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 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     double *const_value;
  51     const char **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     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 /** 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  */
  89 static 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
 121 static 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
 129 struct 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
 147 static 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
 185 static AVEvalExpr * parse_expr(Parser *p);
 186
 187 void 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
 194 static 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
 300 static 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
 309 static 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
 315 static 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
 327 static 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
 336 static 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
 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     };
 358
 359     p->stack_index++;
 360
 361     return e;
 362 }
 363
 364 static 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
 378 AVEvalExpr * ff_parse(const char *s, const char **const_name,
 379                double (**func1)(void *, double), const char **func1_name,
 380                double (**func2)(void *, double, double), 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
 407 double ff_parse_eval(AVEvalExpr * e, 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
 415 double ff_eval2(const char *s, double *const_value, const char **const_name,
 416                double (**func1)(void *, double), const char **func1_name,
 417                double (**func2)(void *, double, double), 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
 429 static double const_values[]={
 430     M_PI,
 431     M_E,
 432     0
 433 };
 434 static const char *const_names[]={
 435     "PI",
 436     "E",
 437     0
 438 };
 439 int main(void){
 440     int i;
 441     printf("%f == 12.7\n", ff_eval("1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)", const_values, const_names, NULL, NULL, NULL, NULL, NULL));
 442     printf("%f == 0.931322575\n", ff_eval("80G/80Gi", const_values, const_names, NULL, NULL, NULL, NULL, NULL));
 443
 444     for(i=0; i<1050; i++){
 445         START_TIMER
 446             ff_eval("1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)", const_values, const_names, NULL, NULL, NULL, NULL, NULL);
 447         STOP_TIMER("ff_eval")
 448     }
 449     return 0;
 450 }
 451 #endif