1/* 2 * simple arithmetic expression evaluator 3 * 4 * Copyright (c) 2002-2006 Michael Niedermayer <michaelni@gmx.at> 5 * Copyright (c) 2006 Oded Shimon <ods15@ods15.dyndns.org> 6 * 7 * This file is part of FFmpeg. 8 * 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. 13 * 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. 18 * 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 22 */ 23 24/** 25 * @file libavcodec/eval.c 26 * simple arithmetic expression evaluator. 27 * 28 * see http://joe.hotchkiss.com/programming/eval/eval.html 29 */ 30 31#include "avcodec.h" 32#include "eval.h" 33 34#include <stdio.h> 35#include <stdlib.h> 36#include <string.h> 37#include <math.h> 38 39#ifndef NAN 40 #define NAN 0.0/0.0 41#endif 42 43#ifndef M_PI 44#define M_PI 3.14159265358979323846 45#endif 46 47typedef struct Parser{ 48 int stack_index; 49 char *s; 50 const double *const_value; 51 const char * const *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 const char **func2_name; // NULL terminated 56 void *opaque; 57 const char **error; 58#define VARS 10 59 double var[VARS]; 60} Parser; 61 62static 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, 83}; 84 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. 88 */ 89static 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) { 95 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++; 105 } 106 } 107 } 108 109 if(*next=='B') { 110 d*=8; 111 next++; 112 } 113 } 114 /* if requested, fill in tail with the position after the last parsed 115 character */ 116 if (tail) 117 *tail = next; 118 return d; 119} 120 121static 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; 125 } 126 return 1; 127} 128 129struct 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]; 145}; 146 147static 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; 162 } 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); 179 } 180 } 181 } 182 return NAN; 183} 184 185static AVEvalExpr * parse_expr(Parser *p); 186 187void 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); 192} 193 194static AVEvalExpr * parse_primary(Parser *p) { 195 AVEvalExpr * d = av_mallocz(sizeof(AVEvalExpr)); 196 char *next= p->s; 197 int i; 198 199 /* 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; 205 } 206 d->value = 1; 207 208 /* 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; 215 } 216 } 217 218 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; 224 } 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; 233 } 234 p->s++; // ")" 235 return d; 236 } 237 d->param[0] = parse_expr(p); 238 if(p->s[0]== ','){ 239 p->s++; // "," 240 d->param[1] = parse_expr(p); 241 } 242 if(p->s[0] != ')'){ 243 *p->error = "missing )"; 244 ff_eval_free(d); 245 return NULL; 246 } 247 p->s++; // ")" 248 249 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; 281 } 282 } 283 284 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; 289 } 290 } 291 292 *p->error = "unknown function"; 293 ff_eval_free(d); 294 return NULL; 295 } 296 297 return d; 298} 299 300static 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; 307} 308 309static AVEvalExpr * parse_pow(Parser *p, int *sign){ 310 *sign= (*p->s == '+') - (*p->s == '-'); 311 p->s += *sign&1; 312 return parse_primary(p); 313} 314 315static 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); 322 } 323 if (e) e->value *= (sign|1); 324 return e; 325} 326 327static 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)); 332 } 333 return e; 334} 335 336static 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)); 340 }; 341 342 return e; 343} 344 345static AVEvalExpr * parse_expr(Parser *p) { 346 AVEvalExpr * e; 347 348 if(p->stack_index <= 0) //protect against stack overflows 349 return NULL; 350 p->stack_index--; 351 352 e = parse_subexpr(p); 353 354 while(*p->s == ';') { 355 p->s++; 356 e= new_eval_expr(e_last, 1, e, parse_subexpr(p)); 357 }; 358 359 p->stack_index++; 360 361 return e; 362} 363 364static 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]); 375 } 376} 377 378AVEvalExpr * ff_parse(const char *s, const char * const *const_name, 379 double (**func1)(void *, double), const char **func1_name, 380 double (**func2)(void *, double, double), const char **func2_name, 381 const char **error){ 382 Parser p; 383 AVEvalExpr * e; 384 char w[strlen(s) + 1], * wp = w; 385 386 while (*s) 387 if (!isspace(*s++)) *wp++ = s[-1]; 388 *wp++ = 0; 389 390 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; 398 399 e = parse_expr(&p); 400 if (!verify_expr(e)) { 401 ff_eval_free(e); 402 return NULL; 403 } 404 return e; 405} 406 407double ff_parse_eval(AVEvalExpr * 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_eval2(const char *s, const double *const_value, const char * const *const_name, 416 double (**func1)(void *, double), const char **func1_name, 417 double (**func2)(void *, double, double), const 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; 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_eval2("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_eval2("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_eval2("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_eval2") 448 } 449 return 0; 450} 451#endif 452