libavcodec/eval.c

   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 <stdio.h>
  32 #include <stdlib.h>
  33 #include <string.h>
  34 #include <math.h>
  35
  36 #include "libavutil/mathematics.h"
  37 #include "avcodec.h"
  38 #include "eval.h"
  39
  40 typedef struct Parser{
  41     int stack_index;
  42     char *s;
  43     const double *const_value;
  44     const char * const *const_name;          // NULL terminated
  45     double (**func1)(void *, double a); // NULL terminated
  46     const char **func1_name;          // NULL terminated
  47     double (**func2)(void *, double a, double b); // NULL terminated
  48     const char **func2_name;          // NULL terminated
  49     void *opaque;
  50     const char **error;
  51 #define VARS 10
  52     double var[VARS];
  53 } Parser;
  54
  55 static const int8_t si_prefixes['z' - 'E' + 1]={
  56     ['y'-'E']= -24,
  57     ['z'-'E']= -21,
  58     ['a'-'E']= -18,
  59     ['f'-'E']= -15,
  60     ['p'-'E']= -12,
  61     ['n'-'E']= - 9,
  62     ['u'-'E']= - 6,
  63     ['m'-'E']= - 3,
  64     ['c'-'E']= - 2,
  65     ['d'-'E']= - 1,
  66     ['h'-'E']=   2,
  67     ['k'-'E']=   3,
  68     ['K'-'E']=   3,
  69     ['M'-'E']=   6,
  70     ['G'-'E']=   9,
  71     ['T'-'E']=  12,
  72     ['P'-'E']=  15,
  73     ['E'-'E']=  18,
  74     ['Z'-'E']=  21,
  75     ['Y'-'E']=  24,
  76 };
  77
  78 double av_strtod(const char *numstr, char **tail) {
  79     double d;
  80     char *next;
  81     d = strtod(numstr, &next);
  82     /* if parsing succeeded, check for and interpret postfixes */
  83     if (next!=numstr) {
  84
  85         if(*next >= 'E' && *next <= 'z'){
  86             int e= si_prefixes[*next - 'E'];
  87             if(e){
  88                 if(next[1] == 'i'){
  89                     d*= pow( 2, e/0.3);
  90                     next+=2;
  91                 }else{
  92                     d*= pow(10, e);
  93                     next++;
  94                 }
  95             }
  96         }
  97
  98         if(*next=='B') {
  99             d*=8;
 100             next++;
 101         }
 102     }
 103     /* if requested, fill in tail with the position after the last parsed
 104        character */
 105     if (tail)
 106         *tail = next;
 107     return d;
 108 }
 109
 110 static int strmatch(const char *s, const char *prefix){
 111     int i;
 112     for(i=0; prefix[i]; i++){
 113         if(prefix[i] != s[i]) return 0;
 114     }
 115     return 1;
 116 }
 117
 118 struct ff_expr_s {
 119     enum {
 120         e_value, e_const, e_func0, e_func1, e_func2,
 121         e_squish, e_gauss, e_ld,
 122         e_mod, e_max, e_min, e_eq, e_gt, e_gte,
 123         e_pow, e_mul, e_div, e_add,
 124         e_last, e_st, e_while,
 125     } type;
 126     double value; // is sign in other types
 127     union {
 128         int const_index;
 129         double (*func0)(double);
 130         double (*func1)(void *, double);
 131         double (*func2)(void *, double, double);
 132     } a;
 133     AVEvalExpr * param[2];
 134 };
 135
 136 static double eval_expr(Parser * p, AVEvalExpr * e) {
 137     switch (e->type) {
 138         case e_value:  return e->value;
 139         case e_const:  return e->value * p->const_value[e->a.const_index];
 140         case e_func0:  return e->value * e->a.func0(eval_expr(p, e->param[0]));
 141         case e_func1:  return e->value * e->a.func1(p->opaque, eval_expr(p, e->param[0]));
