/* A mathematical expression evaluator.
* It uses a recursive descent parser internally.
* Author: Werner Stoop
* This is free and unencumbered software released into the public domain.
* http://unlicense.org/
*/
#include <assert.h>
#include <ctype.h>
#include <math.h> /* remember to compile with -lm */
#include <setjmp.h>
#include <stdlib.h>
#include <string.h>
/* Special tokens used by the lexer function lex()
* they've been chosen as non-printable characters
* so that printable characters can be used for other
* purposes
*/
#define TOK_END 0 /* end of text */
#define TOK_INI 1 /* Initial state */
#define TOK_ID 2 /* identifier */
#define TOK_NUM 3 /* number */
/* Types of errors */
// 0 /* "no error" */
#define ERR_MEMORY 1 /* "out of memory" */
#define ERR_LEXER 2 /* "unknown token" */
#define ERR_LONGID 3 /* "identifier too long" */
#define ERR_VALUE 4 /* "value expected" */
#define ERR_BRACKET 5 /* "missing ')'" */
#define ERR_FUNC 6 /* "unknown function" */
#define ERR_ARGS 7 /* "wrong number of arguments" */
#define ERR_CONST 8 /* "unknown constant" */
/* Other definitions */
#define MAX_ID_LEN 11 /* Max length of an identifier */
#define OPERATORS "+-*/%(),^&|!" /* Valid operators */
#define EVAL_PI 3.141592654
#define EVAL_E 2.718281828
#define EVAL_DEG (EVAL_PI/180)
/* Internal structure for the parser/evaluator */
struct eval {
jmp_buf j; /* For error handling */
const char *p; /* Position in the text being parsed */
double *st; /* Stack */
int st_size; /* Stack size */
int sp; /* Stack pointer */
/* The current and next tokens identified by the lexer */
struct {
int type; /* Type of the token */
double n_val; /* Numeric value of the previous lexed token */
char s_val[MAX_ID_LEN]; /* String (identifier) value of the previous lexed token */
} token[2];
int cur_tok; /* Current token, either 0 or 1 (see the comments of lex()) */
};
/* Prototypes */
static double pop(struct eval *ev);
static void push(struct eval *ev, double d);
static int lex(struct eval *ev);
/* Prototypes for the recursive descent parser */
static void expr(struct eval *ev);
static void add_expr(struct eval *ev);
static void mul_expr(struct eval *ev);
static void pow_expr(struct eval *ev);
static void uni_expr(struct eval *ev);
static void bra_expr(struct eval *ev);
static void id_expr(struct eval *ev);
static void num_expr(struct eval *ev);
/*
* Evaluates a mathemeatical expression
*/
double eval(const char *exp/*, int *ep*/) {
int _ep, *ep = &_ep;
struct eval ev;
double ans = 0.0;
assert(ep != NULL);
/* Allocate a stack */
ev.st_size = 10;
ev.st = CALLOC(ev.st_size, sizeof *ev.st);
if(!ev.st)
{
*ep = ERR_MEMORY;
return NAN; //0.0;
}
ev.sp = 0;
/* Manage errors */
*ep = setjmp(ev.j);
if(*ep != 0)
{
FREE(ev.st);
return NAN; //0.0;
}
/* Initialize the lexer */
ev.token[0].type = TOK_INI;
ev.token[0].s_val[0] = '\0';
ev.token[1].type = TOK_INI;
ev.token[1].s_val[0] = '\0';
ev.cur_tok = 0;
/* Initialize the parser */
ev.p = exp;
/* lex once to initialize the lexer */
if(lex(&ev) != TOK_END)
{
expr(&ev);
ans = pop(&ev);
}
FREE(ev.st);
return ans;
}
/*
* Pushes a value onto the stack, increases the stack size if necessary
*/
static void push(struct eval *ev, double d) {
if(ev->sp == ev->st_size) {
/* Resize the stack by 1.5 */
double *old = ev->st;
int new_size = ev->st_size + (ev->st_size >> 1);
ev->st = REALLOC(ev->st, new_size);
if(!ev->st) {
ev->st = old;
longjmp(ev->j, ERR_MEMORY);
}
ev->st_size = new_size;
}
ev->st[ev->sp++] = d;
}
// Pops a value from the top of the stack
static double pop(struct eval *ev) {
assert(ev->sp > 0);
return ev->st[--ev->sp];
}
// stricmp() is common, but not standard, so I provide my own
static int istrcmp(const char *p, const char *q) {
for(; tolower(p[0]) == tolower(q[0]) && p[0]; p++, q++);
return tolower(p[0]) - tolower(q[0]);
}
/*
* Lexical analyzer function
*
* In order to implement LL(1), struct eval has an array of two token structures,
* and its cur_tok member is used to point to the _current_ token, while the other
* element contains the _next_ token. This implements a 2 element ring buffer where
* the lexer always writes to the _next_ token so that the recursive descent parser can
* _peek_ at the next token.
