2 * Copyright (c) 2002-2006 Michael Niedermayer <michaelni@gmx.at>
3 * Copyright (c) 2006 Oded Shimon <ods15@ods15.dyndns.org>
5 * This file is part of FFmpeg.
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.
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.
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
24 * simple arithmetic expression evaluator.
26 * see http://joe.hotchkiss.com/programming/eval/eval.html
30 #include "attributes.h"
36 #include "mathematics.h"
41 typedef struct Parser {
45 const double *const_values;
46 const char * const *const_names; // NULL terminated
47 double (* const *funcs1)(void *, double a); // NULL terminated
48 const char * const *func1_names; // NULL terminated
49 double (* const *funcs2)(void *, double a, double b); // NULL terminated
50 const char * const *func2_names; // NULL terminated
58 static const AVClass eval_class = { "Eval", av_default_item_name, NULL, LIBAVUTIL_VERSION_INT, offsetof(Parser,log_offset), offsetof(Parser,log_ctx) };
60 static const int8_t si_prefixes['z' - 'E' + 1] = {
90 { "QP2LAMBDA", FF_QP2LAMBDA },
93 double av_strtod(const char *numstr, char **tail)
97 if(numstr[0]=='0' && (numstr[1]|0x20)=='x') {
98 d = strtoul(numstr, &next, 16);
100 d = strtod(numstr, &next);
101 /* if parsing succeeded, check for and interpret postfixes */
103 if (next[0] == 'd' && next[1] == 'B') {
104 /* treat dB as decibels instead of decibytes */
107 } else if (*next >= 'E' && *next <= 'z') {
108 int e= si_prefixes[*next - 'E'];
110 if (next[1] == 'i') {
125 /* if requested, fill in tail with the position after the last parsed
132 #define IS_IDENTIFIER_CHAR(c) ((c) - '0' <= 9U || (c) - 'a' <= 25U || (c) - 'A' <= 25U || (c) == '_')
134 static int strmatch(const char *s, const char *prefix)
137 for (i=0; prefix[i]; i++) {
138 if (prefix[i] != s[i]) return 0;
140 /* return 1 only if the s identifier is terminated */
141 return !IS_IDENTIFIER_CHAR(s[i]);
146 e_value, e_const, e_func0, e_func1, e_func2,
147 e_squish, e_gauss, e_ld, e_isnan, e_isinf,
148 e_mod, e_max, e_min, e_eq, e_gt, e_gte, e_lte, e_lt,
149 e_pow, e_mul, e_div, e_add,
150 e_last, e_st, e_while, e_taylor, e_root, e_floor, e_ceil, e_trunc,
151 e_sqrt, e_not, e_random, e_hypot, e_gcd,
152 e_if, e_ifnot, e_print, e_bitand, e_bitor, e_between, e_clip
154 double value; // is sign in other types
157 double (*func0)(double);
158 double (*func1)(void *, double);
159 double (*func2)(void *, double, double);
161 struct AVExpr *param[3];
165 static double etime(double v)
167 return av_gettime() * 0.000001;
170 static double eval_expr(Parser *p, AVExpr *e)
173 case e_value: return e->value;
174 case e_const: return e->value * p->const_values[e->a.const_index];
175 case e_func0: return e->value * e->a.func0(eval_expr(p, e->param[0]));
176 case e_func1: return e->value * e->a.func1(p->opaque, eval_expr(p, e->param[0]));
177 case e_func2: return e->value * e->a.func2(p->opaque, eval_expr(p, e->param[0]), eval_expr(p, e->param[1]));
178 case e_squish: return 1/(1+exp(4*eval_expr(p, e->param[0])));
179 case e_gauss: { double d = eval_expr(p, e->param[0]); return exp(-d*d/2)/sqrt(2*M_PI); }
180 case e_ld: return e->value * p->var[av_clip(eval_expr(p, e->param[0]), 0, VARS-1)];
181 case e_isnan: return e->value * !!isnan(eval_expr(p, e->param[0]));
182 case e_isinf: return e->value * !!isinf(eval_expr(p, e->param[0]));