 142         case e_func2:  return e->value * e->a.func2(p->opaque, eval_expr(p, e->param[0]), eval_expr(p, e->param[1]));
 143         case e_squish: return 1/(1+exp(4*eval_expr(p, e->param[0])));
 144         case e_gauss: { double d = eval_expr(p, e->param[0]); return exp(-d*d/2)/sqrt(2*M_PI); }
 145         case e_ld:     return e->value * p->var[av_clip(eval_expr(p, e->param[0]), 0, VARS-1)];
 146         case e_while: {
 147             double d = NAN;
 148             while(eval_expr(p, e->param[0]))
 149                 d=eval_expr(p, e->param[1]);
 150             return d;
 151         }
 152         default: {
 153             double d = eval_expr(p, e->param[0]);
 154             double d2 = eval_expr(p, e->param[1]);
 155             switch (e->type) {
 156                 case e_mod: return e->value * (d - floor(d/d2)*d2);
 157                 case e_max: return e->value * (d >  d2 ?   d : d2);
 158                 case e_min: return e->value * (d <  d2 ?   d : d2);
 159                 case e_eq:  return e->value * (d == d2 ? 1.0 : 0.0);
 160                 case e_gt:  return e->value * (d >  d2 ? 1.0 : 0.0);
 161                 case e_gte: return e->value * (d >= d2 ? 1.0 : 0.0);
 162                 case e_pow: return e->value * pow(d, d2);
 163                 case e_mul: return e->value * (d * d2);
 164                 case e_div: return e->value * (d / d2);
 165                 case e_add: return e->value * (d + d2);
 166                 case e_last:return e->value * d2;
 167                 case e_st : return e->value * (p->var[av_clip(d, 0, VARS-1)]= d2);
 168             }
 169         }
 170     }
 171     return NAN;
 172 }
 173
 174 static AVEvalExpr * parse_expr(Parser *p);
 175
 176 void ff_eval_free(AVEvalExpr * e) {
 177     if (!e) return;
 178     ff_eval_free(e->param[0]);
 179     ff_eval_free(e->param[1]);
 180     av_freep(&e);
 181 }
 182
 183 static AVEvalExpr * parse_primary(Parser *p) {
 184     AVEvalExpr * d = av_mallocz(sizeof(AVEvalExpr));
 185     char *next= p->s;
 186     int i;
 187
 188     if (!d)
 189         return NULL;
 190
 191     /* number */
 192     d->value = av_strtod(p->s, &next);
 193     if(next != p->s){
 194         d->type = e_value;
 195         p->s= next;
 196         return d;
 197     }
 198     d->value = 1;
 199
 200     /* named constants */
 201     for(i=0; p->const_name && p->const_name[i]; i++){
 202         if(strmatch(p->s, p->const_name[i])){
 203             p->s+= strlen(p->const_name[i]);
 204             d->type = e_const;
 205             d->a.const_index = i;
 206             return d;
 207         }
 208     }
 209
 210     p->s= strchr(p->s, '(');
 211     if(p->s==NULL){
 212         *p->error = "undefined constant or missing (";
 213         p->s= next;
 214         ff_eval_free(d);
 215         return NULL;
 216     }
 217     p->s++; // "("
 218     if (*next == '(') { // special case do-nothing
 219         av_freep(&d);
 220         d = parse_expr(p);
 221         if(p->s[0] != ')'){
 222             *p->error = "missing )";
 223             ff_eval_free(d);
 224             return NULL;
 225         }
 226         p->s++; // ")"
 227         return d;
 228     }
 229     d->param[0] = parse_expr(p);
 230     if(p->s[0]== ','){
 231         p->s++; // ","
 232         d->param[1] = parse_expr(p);
 233     }
 234     if(p->s[0] != ')'){
 235         *p->error = "missing )";
 236         ff_eval_free(d);
 237         return NULL;
 238     }
 239     p->s++; // ")"
 240
 241     d->type = e_func0;