*/
static int lex(struct eval *ev) {
int next_tok;
start:
/* Cycle the tokens */
next_tok = ev->cur_tok;
ev->cur_tok = ev->cur_tok?0:1;
while(isspace(ev->p[0])) ev->p++;
if(!ev->p[0]) {
/* End of the expression */
ev->token[next_tok].type = TOK_END;
goto end;
}
else if(isdigit(ev->p[0]) || ev->p[0] == '.') {
/* Number */
char *endp;
ev->token[next_tok].type = TOK_NUM;
ev->token[next_tok].n_val = strtod(ev->p, &endp);
ev->p = endp;
goto end;
}
else if(isalpha(ev->p[0])) {
/* Identifier */
int i;
for(i = 0; (isalnum(ev->p[0]) || ev->p[0] == '_') && i < MAX_ID_LEN - 1; i++, ev->p++)
ev->token[next_tok].s_val[i] = ev->p[0];
if(isalpha(ev->p[0])) longjmp(ev->j, ERR_LONGID);
ev->token[next_tok].s_val[i] = '\0';
ev->token[next_tok].type = TOK_ID;
goto end;
}
else if(strchr(OPERATORS, ev->p[0])) {
/* Operator */
ev->token[next_tok].type = ev->p[0];
ev->p++;
goto end;
}
else /* Unknown token */
longjmp(ev->j, ERR_LEXER);
end:
/* If this was the first call, cycle the tokens again */
if(ev->token[ev->cur_tok].type == TOK_INI)
goto start;
return ev->token[ev->cur_tok].type;
}
#define EVAL_TYPE(e) (e->token[e->cur_tok].type)
#define EVAL_ERROR(c) longjmp(ev->j, (c))
// num_expr ::= NUMBER
static void num_expr(struct eval *ev) {
if(EVAL_TYPE(ev) != TOK_NUM)
EVAL_ERROR(ERR_VALUE);
push(ev, ev->token[ev->cur_tok].n_val);
lex(ev);
}
// expr ::= add_expr
static void expr(struct eval *ev) {
add_expr(ev);
}
// add_expr ::= mul_expr [('+'|'-') mul_expr]
static void add_expr(struct eval *ev) {
int t;
mul_expr(ev);
while((t =EVAL_TYPE(ev)) == '+' || t == '-' || t == '|') {
double a,b;
lex(ev);
mul_expr(ev);
b = pop(ev);
a = pop(ev);
if(t == '+')
push(ev, a + b);
else if(t == '-')
push(ev, a - b);
else
push(ev, a || b);
}
}
// mul_expr ::= pow_expr [('*'|'/'|'%') pow_expr]
static void mul_expr(struct eval *ev) {
int t;
pow_expr(ev);
while((t = EVAL_TYPE(ev)) == '*' || t == '/' || t == '%' || t == '&') {
double a,b;
lex(ev);
pow_expr(ev);
b = pop(ev);
a = pop(ev);
if(t == '*')
push(ev, a * b);
else if(t == '/')
push(ev, a / b);
else if(t == '%')
push(ev, fmod(a, b));
else
push(ev, a && b);
}
}
// pow_expr ::= uni_expr ['^' pow_expr]
static void pow_expr(struct eval *ev) {
/* Note that exponentiation is right associative:
2^3^4 is 2^(3^4), not (2^3)^4 */
uni_expr(ev);
if(EVAL_TYPE(ev) == '^') {
double a,b;
lex(ev);
pow_expr(ev);
b = pop(ev);
a = pop(ev);
push(ev, pow(a,b));
}
}
// uni_expr ::= ['+'|'-'] bra_expr
static void uni_expr(struct eval *ev) {
int t = '+';
if(EVAL_TYPE(ev) == '-' || EVAL_TYPE(ev) == '+' || EVAL_TYPE(ev) == '!') {
t = EVAL_TYPE(ev);
lex(ev);
}
bra_expr(ev);
if(t == '-') {
