1/* 2 * Copyright (c) 2002-2006 Michael Niedermayer <michaelni@gmx.at> 3 * Copyright (c) 2006 Oded Shimon <ods15@ods15.dyndns.org> 4 * 5 * This file is part of FFmpeg. 6 * 7 * FFmpeg is free software; you can redistribute it and/or 8 * modify it under the terms of the GNU Lesser General Public 9 * License as published by the Free Software Foundation; either 10 * version 2.1 of the License, or (at your option) any later version. 11 * 12 * FFmpeg is distributed in the hope that it will be useful, 13 * but WITHOUT ANY WARRANTY; without even the implied warranty of 14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 15 * Lesser General Public License for more details. 16 * 17 * You should have received a copy of the GNU Lesser General Public 18 * License along with FFmpeg; if not, write to the Free Software 19 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 20 */ 21 22/** 23 * @file 24 * simple arithmetic expression evaluator. 25 * 26 * see http://joe.hotchkiss.com/programming/eval/eval.html 27 */ 28 29#include "libavutil/avutil.h" 30#include "eval.h" 31 32typedef struct Parser{ 33 int stack_index; 34 char *s; 35 const double *const_value; 36 const char * const *const_name; // NULL terminated 37 double (* const *func1)(void *, double a); // NULL terminated 38 const char * const *func1_name; // NULL terminated 39 double (* const *func2)(void *, double a, double b); // NULL terminated 40 const char * const *func2_name; // NULL terminated 41 void *opaque; 42 const char **error; 43#define VARS 10 44 double var[VARS]; 45} Parser; 46 47static const int8_t si_prefixes['z' - 'E' + 1]={ 48 ['y'-'E']= -24, 49 ['z'-'E']= -21, 50 ['a'-'E']= -18, 51 ['f'-'E']= -15, 52 ['p'-'E']= -12, 53 ['n'-'E']= - 9, 54 ['u'-'E']= - 6, 55 ['m'-'E']= - 3, 56 ['c'-'E']= - 2, 57 ['d'-'E']= - 1, 58 ['h'-'E']= 2, 59 ['k'-'E']= 3, 60 ['K'-'E']= 3, 61 ['M'-'E']= 6, 62 ['G'-'E']= 9, 63 ['T'-'E']= 12, 64 ['P'-'E']= 15, 65 ['E'-'E']= 18, 66 ['Z'-'E']= 21, 67 ['Y'-'E']= 24, 68}; 69 70double av_strtod(const char *numstr, char **tail) { 71 double d; 72 char *next; 73 d = strtod(numstr, &next); 74 /* if parsing succeeded, check for and interpret postfixes */ 75 if (next!=numstr) { 76 77 if(*next >= 'E' && *next <= 'z'){ 78 int e= si_prefixes[*next - 'E']; 79 if(e){ 80 if(next[1] == 'i'){ 81 d*= pow( 2, e/0.3); 82 next+=2; 83 }else{ 84 d*= pow(10, e); 85 next++; 86 } 87 } 88 } 89 90 if(*next=='B') { 91 d*=8; 92 next++; 93 } 94 } 95 /* if requested, fill in tail with the position after the last parsed 96 character */ 97 if (tail) 98 *tail = next; 99 return d; 100} 101 102static int strmatch(const char *s, const char *prefix){ 103 int i; 104 for(i=0; prefix[i]; i++){ 105 if(prefix[i] != s[i]) return 0; 106 } 107 return 1; 108} 109 110struct AVExpr { 111 enum { 112 e_value, e_const, e_func0, e_func1, e_func2, 113 e_squish, e_gauss, e_ld, 114 e_mod, e_max, e_min, e_eq, e_gt, e_gte, 115 e_pow, e_mul, e_div, e_add, 116 e_last, e_st, e_while, 117 } type; 118 double value; // is sign in other types 119 union { 120 int const_index; 121 double (*func0)(double); 122 double (*func1)(void *, double); 123 double (*func2)(void *, double, double); 124 } a; 125 struct AVExpr *param[2]; 126}; 127 128static double eval_expr(Parser * p, AVExpr * e) { 129 switch (e->type) { 130 case e_value: return e->value; 131 case e_const: return e->value * p->const_value[e->a.const_index]; 132 case e_func0: return e->value * e->a.func0(eval_expr(p, e->param[0])); 133 case e_func1: return e->value * e->a.func1(p->opaque, eval_expr(p, e->param[0])); 134 case e_func2: return e->value * e->a.func2(p->opaque, eval_expr(p, e->param[0]), eval_expr(p, e->param[1])); 135 case e_squish: return 1/(1+exp(4*eval_expr(p, e->param[0]))); 136 case e_gauss: { double d = eval_expr(p, e->param[0]); return exp(-d*d/2)/sqrt(2*M_PI); } 137 case e_ld: return e->value * p->var[av_clip(eval_expr(p, e->param[0]), 0, VARS-1)]; 138 case e_while: { 139 double d = NAN; 140 while(eval_expr(p, e->param[0])) 141 d=eval_expr(p, e->param[1]); 142 return d; 143 } 144 default: { 145 double d = eval_expr(p, e->param[0]); 146 double d2 = eval_expr(p, e->param[1]); 147 switch (e->type) { 148 case e_mod: return e->value * (d - floor(d/d2)*d2); 149 case e_max: return e->value * (d > d2 ? d : d2); 150 case e_min: return e->value * (d < d2 ? d : d2); 151 case e_eq: return e->value * (d == d2 ? 1.0 : 0.0); 152 case e_gt: return e->value * (d > d2 ? 1.0 : 0.0); 153 case e_gte: return e->value * (d >= d2 ? 1.0 : 0.0); 154 case e_pow: return e->value * pow(d, d2); 155 case e_mul: return e->value * (d * d2); 156 case e_div: return e->value * (d / d2); 157 case e_add: return e->value * (d + d2); 158 case e_last:return e->value * d2; 159 case e_st : return e->value * (p->var[av_clip(d, 0, VARS-1)]= d2); 160 } 161 } 162 } 163 return NAN; 164} 165 166static AVExpr * parse_expr(Parser *p); 167 168void ff_free_expr(AVExpr * e) { 169 if (!e) return; 170 ff_free_expr(e->param[0]); 171 ff_free_expr(e->param[1]); 172 av_freep(&e); 173} 174 175static AVExpr * parse_primary(Parser *p) { 176 AVExpr * d = av_mallocz(sizeof(AVExpr)); 177 char *next= p->s; 178 int i; 179 180 if (!d) 181 return NULL; 182 183 /* number */ 184 d->value = av_strtod(p->s, &next); 185 if(next != p->s){ 186 d->type = e_value; 187 p->s= next; 188 return d; 189 } 190 d->value = 1; 191 192 /* named constants */ 193 for(i=0; p->const_name && p->const_name[i]; i++){ 194 if(strmatch(p->s, p->const_name[i])){ 195 p->s+= strlen(p->const_name[i]); 196 d->type = e_const; 197 d->a.const_index = i; 198 return d; 199 } 200 } 201 202 p->s= strchr(p->s, '('); 203 if(p->s==NULL){ 204 *p->error = "undefined constant or missing ("; 205 p->s= next; 206 ff_free_expr(d); 207 return NULL; 208 } 209 p->s++; // "(" 210 if (*next == '(') { // special case do-nothing 211 av_freep(&d); 212 d = parse_expr(p); 213 if(p->s[0] != ')'){ 214 *p->error = "missing )"; 215 ff_free_expr(d); 216 return NULL; 217 } 218 p->s++; // ")" 219 return d; 220 } 221 d->param[0] = parse_expr(p); 222 if(p->s[0]== ','){ 223 p->s++; // "," 224 d->param[1] = parse_expr(p); 225 } 226 if(p->s[0] != ')'){ 227 *p->error = "missing )"; 228 ff_free_expr(d); 229 return NULL; 230 } 231 p->s++; // ")" 232 233 d->type = e_func0; 234 