 242          if( strmatch(next, "sinh"  ) ) d->a.func0 = sinh;
 243     else if( strmatch(next, "cosh"  ) ) d->a.func0 = cosh;
 244     else if( strmatch(next, "tanh"  ) ) d->a.func0 = tanh;
 245     else if( strmatch(next, "sin"   ) ) d->a.func0 = sin;
 246     else if( strmatch(next, "cos"   ) ) d->a.func0 = cos;
 247     else if( strmatch(next, "tan"   ) ) d->a.func0 = tan;
 248     else if( strmatch(next, "atan"  ) ) d->a.func0 = atan;
 249     else if( strmatch(next, "asin"  ) ) d->a.func0 = asin;
 250     else if( strmatch(next, "acos"  ) ) d->a.func0 = acos;
 251     else if( strmatch(next, "exp"   ) ) d->a.func0 = exp;
 252     else if( strmatch(next, "log"   ) ) d->a.func0 = log;
 253     else if( strmatch(next, "abs"   ) ) d->a.func0 = fabs;
 254     else if( strmatch(next, "squish") ) d->type = e_squish;
 255     else if( strmatch(next, "gauss" ) ) d->type = e_gauss;
 256     else if( strmatch(next, "mod"   ) ) d->type = e_mod;
 257     else if( strmatch(next, "max"   ) ) d->type = e_max;
 258     else if( strmatch(next, "min"   ) ) d->type = e_min;
 259     else if( strmatch(next, "eq"    ) ) d->type = e_eq;
 260     else if( strmatch(next, "gte"   ) ) d->type = e_gte;
 261     else if( strmatch(next, "gt"    ) ) d->type = e_gt;
 262     else if( strmatch(next, "lte"   ) ) { AVEvalExpr * tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gt; }
 263     else if( strmatch(next, "lt"    ) ) { AVEvalExpr * tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gte; }
 264     else if( strmatch(next, "ld"    ) ) d->type = e_ld;
 265     else if( strmatch(next, "st"    ) ) d->type = e_st;
 266     else if( strmatch(next, "while" ) ) d->type = e_while;
 267     else {
 268         for(i=0; p->func1_name && p->func1_name[i]; i++){
 269             if(strmatch(next, p->func1_name[i])){
 270                 d->a.func1 = p->func1[i];
 271                 d->type = e_func1;
 272                 return d;
 273             }
 274         }
 275
 276         for(i=0; p->func2_name && p->func2_name[i]; i++){
 277             if(strmatch(next, p->func2_name[i])){
 278                 d->a.func2 = p->func2[i];
 279                 d->type = e_func2;
 280                 return d;
 281             }
 282         }
 283
 284         *p->error = "unknown function";
 285         ff_eval_free(d);
 286         return NULL;
 287     }
 288
 289     return d;
 290 }
 291
 292 static AVEvalExpr * new_eval_expr(int type, int value, AVEvalExpr *p0, AVEvalExpr *p1){
 293     AVEvalExpr * e = av_mallocz(sizeof(AVEvalExpr));
 294     if (!e)
 295         return NULL;
 296     e->type     =type   ;
 297     e->value    =value  ;
 298     e->param[0] =p0     ;
 299     e->param[1] =p1     ;
 300     return e;
 301 }
 302
 303 static AVEvalExpr * parse_pow(Parser *p, int *sign){
 304     *sign= (*p->s == '+') - (*p->s == '-');
 305     p->s += *sign&1;
 306     return parse_primary(p);
 307 }
 308
 309 static AVEvalExpr * parse_factor(Parser *p){
 310     int sign, sign2;
 311     AVEvalExpr * e = parse_pow(p, &sign);
 312     while(p->s[0]=='^'){
 313         p->s++;
 314         e= new_eval_expr(e_pow, 1, e, parse_pow(p, &sign2));
 315         if (!e)
 316             return NULL;
 317         if (e->param[1]) e->param[1]->value *= (sign2|1);
 318     }
 319     if (e) e->value *= (sign|1);
 320     return e;
 321 }
 322
 323 static AVEvalExpr * parse_term(Parser *p){
 324     AVEvalExpr * e = parse_factor(p);
 325     while(p->s[0]=='*' || p->s[0]=='/'){
 326         int c= *p->s++;
