libavcodec/eval.c

   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
  32 typedef 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
  47 static 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
  70 double 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
 102 static 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
 110 struct 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
 128 static 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
 166 static AVExpr * parse_expr(Parser *p);
 167
 168 void 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
 175 static 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
 284 static 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
 295 static 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
 301 static 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
 315 static 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
 326 static 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
 337 static 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
 358 static 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
 372 AVExpr *ff_parse_expr(const char *s,
 373                       const char * const *const_name,
 374                       const char * const *func1_name, double (* const *func1)(void *, double),
 375                       const char * const *func2_name, double (* const *func2)(void *, double, double),
 376                const char **error){
 377     Parser p;
 378     AVExpr *e = NULL;
 379     char *w = av_malloc(strlen(s) + 1);
 380     char *wp = w;
 381
 382     if (!w)
 383         goto end;
 384
 385     while (*s)
 386         if (!isspace(*s++)) *wp++ = s[-1];
 387     *wp++ = 0;
 388
 389     p.stack_index=100;
 390     p.s= w;
 391     p.const_name = const_name;
 392     p.func1      = func1;
 393     p.func1_name = func1_name;
 394     p.func2      = func2;
 395     p.func2_name = func2_name;
 396     p.error= error;
 397
 398     e = parse_expr(&p);
 399     if (!verify_expr(e)) {
 400         ff_free_expr(e);
 401         e = NULL;
 402     }
 403 end:
 404     av_free(w);
 405     return e;
 406 }
 407
 408 double ff_eval_expr(AVExpr * e, const double *const_value, void *opaque) {
 409     Parser p;
 410
 411     p.const_value= const_value;
 412     p.opaque     = opaque;
 413     return eval_expr(&p, e);
 414 }
 415
 416 double ff_parse_and_eval_expr(const char *s,
 417                               const char * const *const_name, const double *const_value,
 418                               const char * const *func1_name, double (* const *func1)(void *, double),
 419                               const char * const *func2_name, double (* const *func2)(void *, double, double),
 420                void *opaque, const char **error){
 421     AVExpr *e = ff_parse_expr(s, const_name, func1_name, func1, func2_name, func2, error);
 422     double d;
 423     if (!e) return NAN;
 424     d = ff_eval_expr(e, const_value, opaque);
 425     ff_free_expr(e);
 426     return d;
 427 }
 428
 429 #ifdef TEST
 430 #undef printf
 431 static double const_values[]={
 432     M_PI,
 433     M_E,
 434     0
 435 };
 436 static const char *const_names[]={
 437     "PI",
 438     "E",
 439     0
 440 };
 441 int main(void){
 442     int i;
 443     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_names, const_values, NULL, NULL, NULL, NULL, NULL, NULL));
 444     printf("%f == 0.931322575\n", ff_parse_and_eval_expr("80G/80Gi", const_names, const_values, NULL, NULL, NULL, NULL, NULL, NULL));
 445
 446     for(i=0; i<1050; i++){
 447         START_TIMER
 448             ff_parse_and_eval_expr("1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)", const_names, const_values, NULL, NULL, NULL, NULL, NULL, NULL);
 449         STOP_TIMER("ff_parse_and_eval_expr")
 450     }
 451     return 0;
 452 }
 453 #endif