double a = pop(ev);
push(ev, -a);
}
else if(t == '!') {
double a = pop(ev);
push(ev, !a);
}
}
// bra_expr ::= '(' add_expr ')' | id_expr
static void bra_expr(struct eval *ev) {
if(EVAL_TYPE(ev) == '(') {
lex(ev);
add_expr(ev);
if(EVAL_TYPE(ev) != ')')
EVAL_ERROR(ERR_BRACKET);
lex(ev);
}
else
id_expr(ev);
}
// id_expr ::= ID '(' add_expr [',' add_expr]* ')' | ID | num_expr
static void id_expr(struct eval *ev) {
int nargs = 0;
char id[MAX_ID_LEN];
if(EVAL_TYPE(ev) != TOK_ID) {
num_expr(ev);
} else {
strcpy(id, ev->token[ev->cur_tok].s_val);
lex(ev);
if(EVAL_TYPE(ev) != '(') {
#ifdef EVAL_EXTEND_CONSTANTS
EVAL_EXTEND_CONSTANTS
#else
if(0) {}
#endif
else if(!strcmp(id, "true")) push(ev, 1.0);
else if(!strcmp(id, "false")) push(ev, 0.0);
else if(!strcmp(id, "on")) push(ev, 1.0);
else if(!strcmp(id, "off")) push(ev, 0.0);
// pi - 3.141592654
else if(!strcmp(id, "pi"))
push(ev, EVAL_PI);
// e - base of natural logarithms, 2.718281828
else if(!strcmp(id, "e"))
push(ev, EVAL_E);
// deg - deg2rad, allows to degree conversion `sin(90*deg) = 1`
else if(!strcmp(id, "deg"))
push(ev, EVAL_DEG);
else
EVAL_ERROR(ERR_CONST);
} else {
lex(ev);
while(EVAL_TYPE(ev) != ')') {
add_expr(ev);
nargs++;
if(EVAL_TYPE(ev) == ')') break;
if(EVAL_TYPE(ev) != ',')
EVAL_ERROR(ERR_BRACKET);
lex(ev);
}
lex(ev);
#ifdef EVAL_EXTEND_FUNCTIONS
EVAL_EXTEND_FUNCTIONS
#else
if(0) {}
#endif
// abs(x) - absolute value of x
else if(!istrcmp(id, "abs")) {
if(nargs != 1) EVAL_ERROR(ERR_ARGS);
push(ev, fabs(pop(ev)));
}
// ceil(x) - smallest integer greater than x
else if(!istrcmp(id, "ceil")) {
if(nargs != 1) EVAL_ERROR(ERR_ARGS);
push(ev, ceil(pop(ev)));
}
// floor(x) - largest integer smaller than x
else if(!istrcmp(id, "floor")) {
if(nargs != 1) EVAL_ERROR(ERR_ARGS);
push(ev, floor(pop(ev)));
}
// sin(x) - sine of x, in radians
else if(!istrcmp(id, "sin")) {
if(nargs != 1) EVAL_ERROR(ERR_ARGS);
push(ev, sin(pop(ev)));
}
// asin(x) - arcsine of x, in radians
else if(!istrcmp(id, "asin")) {
if(nargs != 1) EVAL_ERROR(ERR_ARGS);
push(ev, asin(pop(ev)));
}
// cos(x) - cosine of x, in radians
else if(!istrcmp(id, "cos")) {
if(nargs != 1) EVAL_ERROR(ERR_ARGS);
push(ev, cos(pop(ev)));
}
// acos(x) - arccosine of x, in radians
else if(!istrcmp(id, "acos")) {
if(nargs != 1) EVAL_ERROR(ERR_ARGS);
push(ev, acos(pop(ev)));
}
// tan(x) - tangent of x, in radians
else if(!istrcmp(id, "tan")) {
if(nargs != 1) EVAL_ERROR(ERR_ARGS);
push(ev, tan(pop(ev)));
}
// atan(x) - arctangent of x, in radians
else if(!istrcmp(id, "atan")) {
if(nargs != 1) EVAL_ERROR(ERR_ARGS);
push(ev, atan(pop(ev)));
}
// atan(y,x) - arctangent of y/x, in radians.