183 case e_floor: return e->value * floor(eval_expr(p, e->param[0]));
184 case e_ceil : return e->value * ceil (eval_expr(p, e->param[0]));
185 case e_trunc: return e->value * trunc(eval_expr(p, e->param[0]));
186 case e_sqrt: return e->value * sqrt (eval_expr(p, e->param[0]));
187 case e_not: return e->value * (eval_expr(p, e->param[0]) == 0);
188 case e_if: return e->value * (eval_expr(p, e->param[0]) ? eval_expr(p, e->param[1]) :
189 e->param[2] ? eval_expr(p, e->param[2]) : 0);
190 case e_ifnot: return e->value * (!eval_expr(p, e->param[0]) ? eval_expr(p, e->param[1]) :
191 e->param[2] ? eval_expr(p, e->param[2]) : 0);
193 double x = eval_expr(p, e->param[0]);
194 double min = eval_expr(p, e->param[1]), max = eval_expr(p, e->param[2]);
195 if (isnan(min) || isnan(max) || isnan(x) || min > max)
197 return e->value * av_clipd(eval_expr(p, e->param[0]), min, max);
200 double d = eval_expr(p, e->param[0]);
201 return e->value * (d >= eval_expr(p, e->param[1]) &&
202 d <= eval_expr(p, e->param[2]));
205 double x = eval_expr(p, e->param[0]);
206 int level = e->param[1] ? av_clip(eval_expr(p, e->param[1]), INT_MIN, INT_MAX) : AV_LOG_INFO;
207 av_log(p, level, "%f\n", x);
211 int idx= av_clip(eval_expr(p, e->param[0]), 0, VARS-1);
212 uint64_t r= isnan(p->var[idx]) ? 0 : p->var[idx];
213 r= r*1664525+1013904223;
215 return e->value * (r * (1.0/UINT64_MAX));
219 while (eval_expr(p, e->param[0]))
220 d=eval_expr(p, e->param[1]);
224 double t = 1, d = 0, v;
225 double x = eval_expr(p, e->param[1]);
226 int id = e->param[2] ? av_clip(eval_expr(p, e->param[2]), 0, VARS-1) : 0;
228 double var0 = p->var[id];
229 for(i=0; i<1000; i++) {
232 v = eval_expr(p, e->param[0]);
243 double low = -1, high = -1, v, low_v = -DBL_MAX, high_v = DBL_MAX;
244 double var0 = p->var[0];
245 double x_max = eval_expr(p, e->param[1]);
246 for(i=-1; i<1024; i++) {
248 p->var[0] = ff_reverse[i&255]*x_max/255;
250 p->var[0] = x_max*pow(0.9, i-255);
251 if (i&1) p->var[0] *= -1;
252 if (i&2) p->var[0] += low;
253 else p->var[0] += high;
255 v = eval_expr(p, e->param[0]);
256 if (v<=0 && v>low_v) {
260 if (v>=0 && v<high_v) {
264 if (low>=0 && high>=0){
265 for (j=0; j<1000; j++) {
266 p->var[0] = (low+high)*0.5;
267 if (low == p->var[0] || high == p->var[0])
269 v = eval_expr(p, e->param[0]);
270 if (v<=0) low = p->var[0];
271 if (v>=0) high= p->var[0];
281 return -low_v<high_v ? low : high;
284 double d = eval_expr(p, e->param[0]);
285 double d2 = eval_expr(p, e->param[1]);
287 case e_mod: return e->value * (d - floor((!CONFIG_FTRAPV || d2) ? d / d2 : d * INFINITY) * d2);
288 case e_gcd: return e->value * av_gcd(d,d2);
289 case e_max: return e->value * (d > d2 ? d : d2);
290 case e_min: return e->value * (d < d2 ? d : d2);
291 case e_eq: return e->value * (d == d2 ? 1.0 : 0.0);
292 case e_gt: return e->value * (d > d2 ? 1.0 : 0.0);
293 case e_gte: return e->value * (d >= d2 ? 1.0 : 0.0);
294 case e_lt: return e->value * (d < d2 ? 1.0 : 0.0);
295 case e_lte: return e->value * (d <= d2 ? 1.0 : 0.0);
296 case e_pow: return e->value * pow(d, d2);
297 case e_mul: return e->value * (d * d2);
298 case e_div: return e->value * ((!CONFIG_FTRAPV || d2 ) ? (d / d2) : d * INFINITY);
299 case e_add: return e->value * (d + d2);
300 case e_last:return e->value * d2;
301 case e_st : return e->value * (p->var[av_clip(d, 0, VARS-1)]= d2);
302 case e_hypot:return e->value * (sqrt(d*d + d2*d2));
