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EVALX.DOC Monday, September 17, 1990 Page 1 +-----------------------------------+ | | | evalx.c | | | +-----------------------------------+ Algebraic Expression Evaluator/Parser James P. Hawkins - WA2WHV P.O. Box 9146, Trenton, NJ 08650 September 11, 1990 EVALX.DOC Monday, September 17, 1990 Page 2 DESCRIPTION _____________________________________________________________________ Evalx is a convenient, powerful function which, when passed an ASCII string representing an algebraic expression of floating point numbers and math functions, will return the answer in a single floating point number. The expression may contain operators +, -, /, *, ^ and (). Parens may be nested more times than most would need. Embedded white space is allowed. Example: 2.0 + 22 * (3.1415926 * (2.4 - 33) + 3.3 ^ 2)/43 + (22 / 3.14)^3 Also, functions are available and can be used as shown in the following example: ((5.6 ^ 2 + sin(30 * (2 * 3.14159)/360))) which is 5.6 squared plus sin of 30 degrees. The sin function uses the angle in radians, so the conversion ratio is included in the argument to the sin function. MATH FUNCTIONS _____________________________________________________________________ The expression may contain digits representing decimal numbers or the following math functions: sin(expstr) - sine of an angle in radians cos(expstr) - cosine of an angle in radians exp(expstr) - exponentiate log(expstr) - natural log int(expstr) - integerize (truncate to right of dec .) sqr(expstr) - square root abs(expstr) - absolute value atn(expstr) - arctan rnd(expstr) - random number gen tan(expstr) - tangent of an angle fact(expstr) - factorial EVALX.DOC Monday, September 17, 1990 Page 3 CALLING FORMAT _____________________________________________________________________ A pointer to the string expression is passed to evalx() which returns a resulting value as a double precision floating point number. double value; /* declare a double */ double evalx(char *expstr); /* declare the function */ value = evalx(expstr); /* evaluate the expression and */ /* return it in value */ where: expstr is the char string representing the expression to be evaluated. The string must be NULL terminated. To test for an error, simply do a switch(errorflg). Errorflg must be declared as an extern int in the calling program. A zero value indicates no error, otherwise the error condition is defined as follows: ERRFATAL - FATAL ERROR ERRSYNTAX - SYNTAX ERROR ERROVFLOW - OVERFLOW ERROR ERRSQRT- SQUARE ROOT OF NEG NUMBER ERROR ERRFACT - FACTORIAL OF NEG or NUM > 33 ERROR ERRFUNC - UNKNOWN FUNCTION ERROR ERRILLVAR - ILLEGAL VARIABLE TYPE EXAMPLE PROGRAM _____________________________________________________________________ The following is a program example of the use of evalx(). When compiled, it provides a command which when given an expression as an argment (no embedded spaces) will print the answer. Or when invoked with no argment, will prompt for expression input. Embedded space IS allowed when prompted. The parser itself handles embedded spaces, however, an argument to a command with embedded spaces will be interpreted by the command shell as multiple arguments unless it is surrounded by quotes. Also note that in the UNIX shell, parens must be "hidden" from the shell with a preceding '\'. #include <stdio.h> EVALX.DOC Monday, September 17, 1990 Page 4 #include "evalx.h" /* Must be included error constants */ double evalx(char *ptr); /* declare evalx() */ extern int errorflg; /* declare external errorflg */ main(int argc, char **argv) { double val; /* declare double for result */ int exitflg = 0; char str[80]; /* storage for expression string */ while(1) { /* * If expression was in command argument then * Compute, print, then quit. * Else, wait for an input to be typed, compute, * print, then wait again. */ if(argc > 1) { strcpy(str, argv[1]); exitflg++; } else { printf("Input Expression:\n"); gets(str); } val = evalx(str); /* Evaluate the expression */ /* Test error condition if any */ switch(errorflg) { case 0: /* NO ERROR, PRINT RESULT */ printf("Result=%g\n", val); if(exitflg) { exit(0); } break; case ERRFATAL: printf("Fatal error\n"); break; case ERRSYNTAX: printf("Syntax error\n"); break; case ERROVFLOW: printf("Overflow error\n"); break; case ERRSQRT: printf("Square root of neg number error\n"); break; case ERRFACT: EVALX.DOC Monday, September 17, 1990 Page 5 printf("Factorial error\n"); break; case ERRFUNC: printf("Unknown math function error\n"); break; case ERRILLVAR: printf("Illegal variable error\n"); break; default: break; } } } ALGORITHM _____________________________________________________________________ The evalx() function loops until a null character is encountered. t the beginning of each loop, the function class() is called. This is in the file class.c which MUST be compiled and linked with evalx.c and the program. Class() classifies each item as a field of type OPCLASS, NMCLASS or FNCLASS. OPCLASS is returned if, an operator +,-,/,*,^,(,) is encountered. NMCLASS is returned if a number is scanned and FNCLASS is returned if the field is a function containing another expression such as sin(22 + 33). The class of field determines what action, evalx is to take next. There are two stacks, one for numbers or operands called double opndstack[] and one for operators char opstack[]. When a number is encountered in the string it is converted to a double precision floating point number and simply pushed onto the operand stack. When an operator, other than parens, is encountered, the stackop() function is called. Stackop() uses precedence rules to determine what to do with the current operator. The precedence of an operator is computed by passing the