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 "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
  47 typedef 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
  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,
  83 };
  84
  85 double av_strtod(const char *numstr, char **tail) {
  86     double d;
  87     char *next;
  88     d = strtod(numstr, &next);
  89     /* if parsing succeeded, check for and interpret postfixes */
  90     if (next!=numstr) {
  91
  92         if(*next >= 'E' && *next <= 'z'){
  93             int e= si_prefixes[*next - 'E'];
  94             if(e){
  95                 if(next[1] == 'i'){
  96                     d*= pow( 2, e/0.3);
  97                     next+=2;
  98                 }else{
  99                     d*= pow(10, e);
 100                     next++;
 101                 }
 102             }
 103         }
 104
 105         if(*next=='B') {
 106             d*=8;
 107             next++;
 108         }
 109     }
 110     /* if requested, fill in tail with the position after the last parsed
 111        character */
 112     if (tail)
 113         *tail = next;
 114     return d;
 115 }
 116
 117 static int strmatch(const char *s, const char *prefix){
 118     int i;
 119     for(i=0; prefix[i]; i++){
 120         if(prefix[i] != s[i]) return 0;
 121     }
 122     return 1;
 123 }
 124
 125 struct ff_expr_s {
 126     enum {
 127         e_value, e_const, e_func0, e_func1, e_func2,
 128         e_squish, e_gauss, e_ld,
 129         e_mod, e_max, e_min, e_eq, e_gt, e_gte,
 130         e_pow, e_mul, e_div, e_add,
 131         e_last, e_st, e_while,
 132     } type;
 133     double value; // is sign in other types
 134     union {
 135         int const_index;
 136         double (*func0)(double);
 137         double (*func1)(void *, double);
 138         double (*func2)(void *, double, double);
 139     } a;
 140     AVEvalExpr * param[2];
 141 };
 142
 143 static double eval_expr(Parser * p, AVEvalExpr * e) {
 144     switch (e->type) {
 145         case e_value:  return e->value;
 146         case e_const:  return e->value * p->const_value[e->a.const_index];
 147         case e_func0:  return e->value * e->a.func0(eval_expr(p, e->param[0]));
 148         case e_func1:  return e->value * e->a.func1(p->opaque, eval_expr(p, e->param[0]));
 149         case e_func2:  return e->value * e->a.func2(p->opaque, eval_expr(p, e->param[0]), eval_expr(p, e->param[1]));
 150         case e_squish: return 1/(1+exp(4*eval_expr(p, e->param[0])));
 151         case e_gauss: { double d = eval_expr(p, e->param[0]); return exp(-d*d/2)/sqrt(2*M_PI); }
 152         case e_ld:     return e->value * p->var[av_clip(eval_expr(p, e->param[0]), 0, VARS-1)];
 153         case e_while: {
 154             double d = NAN;
 155             while(eval_expr(p, e->param[0]))
 156                 d=eval_expr(p, e->param[1]);
 157             return d;
 158         }
 159         default: {
 160             double d = eval_expr(p, e->param[0]);
 161             double d2 = eval_expr(p, e->param[1]);
 162             switch (e->type) {
 163                 case e_mod: return e->value * (d - floor(d/d2)*d2);
 164                 case e_max: return e->value * (d >  d2 ?   d : d2);
 165                 case e_min: return e->value * (d <  d2 ?   d : d2);
 166                 case e_eq:  return e->value * (d == d2 ? 1.0 : 0.0);
 167                 case e_gt:  return e->value * (d >  d2 ? 1.0 : 0.0);
 168                 case e_gte: return e->value * (d >= d2 ? 1.0 : 0.0);
 169                 case e_pow: return e->value * pow(d, d2);
 170                 case e_mul: return e->value * (d * d2);
 171                 case e_div: return e->value * (d / d2);
 172                 case e_add: return e->value * (d + d2);
 173                 case e_last:return e->value * d2;
 174                 case e_st : return e->value * (p->var[av_clip(d, 0, VARS-1)]= d2);
 175             }
 176         }
 177     }
 178     return NAN;
 179 }
 180
 181 static AVEvalExpr * parse_expr(Parser *p);
 182
 183 void ff_eval_free(AVEvalExpr * e) {
 184     if (!e) return;
 185     ff_eval_free(e->param[0]);
