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1 /*
2 * simple arithmetic expression evaluator
4 * Copyright (c) 2002-2006 Michael Niedermayer <michaelni@gmx.at>
5 * Copyright (c) 2006 Oded Shimon <ods15@ods15.dyndns.org>
7 * This file is part of FFmpeg.
9 * FFmpeg is free software; you can redistribute it and/or
10 * modify it under the terms of the GNU Lesser General Public
11 * License as published by the Free Software Foundation; either
12 * version 2.1 of the License, or (at your option) any later version.
14 * FFmpeg is distributed in the hope that it will be useful,
15 * but WITHOUT ANY WARRANTY; without even the implied warranty of
16 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
17 * Lesser General Public License for more details.
19 * You should have received a copy of the GNU Lesser General Public
20 * License along with FFmpeg; if not, write to the Free Software
21 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
24 /**
25 * @file eval.c
26 * simple arithmetic expression evaluator.
28 * see http://joe.hotchkiss.com/programming/eval/eval.html
31 #include "avcodec.h"
32 #include "eval.h"
34 #include <stdio.h>
35 #include <stdlib.h>
36 #include <string.h>
37 #include <math.h>
39 #ifndef NAN
40 #define NAN 0.0/0.0
41 #endif
43 #ifndef M_PI
44 #define M_PI 3.14159265358979323846
45 #endif
47 typedef struct Parser{
48 int stack_index;
49 char *s;
50 double *const_value;
51 const char **const_name; // NULL terminated
52 double (**func1)(void *, double a); // NULL terminated
53 const char **func1_name; // NULL terminated
54 double (**func2)(void *, double a, double b); // NULL terminated
55 char **func2_name; // NULL terminated
56 void *opaque;
57 const char **error;
58 #define VARS 10
59 double var[VARS];
60 } Parser;
62 static const int8_t si_prefixes['z' - 'E' + 1]={
63 ['y'-'E']= -24,
64 ['z'-'E']= -21,
65 ['a'-'E']= -18,
66 ['f'-'E']= -15,
67 ['p'-'E']= -12,
68 ['n'-'E']= - 9,
69 ['u'-'E']= - 6,
70 ['m'-'E']= - 3,
71 ['c'-'E']= - 2,
72 ['d'-'E']= - 1,
73 ['h'-'E']= 2,
74 ['k'-'E']= 3,
75 ['K'-'E']= 3,
76 ['M'-'E']= 6,
77 ['G'-'E']= 9,
78 ['T'-'E']= 12,
79 ['P'-'E']= 15,
80 ['E'-'E']= 18,
81 ['Z'-'E']= 21,
82 ['Y'-'E']= 24,
85 /** strtod() function extended with 'k', 'M', 'G', 'ki', 'Mi', 'Gi' and 'B'
86 * postfixes. This allows using f.e. kB, MiB, G and B as a postfix. This
87 * function assumes that the unit of numbers is bits not bytes.