303 case e_bitand: return isnan(d) || isnan(d2) ? NAN : e->value * ((long int)d & (long int)d2);
304 case e_bitor: return isnan(d) || isnan(d2) ? NAN : e->value * ((long int)d | (long int)d2);
311 static int parse_expr(AVExpr **e, Parser *p);
313 void av_expr_free(AVExpr *e)
316 av_expr_free(e->param[0]);
317 av_expr_free(e->param[1]);
318 av_expr_free(e->param[2]);
323 static int parse_primary(AVExpr **e, Parser *p)
325 AVExpr *d = av_mallocz(sizeof(AVExpr));
326 char *next = p->s, *s0 = p->s;
330 return AVERROR(ENOMEM);
333 d->value = av_strtod(p->s, &next);
342 /* named constants */
343 for (i=0; p->const_names && p->const_names[i]; i++) {
344 if (strmatch(p->s, p->const_names[i])) {
345 p->s+= strlen(p->const_names[i]);
347 d->a.const_index = i;
352 for (i = 0; i < FF_ARRAY_ELEMS(constants); i++) {
353 if (strmatch(p->s, constants[i].name)) {
354 p->s += strlen(constants[i].name);
356 d->value = constants[i].value;
362 p->s= strchr(p->s, '(');
364 av_log(p, AV_LOG_ERROR, "Undefined constant or missing '(' in '%s'\n", s0);
367 return AVERROR(EINVAL);
370 if (*next == '(') { // special case do-nothing
372 if ((ret = parse_expr(&d, p)) < 0)
374 if (p->s[0] != ')') {
375 av_log(p, AV_LOG_ERROR, "Missing ')' in '%s'\n", s0);
377 return AVERROR(EINVAL);
383 if ((ret = parse_expr(&(d->param[0]), p)) < 0) {
389 parse_expr(&d->param[1], p);
393 parse_expr(&d->param[2], p);
395 if (p->s[0] != ')') {
396 av_log(p, AV_LOG_ERROR, "Missing ')' or too many args in '%s'\n", s0);
398 return AVERROR(EINVAL);
403 if (strmatch(next, "sinh" )) d->a.func0 = sinh;
404 else if (strmatch(next, "cosh" )) d->a.func0 = cosh;
405 else if (strmatch(next, "tanh" )) d->a.func0 = tanh;
406 else if (strmatch(next, "sin" )) d->a.func0 = sin;
407 else if (strmatch(next, "cos" )) d->a.func0 = cos;
408 else if (strmatch(next, "tan" )) d->a.func0 = tan;
409 else if (strmatch(next, "atan" )) d->a.func0 = atan;
410 else if (strmatch(next, "asin" )) d->a.func0 = asin;
411 else if (strmatch(next, "acos" )) d->a.func0 = acos;
412 else if (strmatch(next, "exp" )) d->a.func0 = exp;
413 else if (strmatch(next, "log" )) d->a.func0 = log;
414 else if (strmatch(next, "abs" )) d->a.func0 = fabs;
415 else if (strmatch(next, "time" )) d->a.func0 = etime;
416 else if (strmatch(next, "squish")) d->type = e_squish;
417 else if (strmatch(next, "gauss" )) d->type = e_gauss;
418 else if (strmatch(next, "mod" )) d->type = e_mod;
419 else if (strmatch(next, "max" )) d->type = e_max;
420 else if (strmatch(next, "min" )) d->type = e_min;
421 else if (strmatch(next, "eq" )) d->type = e_eq;
422 else if (strmatch(next, "gte" )) d->type = e_gte;
423 else if (strmatch(next, "gt" )) d->type = e_gt;
424 else if (strmatch(next, "lte" )) d->type = e_lte;
425 else if (strmatch(next, "lt" )) d->type = e_lt;
426 else if (strmatch(next, "ld" )) d->type = e_ld;
427 else if (strmatch(next, "isnan" )) d->type = e_isnan;
428 else if (strmatch(next, "isinf" )) d->type = e_isinf;
429 else if (strmatch(next, "st" )) d->type = e_st;
430 else if (strmatch(next, "while" )) d->type = e_while;
431 else if (strmatch(next, "taylor")) d->type = e_taylor;
432 else if (strmatch(next, "root" )) d->type = e_root;
433 else if (strmatch(next, "floor" )) d->type = e_floor;
434 else if (strmatch(next, "ceil" )) d->type = e_ceil;
435 else if (strmatch(next, "trunc" )) d->type = e_trunc;
436 else if (strmatch(next, "sqrt" )) d->type = e_sqrt;