 186     ff_eval_free(e->param[1]);
 187     av_freep(&e);
 188 }
 189
 190 static AVEvalExpr * parse_primary(Parser *p) {
 191     AVEvalExpr * d = av_mallocz(sizeof(AVEvalExpr));
 192     char *next= p->s;
 193     int i;
 194
 195     /* number */
 196     d->value = av_strtod(p->s, &next);
 197     if(next != p->s){
 198         d->type = e_value;
 199         p->s= next;
 200         return d;
 201     }
 202     d->value = 1;
 203
 204     /* named constants */
 205     for(i=0; p->const_name && p->const_name[i]; i++){
 206         if(strmatch(p->s, p->const_name[i])){
 207             p->s+= strlen(p->const_name[i]);
 208             d->type = e_const;
 209             d->a.const_index = i;
 210             return d;
 211         }
 212     }
 213
 214     p->s= strchr(p->s, '(');
 215     if(p->s==NULL){
 216         *p->error = "undefined constant or missing (";
 217         p->s= next;
 218         ff_eval_free(d);
 219         return NULL;
 220     }
 221     p->s++; // "("
 222     if (*next == '(') { // special case do-nothing
 223         av_freep(&d);
 224         d = parse_expr(p);
 225         if(p->s[0] != ')'){
 226             *p->error = "missing )";
 227             ff_eval_free(d);
 228             return NULL;
 229         }
 230         p->s++; // ")"
 231         return d;
 232     }
 233     d->param[0] = parse_expr(p);
 234     if(p->s[0]== ','){
 235         p->s++; // ","
 236         d->param[1] = parse_expr(p);
 237     }
 238     if(p->s[0] != ')'){
 239         *p->error = "missing )";
 240         ff_eval_free(d);
 241         return NULL;
 242     }
 243     p->s++; // ")"
 244
 245     d->type = e_func0;
 246          if( strmatch(next, "sinh"  ) ) d->a.func0 = sinh;
 247     else if( strmatch(next, "cosh"  ) ) d->a.func0 = cosh;
 248     else if( strmatch(next, "tanh"  ) ) d->a.func0 = tanh;
 249     else if( strmatch(next, "sin"   ) ) d->a.func0 = sin;
 250     else if( strmatch(next, "cos"   ) ) d->a.func0 = cos;
 251     else if( strmatch(next, "tan"   ) ) d->a.func0 = tan;
 252     else if( strmatch(next, "atan"  ) ) d->a.func0 = atan;
 253     else if( strmatch(next, "asin"  ) ) d->a.func0 = asin;
 254     else if( strmatch(next, "acos"  ) ) d->a.func0 = acos;
 255     else if( strmatch(next, "exp"   ) ) d->a.func0 = exp;
 256     else if( strmatch(next, "log"   ) ) d->a.func0 = log;
 257     else if( strmatch(next, "abs"   ) ) d->a.func0 = fabs;
 258     else if( strmatch(next, "squish") ) d->type = e_squish;
 259     else if( strmatch(next, "gauss" ) ) d->type = e_gauss;
 260     else if( strmatch(next, "mod"   ) ) d->type = e_mod;
 261     else if( strmatch(next, "max"   ) ) d->type = e_max;
 262     else if( strmatch(next, "min"   ) ) d->type = e_min;
 263     else if( strmatch(next, "eq"    ) ) d->type = e_eq;
 264     else if( strmatch(next, "gte"   ) ) d->type = e_gte;
 265     else if( strmatch(next, "gt"    ) ) d->type = e_gt;
 266     else if( strmatch(next, "lte"   ) ) { AVEvalExpr * tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gt; }
 267     else if( strmatch(next, "lt"    ) ) { AVEvalExpr * tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gte; }
 268     else if( strmatch(next, "ld"    ) ) d->type = e_ld;
 269     else if( strmatch(next, "st"    ) ) d->type = e_st;
 270     else if( strmatch(next, "while" ) ) d->type = e_while;
 271     else {
 272         for(i=0; p->func1_name && p->func1_name[i]; i++){
 273             if(strmatch(next, p->func1_name[i])){
 274                 d->a.func1 = p->func1[i];
 275                 d->type = e_func1;
 276                 return d;
 277             }
 278         }
 279
 280         for(i=0; p->func2_name && p->func2_name[i]; i++){
 281             if(strmatch(next, p->func2_name[i])){
 282                 d->a.func2 = p->func2[i];
 283                 d->type = e_func2;
 284                 return d;
 285             }
 286         }
 287
 288         *p->error = "unknown function";
 289         ff_eval_free(d);
 290         return NULL;
 291     }
 292
 293     return d;
 294 }
 295
 296 static AVEvalExpr * new_eval_expr(int type, int value, AVEvalExpr *p0, AVEvalExpr *p1){