else if(!istrcmp(id, "atan2")) {
double a, b;
if(nargs != 2) EVAL_ERROR(ERR_ARGS);
b = pop(ev);
a = pop(ev);
push(ev, atan2(a,b));
}
// sinh(x) - hyperbolic sine of x, in radians
else if(!istrcmp(id, "sinh")) {
if(nargs != 1) EVAL_ERROR(ERR_ARGS);
push(ev, sinh(pop(ev)));
}
// cosh(x) - hyperbolic cosine of x, in radians
else if(!istrcmp(id, "cosh")) {
if(nargs != 1) EVAL_ERROR(ERR_ARGS);
push(ev, cosh(pop(ev)));
}
// tanh(x) - hyperbolic tangent of x, in radians
else if(!istrcmp(id, "tanh")) {
if(nargs != 1) EVAL_ERROR(ERR_ARGS);
push(ev, tanh(pop(ev)));
}
// log(x) - natural logarithm of x
else if(!istrcmp(id, "log")) {
if(nargs != 1) EVAL_ERROR(ERR_ARGS);
push(ev, log(pop(ev)));
}
// log10(x) - logarithm of x, base-10
else if(!istrcmp(id, "log10")) {
if(nargs != 1) EVAL_ERROR(ERR_ARGS);
push(ev, log10(pop(ev)));
}
// exp(x) - computes e^x
else if(!istrcmp(id, "exp")) {
if(nargs != 1) EVAL_ERROR(ERR_ARGS);
push(ev, exp(pop(ev)));
}
// sqrt(x) - square root of x
else if(!istrcmp(id, "sqrt")) {
if(nargs != 1) EVAL_ERROR(ERR_ARGS);
push(ev, sqrt(pop(ev)));
}
// rad(x) - converts x from degrees to radians
else if(!istrcmp(id, "rad")) {
if(nargs != 1) EVAL_ERROR(ERR_ARGS);
push(ev, pop(ev)*EVAL_PI/180);
}
// deg(x) - converts x from radians to degrees
else if(!istrcmp(id, "deg")) {
if(nargs != 1) EVAL_ERROR(ERR_ARGS);
push(ev, pop(ev)*180/EVAL_PI);
}
// pow(x,y) - computes x^y
else if(!istrcmp(id, "pow")) {
double a, b;
if(nargs != 2) EVAL_ERROR(ERR_ARGS);
b = pop(ev);
a = pop(ev);
push(ev, pow(a,b));
}
// hypot(x,y) - computes sqrt(x*x + y*y)
else if(!istrcmp(id, "hypot")) {
double a, b;
if(nargs != 2) EVAL_ERROR(ERR_ARGS);
b = pop(ev);
a = pop(ev);
push(ev, sqrt(a*a + b*b));
}
else
EVAL_ERROR(ERR_FUNC);
}
}
}
//
#ifdef EVALDEMO
#include <stdio.h>
int main() {
assert( eval("1+1") == 2 ); // common path
assert( eval("1+") != eval("1+") ); // check that errors return NAN
assert(~puts("Ok") );
}
#endif