if( strmatch(next, "sinh" ) ) d->a.func0 = sinh; 235 else if( strmatch(next, "cosh" ) ) d->a.func0 = cosh; 236 else if( strmatch(next, "tanh" ) ) d->a.func0 = tanh; 237 else if( strmatch(next, "sin" ) ) d->a.func0 = sin; 238 else if( strmatch(next, "cos" ) ) d->a.func0 = cos; 239 else if( strmatch(next, "tan" ) ) d->a.func0 = tan; 240 else if( strmatch(next, "atan" ) ) d->a.func0 = atan; 241 else if( strmatch(next, "asin" ) ) d->a.func0 = asin; 242 else if( strmatch(next, "acos" ) ) d->a.func0 = acos; 243 else if( strmatch(next, "exp" ) ) d->a.func0 = exp; 244 else if( strmatch(next, "log" ) ) d->a.func0 = log; 245 else if( strmatch(next, "abs" ) ) d->a.func0 = fabs; 246 else if( strmatch(next, "squish") ) d->type = e_squish; 247 else if( strmatch(next, "gauss" ) ) d->type = e_gauss; 248 else if( strmatch(next, "mod" ) ) d->type = e_mod; 249 else if( strmatch(next, "max" ) ) d->type = e_max; 250 else if( strmatch(next, "min" ) ) d->type = e_min; 251 else if( strmatch(next, "eq" ) ) d->type = e_eq; 252 else if( strmatch(next, "gte" ) ) d->type = e_gte; 253 else if( strmatch(next, "gt" ) ) d->type = e_gt; 254 else if( strmatch(next, "lte" ) ) { AVExpr * tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gt; } 255 else if( strmatch(next, "lt" ) ) { AVExpr * tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gte; } 256 else if( strmatch(next, "ld" ) ) d->type = e_ld; 257 else if( strmatch(next, "st" ) ) d->type = e_st; 258 else if( strmatch(next, "while" ) ) d->type = e_while; 259 else { 260 for(i=0; p->func1_name && p->func1_name[i]; i++){ 261 if(strmatch(next, p->func1_name[i])){ 262 d->a.func1 = p->func1[i]; 263 d->type = e_func1; 264 return d; 265 } 266 } 267 268 for(i=0; p->func2_name && p->func2_name[i]; i++){ 269 if(strmatch(next, p->func2_name[i])){ 270 d->a.func2 = p->func2[i]; 271 d->type = e_func2; 272 return d; 273 } 274 } 275 276 *p->error = "unknown function"; 277 ff_free_expr(d); 278 return NULL; 279 } 280 281 return d; 282} 283 284static AVExpr * new_eval_expr(int type, int value, AVExpr *p0, AVExpr *p1){ 285 AVExpr * e = av_mallocz(sizeof(AVExpr)); 286 if (!e) 287 return NULL; 288 e->type =type ; 289 e->value =value ; 290 e->param[0] =p0 ; 291 e->param[1] =p1 ; 292 return e; 293} 294 295static AVExpr * parse_pow(Parser *p, int *sign){ 296 *sign= (*p->s == '+') - (*p->s == '-'); 297 p->s += *sign&1; 298 return parse_primary(p); 299} 300 301static AVExpr * parse_factor(Parser *p){ 302 int sign, sign2; 303 AVExpr * e = parse_pow(p, &sign); 304 while(p->s[0]=='^'){ 305 p->s++; 306 e= new_eval_expr(e_pow, 1, e, parse_pow(p, &sign2)); 307 if (!e) 308 return NULL; 309 if (e->param[1]) e->param[1]->value *= (sign2|1); 310 } 311 if (e) e->value *= (sign|1); 312 return e; 313} 314 315static AVExpr * parse_term(Parser *p){ 316 AVExpr * e = parse_factor(p); 317 while(p->s[0]=='*' || p->s[0]=='/'){ 318 int c= *p->s++; 319 e= new_eval_expr(c == '*' ? e_mul : e_div, 1, e, parse_factor(p)); 320 if (!e) 321 return NULL; 322 } 323 return e; 324} 325 326static AVExpr * parse_subexpr(Parser *p) { 327 AVExpr * e = parse_term(p); 328 while(*p->s == '+' || *p->s == '-') { 329 