89 static double av_strtod(const char *name, char **tail) {
90 double d;
91 char *next;
92 d = strtod(name, &next);
93 /* if parsing succeeded, check for and interpret postfixes */
94 if (next!=name) {
96 if(*next >= 'E' && *next <= 'z'){
97 int e= si_prefixes[*next - 'E'];
98 if(e){
99 if(next[1] == 'i'){
100 d*= pow( 2, e/0.3);
101 next+=2;
102 }else{
103 d*= pow(10, e);
104 next++;
109 if(*next=='B') {
110 d*=8;
111 next++;
114 /* if requested, fill in tail with the position after the last parsed
115 character */
116 if (tail)
117 *tail = next;
118 return d;
121 static int strmatch(const char *s, const char *prefix){
122 int i;
123 for(i=0; prefix[i]; i++){
124 if(prefix[i] != s[i]) return 0;
126 return 1;
129 struct ff_expr_s {
130 enum {
131 e_value, e_const, e_func0, e_func1, e_func2,
132 e_squish, e_gauss, e_ld,
133 e_mod, e_max, e_min, e_eq, e_gt, e_gte,
134 e_pow, e_mul, e_div, e_add,
135 e_last, e_st, e_while,
136 } type;
137 double value; // is sign in other types
138 union {
139 int const_index;
140 double (*func0)(double);
141 double (*func1)(void *, double);
142 double (*func2)(void *, double, double);
143 } a;
144 AVEvalExpr * param[2];
147 static double eval_expr(Parser * p, AVEvalExpr * e) {
148 switch (e->type) {
149 case e_value: return e->value;
150 case e_const: return e->value * p->const_value[e->a.const_index];
151 case e_func0: return e->value * e->a.func0(eval_expr(p, e->param[0]));
152 case e_func1: return e->value * e->a.func1(p->opaque, eval_expr(p, e->param[0]));
153 case e_func2: return e->value * e->a.func2(p->opaque, eval_expr(p, e->param[0]), eval_expr(p, e->param[1]));
154 case e_squish: return 1/(1+exp(4*eval_expr(p, e->param[0])));
155 case e_gauss: { double d = eval_expr(p, e->param[0]); return exp(-d*d/2)/sqrt(2*M_PI); }
156 case e_ld: return e->value * p->var[av_clip(eval_expr(p, e->param[0]), 0, VARS-1)];
157 case e_while: {
158 double d = NAN;
159 while(eval_expr(p, e->param[0]))
160 d=eval_expr(p, e->param[1]);
161 return d;
163 default: {
164 double d = eval_expr(p, e->param[0]);
165 double d2 = eval_expr(p, e->param[1]);
166 switch (e->type) {
167 case e_mod: return e->value * (d - floor(d/d2)*d2);
168 case e_max: return e->value * (d > d2 ? d : d2);
169 case e_min: return e->value * (d < d2 ? d : d2);
170 case e_eq: return e->value * (d == d2 ? 1.0 : 0.0);
171 case e_gt: return e->value * (d > d2 ? 1.0 : 0.0);
172 case e_gte: return e->value * (d >= d2 ? 1.0 : 0.0);
173 case e_pow: return e->value * pow(d, d2);
174 case e_mul: return e->value * (d * d2);
175 case e_div: return e->value * (d / d2);
176 case e_add: return e->value * (d + d2);
177 case e_last:return e->value * d2;
178 case e_st : return e->value * (p->var[av_clip(d, 0, VARS-1)]= d2);
182 return NAN;
185 static AVEvalExpr * parse_expr(Parser *p);
187 void ff_eval_free(AVEvalExpr * e) {
188 if (!e) return;
189 ff_eval_free(e->param[0]);
190 ff_eval_free(e->param[1]);
191 av_freep(&e);
194 static AVEvalExpr * parse_primary(Parser *p) {
195 AVEvalExpr * d = av_mallocz(sizeof(AVEvalExpr));
196 char *next= p->s;
197 int i;
199 /* number */
200 d->value = av_strtod(p->s, &next);
201 if(next != p->s){
202 d->type = e_value;
203 p->s= next;
204 return d;
206 d->value = 1;
208 /* named constants */
209 for(i=0; p->const_name && p->const_name[i]; i++){
210 if(strmatch(p->s, p->const_name[i])){
211 p->s+= strlen(p->const_name[i]);
212 d->type = e_const;
213 d->a.const_index = i;