437 else if (strmatch(next, "not" )) d->type = e_not;
438 else if (strmatch(next, "pow" )) d->type = e_pow;
439 else if (strmatch(next, "print" )) d->type = e_print;
440 else if (strmatch(next, "random")) d->type = e_random;
441 else if (strmatch(next, "hypot" )) d->type = e_hypot;
442 else if (strmatch(next, "gcd" )) d->type = e_gcd;
443 else if (strmatch(next, "if" )) d->type = e_if;
444 else if (strmatch(next, "ifnot" )) d->type = e_ifnot;
445 else if (strmatch(next, "bitand")) d->type = e_bitand;
446 else if (strmatch(next, "bitor" )) d->type = e_bitor;
447 else if (strmatch(next, "between"))d->type = e_between;
448 else if (strmatch(next, "clip" )) d->type = e_clip;
450 for (i=0; p->func1_names && p->func1_names[i]; i++) {
451 if (strmatch(next, p->func1_names[i])) {
452 d->a.func1 = p->funcs1[i];
459 for (i=0; p->func2_names && p->func2_names[i]; i++) {
460 if (strmatch(next, p->func2_names[i])) {
461 d->a.func2 = p->funcs2[i];
468 av_log(p, AV_LOG_ERROR, "Unknown function in '%s'\n", s0);
470 return AVERROR(EINVAL);
477 static AVExpr *make_eval_expr(int type, int value, AVExpr *p0, AVExpr *p1)
479 AVExpr *e = av_mallocz(sizeof(AVExpr));
489 static int parse_pow(AVExpr **e, Parser *p, int *sign)
491 *sign= (*p->s == '+') - (*p->s == '-');
493 return parse_primary(e, p);
496 static int parse_dB(AVExpr **e, Parser *p, int *sign)
498 /* do not filter out the negative sign when parsing a dB value.
499 for example, -3dB is not the same as -(3dB) */
502 double av_unused ignored = strtod(p->s, &next);
503 if (next != p->s && next[0] == 'd' && next[1] == 'B') {
505 return parse_primary(e, p);
508 return parse_pow(e, p, sign);
511 static int parse_factor(AVExpr **e, Parser *p)
513 int sign, sign2, ret;
514 AVExpr *e0, *e1, *e2;
515 if ((ret = parse_dB(&e0, p, &sign)) < 0)
520 if ((ret = parse_dB(&e2, p, &sign2)) < 0) {
524 e0 = make_eval_expr(e_pow, 1, e1, e2);
528 return AVERROR(ENOMEM);
530 if (e0->param[1]) e0->param[1]->value *= (sign2|1);
532 if (e0) e0->value *= (sign|1);
538 static int parse_term(AVExpr **e, Parser *p)
541 AVExpr *e0, *e1, *e2;
542 if ((ret = parse_factor(&e0, p)) < 0)
544 while (p->s[0]=='*' || p->s[0]=='/') {
547 if ((ret = parse_factor(&e2, p)) < 0) {
551 e0 = make_eval_expr(c == '*' ? e_mul : e_div, 1, e1, e2);
555 return AVERROR(ENOMEM);
562 static int parse_subexpr(AVExpr **e, Parser *p)
565 AVExpr *e0, *e1, *e2;
566 if ((ret = parse_term(&e0, p)) < 0)
568 while (*p->s == '+' || *p->s == '-') {
570 if ((ret = parse_term(&e2, p)) < 0) {
574 e0 = make_eval_expr(e_add, 1, e1, e2);
578 return AVERROR(ENOMEM);
586 static int parse_expr(AVExpr **e, Parser *p)
589 AVExpr *e0, *e1, *e2;
590 if (p->stack_index <= 0) //protect against stack overflows
591 return AVERROR(EINVAL);
594 if ((ret = parse_subexpr(&e0, p)) < 0)
596 while (*p->s == ';') {
599 if ((ret = parse_subexpr(&e2, p)) < 0) {
603 e0 = make_eval_expr(e_last, 1, e1, e2);
607 return AVERROR(ENOMEM);
616 static int verify_expr(AVExpr *e)
621 case e_const: return 1;
635 return verify_expr(e->param[0]) && !e->param[1];
637 return verify_expr(e->param[0])
638 && (!e->param[1] || verify_expr(e->param[1]));
642 return verify_expr(e->param[0]) && verify_expr(e->param[1])
643 && (!e->param[2] || verify_expr(e->param[2]));
646 return verify_expr(e->param[0]) &&
647 verify_expr(e->param[1]) &&
648 verify_expr(e->param[2]);
649 default: return verify_expr(e->param[0]) && verify_expr(e->param[1]) && !e->param[2];