 297     AVEvalExpr * e = av_mallocz(sizeof(AVEvalExpr));
 298     e->type     =type   ;
 299     e->value    =value  ;
 300     e->param[0] =p0     ;
 301     e->param[1] =p1     ;
 302     return e;
 303 }
 304
 305 static AVEvalExpr * parse_pow(Parser *p, int *sign){
 306     *sign= (*p->s == '+') - (*p->s == '-');
 307     p->s += *sign&1;
 308     return parse_primary(p);
 309 }
 310
 311 static AVEvalExpr * parse_factor(Parser *p){
 312     int sign, sign2;
 313     AVEvalExpr * e = parse_pow(p, &sign);
 314     while(p->s[0]=='^'){
 315         p->s++;
 316         e= new_eval_expr(e_pow, 1, e, parse_pow(p, &sign2));
 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     }
 329     return e;
 330 }
 331
 332 static AVEvalExpr * parse_subexpr(Parser *p) {
 333     AVEvalExpr * e = parse_term(p);
 334     while(*p->s == '+' || *p->s == '-') {
 335         e= new_eval_expr(e_add, 1, e, parse_term(p));
 336     };
 337
 338     return e;
 339 }
 340
 341 static AVEvalExpr * parse_expr(Parser *p) {
 342     AVEvalExpr * e;
 343
 344     if(p->stack_index <= 0) //protect against stack overflows
 345         return NULL;
 346     p->stack_index--;
 347
 348     e = parse_subexpr(p);
 349
 350     while(*p->s == ';') {
 351         p->s++;
 352         e= new_eval_expr(e_last, 1, e, parse_subexpr(p));
 353     };
 354
 355     p->stack_index++;
 356
 357     return e;
 358 }
 359
 360 static int verify_expr(AVEvalExpr * e) {
 361     if (!e) return 0;
 362     switch (e->type) {
 363         case e_value:
 364         case e_const: return 1;
 365         case e_func0:
 366         case e_func1:
 367         case e_squish:
 368         case e_ld:
 369         case e_gauss: return verify_expr(e->param[0]);
 370         default: return verify_expr(e->param[0]) && verify_expr(e->param[1]);
 371     }
 372 }
 373
 374 AVEvalExpr * ff_parse(const char *s, const char * const *const_name,
 375                double (**func1)(void *, double), const char **func1_name,
 376                double (**func2)(void *, double, double), const char **func2_name,
 377                const char **error){
 378     Parser p;
 379     AVEvalExpr * e;
 380     char w[strlen(s) + 1], * wp = w;
 381
 382     while (*s)
 383         if (!isspace(*s++)) *wp++ = s[-1];
 384     *wp++ = 0;
 385
 386     p.stack_index=100;
 387     p.s= w;
 388     p.const_name = const_name;
 389     p.func1      = func1;
 390     p.func1_name = func1_name;
 391     p.func2      = func2;
 392     p.func2_name = func2_name;
 393     p.error= error;
 394
 395     e = parse_expr(&p);
 396     if (!verify_expr(e)) {
 397         ff_eval_free(e);
 398         return NULL;
 399     }
 400     return e;
 401 }
 402
 403 double ff_parse_eval(AVEvalExpr * e, const double *const_value, void *opaque) {
 404     Parser p;
 405
 406     p.const_value= const_value;
 407     p.opaque     = opaque;
 408     return eval_expr(&p, e);
 409 }
 410
 411 double ff_eval2(const char *s, const double *const_value, const char * const *const_name,
 412                double (**func1)(void *, double), const char **func1_name,
 413                double (**func2)(void *, double, double), const char **func2_name,
 414                void *opaque, const char **error){
 415     AVEvalExpr * e = ff_parse(s, const_name, func1, func1_name, func2, func2_name, error);
 416     double d;
 417     if (!e) return NAN;
 418     d = ff_parse_eval(e, const_value, opaque);
 419     ff_eval_free(e);
 420     return d;
 421 }
 422
 423 #ifdef TEST
 424 #undef printf
 425 static double const_values[]={
 426     M_PI,
 427     M_E,
 428     0
 429 };
 430 static const char *const_names[]={
 431     "PI",
 432     "E",
 433     0
 434 };
 435 int main(void){
 436     int i;
 437     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));
 438     printf("%f == 0.931322575\n", ff_eval2("80G/80Gi", const_values, const_names, NULL, NULL, NULL, NULL, NULL, NULL));
 439
 440     for(i=0; i<1050; i++){
 441         START_TIMER
 442             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);
 443         STOP_TIMER("ff_eval2")
 444     }
 445     return 0;
 446 }
 447 #endif