214 return d;
218 p->s= strchr(p->s, '(');
219 if(p->s==NULL){
220 *p->error = "undefined constant or missing (";
221 p->s= next;
222 ff_eval_free(d);
223 return NULL;
225 p->s++; // "("
226 if (*next == '(') { // special case do-nothing
227 av_freep(&d);
228 d = parse_expr(p);
229 if(p->s[0] != ')'){
230 *p->error = "missing )";
231 ff_eval_free(d);
232 return NULL;
234 p->s++; // ")"
235 return d;
237 d->param[0] = parse_expr(p);
238 if(p->s[0]== ','){
239 p->s++; // ","
240 d->param[1] = parse_expr(p);
242 if(p->s[0] != ')'){
243 *p->error = "missing )";
244 ff_eval_free(d);
245 return NULL;
247 p->s++; // ")"
249 d->type = e_func0;
250 if( strmatch(next, "sinh" ) ) d->a.func0 = sinh;
251 else if( strmatch(next, "cosh" ) ) d->a.func0 = cosh;
252 else if( strmatch(next, "tanh" ) ) d->a.func0 = tanh;
253 else if( strmatch(next, "sin" ) ) d->a.func0 = sin;
254 else if( strmatch(next, "cos" ) ) d->a.func0 = cos;
255 else if( strmatch(next, "tan" ) ) d->a.func0 = tan;
256 else if( strmatch(next, "atan" ) ) d->a.func0 = atan;
257 else if( strmatch(next, "asin" ) ) d->a.func0 = asin;
258 else if( strmatch(next, "acos" ) ) d->a.func0 = acos;
259 else if( strmatch(next, "exp" ) ) d->a.func0 = exp;
260 else if( strmatch(next, "log" ) ) d->a.func0 = log;
261 else if( strmatch(next, "abs" ) ) d->a.func0 = fabs;
262 else if( strmatch(next, "squish") ) d->type = e_squish;
263 else if( strmatch(next, "gauss" ) ) d->type = e_gauss;
264 else if( strmatch(next, "mod" ) ) d->type = e_mod;
265 else if( strmatch(next, "max" ) ) d->type = e_max;
266 else if( strmatch(next, "min" ) ) d->type = e_min;
267 else if( strmatch(next, "eq" ) ) d->type = e_eq;
268 else if( strmatch(next, "gte" ) ) d->type = e_gte;
269 else if( strmatch(next, "gt" ) ) d->type = e_gt;
270 else if( strmatch(next, "lte" ) ) { AVEvalExpr * tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gt; }
271 else if( strmatch(next, "lt" ) ) { AVEvalExpr * tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gte; }
272 else if( strmatch(next, "ld" ) ) d->type = e_ld;
273 else if( strmatch(next, "st" ) ) d->type = e_st;
274 else if( strmatch(next, "while" ) ) d->type = e_while;
275 else {
276 for(i=0; p->func1_name && p->func1_name[i]; i++){
277 if(strmatch(next, p->func1_name[i])){
278 d->a.func1 = p->func1[i];
279 d->type = e_func1;
280 return d;
284 for(i=0; p->func2_name && p->func2_name[i]; i++){
285 if(strmatch(next, p->func2_name[i])){
286 d->a.func2 = p->func2[i];
287 d->type = e_func2;
288 return d;
292 *p->error = "unknown function";
293 ff_eval_free(d);
294 return NULL;
297 return d;
300 static AVEvalExpr * new_eval_expr(int type, int value, AVEvalExpr *p0, AVEvalExpr *p1){
301 AVEvalExpr * e = av_mallocz(sizeof(AVEvalExpr));
302 e->type =type ;
303 e->value =value ;
304 e->param[0] =p0 ;
305 e->param[1] =p1 ;
306 return e;
309 static AVEvalExpr * parse_pow(Parser *p, int *sign){
310 *sign= (*p->s == '+') - (*p->s == '-');
311 p->s += *sign&1;
312 return parse_primary(p);
315 static AVEvalExpr * parse_factor(Parser *p){
316 int sign, sign2;
317 AVEvalExpr * e = parse_pow(p, &sign);
318 while(p->s[0]=='^'){
319 p->s++;
320 e= new_eval_expr(e_pow, 1, e, parse_pow(p, &sign2));
321 if (e->param[1]) e->param[1]->value *= (sign2|1);
323 if (e) e->value *= (sign|1);
324 return e;
327 static AVEvalExpr * parse_term(Parser *p){
328 AVEvalExpr * e = parse_factor(p);
329 while(p->s[0]=='*' || p->s[0]=='/'){
330 int c= *p->s++;