e= new_eval_expr(e_add, 1, e, parse_term(p)); 330 if (!e) 331 return NULL; 332 }; 333 334 return e; 335} 336 337static AVExpr * parse_expr(Parser *p) { 338 AVExpr * e; 339 340 if(p->stack_index <= 0) //protect against stack overflows 341 return NULL; 342 p->stack_index--; 343 344 e = parse_subexpr(p); 345 346 while(*p->s == ';') { 347 p->s++; 348 e= new_eval_expr(e_last, 1, e, parse_subexpr(p)); 349 if (!e) 350 return NULL; 351 }; 352 353 p->stack_index++; 354 355 return e; 356} 357 358static int verify_expr(AVExpr * e) { 359 if (!e) return 0; 360 switch (e->type) { 361 case e_value: 362 case e_const: return 1; 363 case e_func0: 364 case e_func1: 365 case e_squish: 366 case e_ld: 367 case e_gauss: return verify_expr(e->param[0]); 368 default: return verify_expr(e->param[0]) && verify_expr(e->param[1]); 369 } 370} 371 372AVExpr *ff_parse_expr(const char *s, const char * const *const_name, 373 double (* const *func1)(void *, double), const char * const *func1_name, 374 double (* const *func2)(void *, double, double), const char * const *func2_name, 375 const char **error){ 376 Parser p; 377 AVExpr *e = NULL; 378 char *w = av_malloc(strlen(s) + 1); 379 char *wp = w; 380 381 if (!w) 382 goto end; 383 384 while (*s) 385 if (!isspace(*s++)) *wp++ = s[-1]; 386 *wp++ = 0; 387 388 p.stack_index=100; 389 p.s= w; 390 p.const_name = const_name; 391 p.func1 = func1; 392 p.func1_name = func1_name; 393 p.func2 = func2; 394 p.func2_name = func2_name; 395 p.error= error; 396 397 e = parse_expr(&p); 398 if (!verify_expr(e)) { 399 ff_free_expr(e); 400 e = NULL; 401 } 402end: 403 av_free(w); 404 return e; 405} 406 407double ff_eval_expr(AVExpr * e, const double *const_value, void *opaque) { 408 Parser p; 409 410 p.const_value= const_value; 411 p.opaque = opaque; 412 return eval_expr(&p, e); 413} 414 415double ff_parse_and_eval_expr(const char *s, const double *const_value, const char * const *const_name, 416 double (* const *func1)(void *, double), const char * const *func1_name, 417 double (* const *func2)(void *, double, double), const char * const *func2_name, 418 void *opaque, const char **error){ 419 AVExpr * e = ff_parse_expr(s, const_name, func1, func1_name, func2, func2_name, error); 420 double d; 421 if (!e) return NAN; 422 d = ff_eval_expr(e, const_value, opaque); 423 ff_free_expr(e); 424 return d; 425} 426 427#ifdef TEST 428#undef printf 429static double const_values[]={ 430 M_PI, 431 M_E, 432 0 433}; 434static const char *const_names[]={ 435 "PI", 436 "E", 437 0 438}; 439int main(void){ 440 int i; 441 printf("%f == 12.7\n", ff_parse_and_eval_expr("1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)", const_values, const_names, NULL, NULL, NULL, NULL, NULL, NULL)); 442 printf("%f == 0.931322575\n", ff_parse_and_eval_expr("80G/80Gi", const_values, const_names, NULL, NULL, NULL, NULL, NULL, NULL)); 443 444 for(i=0; i<1050; i++){ 445 START_TIMER 446 ff_parse_and_eval_expr("1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)", const_values, const_names, NULL, NULL, NULL, NULL, NULL, NULL); 447 STOP_TIMER("ff_parse_and_eval_expr") 448 } 449 return 0; 450} 451#endif 452