operator to the preced() function. The preced function returns a value of 1 for the operators '+' and '-', 2 for '*' and '/' and finally 3 for '^' or exponentiate. The precedence of the current operator is compared with the precedence of the operator on the top of the stack. If precedence of current operator is higher than the operator on top of the stack or the operator stack is empty, the precedence test has "passed" so just push the current operator onto the operator stack. If the current operator precedence is less than or equal to the operator on the top of the stack, the topmost operator is applied to the two topmost two operands in the operand stack by a call to unstack(). Unstack() is called until either the stack is empty or the precedence test passes in which the current operator is finally placed on the operator stack. That is, the unstack() function does the actual arithmetic operations EVALX.DOC Monday, September 17, 1990 Page 6 in evalx(). Examination of the unstack() function will show that it contains a simple switch() statement which uses the operator to determine which operation is to be performed on the topmost operands. Then, the operator and operand stcks are popped. When an open parenthesis '(' operator is encountered, evalx() is recursively called to evaluate whatever is inside of a pair of balanced parenthesis. When a close paren ')' operator is encountered, the cleanup() function is called which simply cleans up both stacks by doing all remaining calculations. Then evalx() returns to either a higher instance of evalx() or the original calling function. Since the operator opstack[] and the operand stack opndstack[] are automatic variables, the stack size need only be as large as there are precedence values, because each instance of nested parens results in another call to evalx(), which creates another instance of these small stacks. Each time evalx() returns, that instance of stacks is no longer needed. Remember that automatic generation is implicitly handled by stack management. Throughout the evaluation, eoexpr is a global string place holder. This probably could have been handled with automatic variables also. When the first or highest instance of evalx() is finished when the end of string is encountered, a final cleanup() is done to evaluate whatever is left on the operand stack. If the class() function encounters a function, it copies everything within balanced parenthesis of the function and places it in the field[] array. Then mathcall() is called with this string passed to it. Mathcall() does a string search for the math function in a table which consists of name, function address pairs. If the function, such as "sin" is encountered, the string value that is passed to mathcall() is evaluated by a call to evalx() (another recursion), and the returned number is passed to the appropriate function. The return value of the function is returned by mathcall() to the calling instance of evalx() which is put on the operator or operand stack and treated like any other number for the rest of the evaluation within the current level of parenthesis. If a function field is encountered, the mathcall() function is called. The operation of the class function is left as an exersize for the reader! COMPILATION WITH EXAMPLE PROGRAM _____________________________________________________________________ Included in this package are the following files: calc.c - Example calling program evalx.c - Evaluator. class.c - Expression field classifier. evalx.h - Header for evalx.c and class.c EVALX.DOC Monday, September 17, 1990 Page 7 This must be #included in calling program! calc.mak - Makefile for Microsoft 5.1 make evalx.doc - This document calc.exe - Example program compiled. Try it! This program was compiled using Microsoft C 5.1. If you have Microsoft C 5.1 use make as follows. make calc.mak calc.exe However you compile the program, class.c must also be linked in. Also, the calling program must have #include "evalx.h" and a declaration extern int errorflg. IMPORTANT NOTICE! _____________________________________________________________________ This software is free, however I would appreciate a small donation of $5.00 if you find it useful, or whatever you wish to help support my continued efforts in providing more useful software. Please send to address below. Thankyou! You may distribute this software by any means, but you may NOT charge for this software by itself, except to cover distribution costs. You may use it in software you develop and charge for your software. Unless drastically altered, please do not remove my name as author from the software. All documentation and files must be included. WARRANTEE: This program is being provided "AS IS". It is up to the user to determine the suitability of this program for their purposes. The user takes all responsibility for any direct or consequential damages. _____________________________________________________________________ James P. Hawkins - WA2WHV P.O. Box 9146 Trenton, NJ 08650 CompuServe 76446,613 ----------------end-of-author's-documentation--------------- Software Library Information: This disk copy provided as a service of Public (software) Library We are not the authors of this program, nor are we associated with the author in any way other than as a distributor of the program in accordance with the author's terms of distribution. Please direct shareware payments and specific questions about this program to the author of the program, whose name appears elsewhere in this documentation. If you have trouble getting in touch with the author, we will do whatever we can to help you with your questions. All programs have been tested and do run. 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