit precision subroutines (if the third argument is missing, the default precision is used). If the other AccuMath functions are required, call the explicit precision mode BASIC subroutines. For compatibility with Ultimate string arithmetic, use only two arguments in the string arithmetic functions. The third argument, allowing the specification of function precision, is an extension added to AccuMath. ## Pre-compiler When using the string arithmetic functions, it is necessary to compile your programs using the AccuMath pre-compiler: XP-BASIC. The pre-compiler translates the string arithmetic functions into OCONV() functions. It then calls the BASIC compiler to compile the program. When using the pre-compiler, it is necessary to include the following statement in your program: ``` INCLUDE XP XPA.DEFS ``` If a program INCLUDEs a program fragment which contains string arithmetic functions, they will not be converted by the pre-compiler, and will not compile properly. In this case, the pre-compiler may be used to translate the INCLUDEd program fragment and update the source code with the translated version. To do this, copy the original source program fragment to another file (since the source code will be updated). Next, execute the XP-PRECOMP verb with the (O) option to update the source code. Now when you compile the main program, the INCLUDEd program fragment will have been translated by XP-PRECOMP, and the program will compile successfully. The syntax for the XP-BASIC and XP-PRECOMP verbs is exactly the same as the BASIC verb. Note: for Open Architecture only, XP-BASIC and XP-PREBASIC are case insensitive, and XP-COMPILE and XP-PRECOMP are case sensitive. The following sections describe the string arithmetic functions in more detail. ## Addition Two arguments may be added together using the SADD function. If the third argument is omitted, the precision of the result will be the greater of the precision of either of the arguments. If the third argument is specified, the result will be rounded to the specified precision. ``` RESULT = SADD(ARG1,ARG2) RESULT = SADD(ARG1,ARG2,PRECISION) ``` ## Subtraction The difference between two arguments (ARG1 - ARG2) may be computed using the SSUB function. If the third argument is omitted, the precision of the result will be the greater of the precision of either of the arguments. If the third argument is specified, the result will be rounded to the specified precision. ``` RESULT = SSUB(ARG1,ARG2) RESULT = SSUB(ARG1,ARG2,PRECISION) ``` ## Multiplication The product of two arguments may be computed using the SMUL function. If the third argument is omitted, the precision of the result will be sum of the precision of each of the arguments. For example, if ARG1=1.25 (precision=2) and ARG2=0.375 (precision=3), then RESULT=0.46875 (precision=5). If the third argument is specified, the product will be rounded to the specified precision. ``` RESULT = SMUL(ARG1,ARG2) RESULT = SMUL(ARG1,ARG2,PRECISION) ``` ## Division The quotient of two arguments (ARG1 / ARG2) may be computed using the SDIV function. If the third argument is omitted, the precision of the result will be the default precision (standard default is 14). If the third argument is specified, the result will be rounded to the specified precision. ``` RESULT = SDIV(ARG1,ARG2) RESULT = SDIV(ARG1,ARG2,PRECISION) ``` ## Comparison Two arguments may be compared, and the results (lower, equal, higher) determined. If the first argument is less than the second argument then -1 is returned. If the first argument is greater than the second argument then 1 is returned. If the first argument is equal to the second argument then 0 is returned. A third argument, if specified, is ignored. ``` RESULT = SCMP(ARG1,ARG2) RESULT = SCMP(ARG1,ARG2,PRECISION) ``` ## Calculator The AccuMath package contains two algebraic calculator programs. These may be used to aid in developing programs utilizing the AccuMath subroutines, testing formulas, and for general use. One of the calculators (ALG) uses the implicit precision mode, the other (ALGX) uses the explicit precision mode. To use the calculator program, type ALG or ALGX at TCL. If you run ALGX, the program will prompt: ``` Maximum precision for calculations (RETURN for default)? ``` Enter any valid precision (4-50), or press RETURN to use the default precision (standard default precision is 14). Next, either ALG or ALGX will prompt: ``` Enter Expression: ``` At this prompt, you can enter any valid expression in standard algebraic notation. The syntax is similar to BASIC, except that the only operands allowed are numbers or references to the calculator's memory elements. If a valid expression was entered, the calculator will print the result: ``` 1>  result ```  After the result is printed, the calculator will again prompt for an expression. As each result is displayed, a memory element number is printed before it. The result may be used as an operand in another expression by preceding the memory element number by a percent sign. For example, consider the following sequence: ``` Enter Expression: SIN(23)   1>  0.39073112848927   Enter Expression: COS(23)   2>  0.92050485345244   Enter Expression: (%1)^2 + (%2)^2   3>  1   Enter Expression: 2*(1.34563421349784/.20145265)^3   4>  596.06291722886108   Enter Expression: 100000^1.1875/(5*.140328642283449)   5>  1234194.68651440253212   Enter Expression: LN(1.12)   6>  0.113328685307   Enter Expression: 500000/(1+0.0675)^5   7>  360687.07992475241642 ``` --- Source: https://d3codex.com/accumath/string-arithmetic-functions/ - part of the D3Codex reference.