 327         e= new_eval_expr(c == '*' ? e_mul : e_div, 1, e, parse_factor(p));
 328         if (!e)
 329             return NULL;
 330     }
 331     return e;
 332 }
 333
 334 static AVEvalExpr * parse_subexpr(Parser *p) {
 335     AVEvalExpr * e = parse_term(p);
 336     while(*p->s == '+' || *p->s == '-') {
 337         e= new_eval_expr(e_add, 1, e, parse_term(p));
 338         if (!e)
 339             return NULL;
 340     };
 341
 342     return e;
 343 }
 344
 345 static 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         if (!e)
 358             return NULL;
 359     };
 360
 361     p->stack_index++;
 362
 363     return e;
 364 }
 365
 366 static int verify_expr(AVEvalExpr * e) {
 367     if (!e) return 0;
 368     switch (e->type) {
 369         case e_value:
 370         case e_const: return 1;
 371         case e_func0:
 372         case e_func1:
 373         case e_squish:
 374         case e_ld:
 375         case e_gauss: return verify_expr(e->param[0]);
 376         default: return verify_expr(e->param[0]) && verify_expr(e->param[1]);
 377     }
 378 }
 379
 380 AVEvalExpr * ff_parse(const char *s, const char * const *const_name,
 381                double (**func1)(void *, double), const char **func1_name,
 382                double (**func2)(void *, double, double), const char **func2_name,
 383                const char **error){
 384     Parser p;
 385     AVEvalExpr *e = NULL;
 386     char *w = av_malloc(strlen(s) + 1);
 387     char *wp = w;
 388
 389     if (!w)
 390         goto end;
 391
 392     while (*s)
 393         if (!isspace(*s++)) *wp++ = s[-1];
 394     *wp++ = 0;
 395
 396     p.stack_index=100;
 397     p.s= w;
 398     p.const_name = const_name;
 399     p.func1      = func1;
 400     p.func1_name = func1_name;
 401     p.func2      = func2;
 402     p.func2_name = func2_name;
 403     p.error= error;
 404
 405     e = parse_expr(&p);
 406     if (!verify_expr(e)) {
 407         ff_eval_free(e);
 408         e = NULL;
 409     }
 410 end:
 411     av_free(w);
 412     return e;
 413 }
 414
 415 double ff_parse_eval(AVEvalExpr * e, const double *const_value, void *opaque) {
 416     Parser p;
 417
 418     p.const_value= const_value;
 419     p.opaque     = opaque;
 420     return eval_expr(&p, e);
 421 }
 422
 423 double ff_eval2(const char *s, const double *const_value, const char * const *const_name,
 424                double (**func1)(void *, double), const char **func1_name,
 425                double (**func2)(void *, double, double), const char **func2_name,
 426                void *opaque, const char **error){
 427     AVEvalExpr * e = ff_parse(s, const_name, func1, func1_name, func2, func2_name, error);
 428     double d;
 429     if (!e) return NAN;
 430     d = ff_parse_eval(e, const_value, opaque);
 431     ff_eval_free(e);
 432     return d;
 433 }
 434
 435 #ifdef TEST
 436 #undef printf
 437 static double const_values[]={
 438     M_PI,
 439     M_E,
 440     0
 441 };
 442 static const char *const_names[]={
 443     "PI",
 444     "E",
 445     0
 446 };
 447 int main(void){
 448     int i;
 449     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));
 450     printf("%f == 0.931322575\n", ff_eval2("80G/80Gi", const_values, const_names, NULL, NULL, NULL, NULL, NULL, NULL));
 451
 452     for(i=0; i<1050; i++){
 453         START_TIMER
 454             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);
 455         STOP_TIMER("ff_eval2")
 456     }
 457     return 0;
 458 }
 459 #endif