653 int av_expr_parse(AVExpr **expr, const char *s,
654 const char * const *const_names,
655 const char * const *func1_names, double (* const *funcs1)(void *, double),
656 const char * const *func2_names, double (* const *funcs2)(void *, double, double),
657 int log_offset, void *log_ctx)
661 char *w = av_malloc(strlen(s) + 1);
667 return AVERROR(ENOMEM);
670 if (!av_isspace(*s++)) *wp++ = s[-1];
673 p.class = &eval_class;
676 p.const_names = const_names;
678 p.func1_names = func1_names;
680 p.func2_names = func2_names;
681 p.log_offset = log_offset;
684 if ((ret = parse_expr(&e, &p)) < 0)
687 av_log(&p, AV_LOG_ERROR, "Invalid chars '%s' at the end of expression '%s'\n", p.s, s0);
688 ret = AVERROR(EINVAL);
691 if (!verify_expr(e)) {
692 ret = AVERROR(EINVAL);
695 e->var= av_mallocz(sizeof(double) *VARS);
697 ret = AVERROR(ENOMEM);
708 double av_expr_eval(AVExpr *e, const double *const_values, void *opaque)
713 p.const_values = const_values;
715 return eval_expr(&p, e);
718 int av_expr_parse_and_eval(double *d, const char *s,
719 const char * const *const_names, const double *const_values,
720 const char * const *func1_names, double (* const *funcs1)(void *, double),
721 const char * const *func2_names, double (* const *funcs2)(void *, double, double),
722 void *opaque, int log_offset, void *log_ctx)
725 int ret = av_expr_parse(&e, s, const_names, func1_names, funcs1, func2_names, funcs2, log_offset, log_ctx);
731 *d = av_expr_eval(e, const_values, opaque);
733 return isnan(*d) ? AVERROR(EINVAL) : 0;
739 static const double const_values[] = {
745 static const char *const const_names[] = {
751 int main(int argc, char **argv)
755 const char *const *expr;
756 static const char *const exprs[] = {
762 "1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)",
783 "bar + PI + E + 100f*2 + foo",
784 "13k + 12f - foo(1, 2)",
797 /* compute 1+2+...+N */
798 "st(0, 1); while(lte(ld(0), 100), st(1, ld(1)+ld(0));st(0, ld(0)+1)); ld(1)",
800 "st(1, 1); st(2, 2); st(0, 1); while(lte(ld(0),10), st(3, ld(1)+ld(2)); st(1, ld(2)); st(2, ld(3)); st(0, ld(0)+1)); ld(3)",
802 "st(0, 1); while(lte(ld(0),100), st(1, ld(1)+ld(0)); st(0, ld(0)+1))",
831 "ifnot(1, NaN) + if(0, 1)",
835 "taylor(eq(mod(ld(1),4),1)-eq(mod(ld(1),4),3), PI/2, 1)",
836 "root(sin(ld(0))-1, 2)",
837 "root(sin(ld(0))+6+sin(ld(0)/12)-log(ld(0)), 100)",
838 "7000000B*random(0)",
842 "gcd(30,55)*print(min(9,1))",
846 "between(10, -3, 10)",
847 "between(-4, -2, -1)",
855 for (expr = exprs; *expr; expr++) {
856 printf("Evaluating '%s'\n", *expr);
857 av_expr_parse_and_eval(&d, *expr,
858 const_names, const_values,
859 NULL, NULL, NULL, NULL, NULL, 0, NULL);
861 printf("'%s' -> nan\n\n", *expr);
863 printf("'%s' -> %f\n\n", *expr, d);
866 av_expr_parse_and_eval(&d, "1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)",
867 const_names, const_values,
868 NULL, NULL, NULL, NULL, NULL, 0, NULL);
869 printf("%f == 12.7\n", d);
870 av_expr_parse_and_eval(&d, "80G/80Gi",
871 const_names, const_values,
872 NULL, NULL, NULL, NULL, NULL, 0, NULL);
873 printf("%f == 0.931322575\n", d);
875 if (argc > 1 && !strcmp(argv[1], "-t")) {
876 for (i = 0; i < 1050; i++) {
878 av_expr_parse_and_eval(&d, "1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)",
879 const_names, const_values,
880 NULL, NULL, NULL, NULL, NULL, 0, NULL);
881 STOP_TIMER("av_expr_parse_and_eval");