331 e= new_eval_expr(c == '*' ? e_mul : e_div, 1, e, parse_factor(p));
333 return e;
336 static AVEvalExpr * parse_subexpr(Parser *p) {
337 AVEvalExpr * e = parse_term(p);
338 while(*p->s == '+' || *p->s == '-') {
339 e= new_eval_expr(e_add, 1, e, parse_term(p));
342 return e;
345 static AVEvalExpr * parse_expr(Parser *p) {
346 AVEvalExpr * e;
348 if(p->stack_index <= 0) //protect against stack overflows
349 return NULL;
350 p->stack_index--;
352 e = parse_subexpr(p);
354 while(*p->s == ';') {
355 p->s++;
356 e= new_eval_expr(e_last, 1, e, parse_subexpr(p));
359 p->stack_index++;
361 return e;
364 static int verify_expr(AVEvalExpr * e) {
365 if (!e) return 0;
366 switch (e->type) {
367 case e_value:
368 case e_const: return 1;
369 case e_func0:
370 case e_func1:
371 case e_squish:
372 case e_ld:
373 case e_gauss: return verify_expr(e->param[0]);
374 default: return verify_expr(e->param[0]) && verify_expr(e->param[1]);
378 AVEvalExpr * ff_parse(const char *s, const char **const_name,
379 double (**func1)(void *, double), const char **func1_name,
380 double (**func2)(void *, double, double), char **func2_name,
381 const char **error){
382 Parser p;
383 AVEvalExpr * e;
384 char w[strlen(s) + 1], * wp = w;
386 while (*s)
387 if (!isspace(*s++)) *wp++ = s[-1];
388 *wp++ = 0;
390 p.stack_index=100;
391 p.s= w;
392 p.const_name = const_name;
393 p.func1 = func1;
394 p.func1_name = func1_name;
395 p.func2 = func2;
396 p.func2_name = func2_name;
397 p.error= error;
399 e = parse_expr(&p);
400 if (!verify_expr(e)) {
401 ff_eval_free(e);
402 return NULL;
404 return e;
407 double ff_parse_eval(AVEvalExpr * e, double *const_value, void *opaque) {
408 Parser p;
410 p.const_value= const_value;
411 p.opaque = opaque;
412 return eval_expr(&p, e);
415 double ff_eval2(const char *s, double *const_value, const char **const_name,
416 double (**func1)(void *, double), const char **func1_name,
417 double (**func2)(void *, double, double), char **func2_name,
418 void *opaque, const char **error){
419 AVEvalExpr * e = ff_parse(s, const_name, func1, func1_name, func2, func2_name, error);
420 double d;
421 if (!e) return NAN;
422 d = ff_parse_eval(e, const_value, opaque);
423 ff_eval_free(e);
424 return d;
427 #if LIBAVCODEC_VERSION_INT < ((52<<16)+(0<<8)+0)
428 attribute_deprecated double ff_eval(char *s, double *const_value, const char **const_name,
429 double (**func1)(void *, double), const char **func1_name,
430 double (**func2)(void *, double, double), char **func2_name,
431 void *opaque){
432 const char *error=NULL;
433 double ret;
434 ret = ff_eval2(s, const_value, const_name, func1, func1_name, func2, func2_name, opaque, &error);
435 if (error)
436 av_log(NULL, AV_LOG_ERROR, "Error evaluating \"%s\": %s\n", s, error);
437 return ret;
439 #endif
441 #ifdef TEST
442 #undef printf
443 static double const_values[]={
444 M_PI,
445 M_E,
448 static const char *const_names[]={
449 "PI",
450 "E",
453 int main(void){
454 int i;
455 printf("%f == 12.7\n", ff_eval("1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)", const_values, const_names, NULL, NULL, NULL, NULL, NULL));
456 printf("%f == 0.931322575\n", ff_eval("80G/80Gi", const_values, const_names, NULL, NULL, NULL, NULL, NULL));
458 for(i=0; i<1050; i++){
459 START_TIMER
460 ff_eval("1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)", const_values, const_names, NULL, NULL, NULL, NULL, NULL);
461 STOP_TIMER("ff_eval")
463 return 0;
465 #endif