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
34 #include "mathematics.h"
38 typedef struct Parser {
42 const double *const_values;
43 const char * const *const_names; // NULL terminated
44 double (* const *funcs1)(void *, double a); // NULL terminated
45 const char * const *func1_names; // NULL terminated
46 double (* const *funcs2)(void *, double a, double b); // NULL terminated
47 const char * const *func2_names; // NULL terminated
55 static const AVClass class = { "Eval", av_default_item_name, NULL, LIBAVUTIL_VERSION_INT, offsetof(Parser,log_offset), offsetof(Parser,log_ctx) };
57 static const int8_t si_prefixes['z' - 'E' + 1] = {
89 double av_strtod(const char *numstr, char **tail)
93 if(numstr[0]=='0' && (numstr[1]|0x20)=='x') {
94 d = strtoul(numstr, &next, 16);
96 d = strtod(numstr, &next);
97 /* if parsing succeeded, check for and interpret postfixes */
99 if (next[0] == 'd' && next[1] == 'B') {
100 /* treat dB as decibels instead of decibytes */
103 } else if (*next >= 'E' && *next <= 'z') {
104 int e= si_prefixes[*next - 'E'];
106 if (next[1] == 'i') {
121 /* if requested, fill in tail with the position after the last parsed
128 #define IS_IDENTIFIER_CHAR(c) ((c) - '0' <= 9U || (c) - 'a' <= 25U || (c) - 'A' <= 25U || (c) == '_')
130 static int strmatch(const char *s, const char *prefix)
133 for (i=0; prefix[i]; i++) {
134 if (prefix[i] != s[i]) return 0;
136 /* return 1 only if the s identifier is terminated */
137 return !IS_IDENTIFIER_CHAR(s[i]);
142 e_value, e_const, e_func0, e_func1, e_func2,
143 e_squish, e_gauss, e_ld, e_isnan, e_isinf,
144 e_mod, e_max, e_min, e_eq, e_gt, e_gte, e_lte, e_lt,
145 e_pow, e_mul, e_div, e_add,
146 e_last, e_st, e_while, e_taylor, e_root, e_floor, e_ceil, e_trunc,
147 e_sqrt, e_not, e_random, e_hypot, e_gcd,
148 e_if, e_ifnot, e_print,
150 double value; // is sign in other types
153 double (*func0)(double);
154 double (*func1)(void *, double);
155 double (*func2)(void *, double, double);
157 struct AVExpr *param[3];
161 static double etime(double v)
163 return av_gettime() * 0.000001;
166 static double eval_expr(Parser *p, AVExpr *e)
169 case e_value: return e->value;
170 case e_const: return e->value * p->const_values[e->a.const_index];
171 case e_func0: return e->value * e->a.func0(eval_expr(p, e->param[0]));
172 case e_func1: return e->value * e->a.func1(p->opaque, eval_expr(p, e->param[0]));
173 case e_func2: return e->value * e->a.func2(p->opaque, eval_expr(p, e->param[0]), eval_expr(p, e->param[1]));
174 case e_squish: return 1/(1+exp(4*eval_expr(p, e->param[0])));
175 case e_gauss: { double d = eval_expr(p, e->param[0]); return exp(-d*d/2)/sqrt(2*M_PI); }
176 case e_ld: return e->value * p->var[av_clip(eval_expr(p, e->param[0]), 0, VARS-1)];
177 case e_isnan: return e->value * !!isnan(eval_expr(p, e->param[0]));
178 case e_isinf: return e->value * !!isinf(eval_expr(p, e->param[0]));
179 case e_floor: return e->value * floor(eval_expr(p, e->param[0]));
180 case e_ceil : return e->value * ceil (eval_expr(p, e->param[0]));
181 case e_trunc: return e->value * trunc(eval_expr(p, e->param[0]));
182 case e_sqrt: return e->value * sqrt (eval_expr(p, e->param[0]));
183 case e_not: return e->value * (eval_expr(p, e->param[0]) == 0);
184 case e_if: return e->value * (eval_expr(p, e->param[0]) ? eval_expr(p, e->param[1]) :
185 e->param[2] ? eval_expr(p, e->param[2]) : 0);
186 case e_ifnot: return e->value * (!eval_expr(p, e->param[0]) ? eval_expr(p, e->param[1]) :
187 e->param[2] ? eval_expr(p, e->param[2]) : 0);
189 double x = eval_expr(p, e->param[0]);
190 int level = e->param[1] ? av_clip(eval_expr(p, e->param[1]), INT_MIN, INT_MAX) : AV_LOG_INFO;
191 av_log(p, level, "%f\n", x);
195 int idx= av_clip(eval_expr(p, e->param[0]), 0, VARS-1);
196 uint64_t r= isnan(p->var[idx]) ? 0 : p->var[idx];
197 r= r*1664525+1013904223;
199 return e->value * (r * (1.0/UINT64_MAX));
203 while (eval_expr(p, e->param[0]))
204 d=eval_expr(p, e->param[1]);
208 double t = 1, d = 0, v;
209 double x = eval_expr(p, e->param[1]);
210 int id = e->param[2] ? av_clip(eval_expr(p, e->param[2]), 0, VARS-1) : 0;
212 double var0 = p->var[id];
213 for(i=0; i<1000; i++) {
216 v = eval_expr(p, e->param[0]);
227 double low = -1, high = -1, v, low_v = -DBL_MAX, high_v = DBL_MAX;
228 double var0 = p->var[0];
229 double x_max = eval_expr(p, e->param[1]);
230 for(i=-1; i<1024; i++) {
232 p->var[0] = av_reverse[i&255]*x_max/255;
234 p->var[0] = x_max*pow(0.9, i-255);
235 if (i&1) p->var[0] *= -1;
236 if (i&2) p->var[0] += low;
237 else p->var[0] += high;
239 v = eval_expr(p, e->param[0]);
240 if (v<=0 && v>low_v) {
244 if (v>=0 && v<high_v) {
248 if (low>=0 && high>=0){
249 for (j=0; j<1000; j++) {
250 p->var[0] = (low+high)*0.5;
251 if (low == p->var[0] || high == p->var[0])
253 v = eval_expr(p, e->param[0]);
254 if (v<=0) low = p->var[0];
255 if (v>=0) high= p->var[0];
265 return -low_v<high_v ? low : high;
268 double d = eval_expr(p, e->param[0]);
269 double d2 = eval_expr(p, e->param[1]);
271 case e_mod: return e->value * (d - floor((!CONFIG_FTRAPV || d2) ? d / d2 : d * INFINITY) * d2);
272 case e_gcd: return e->value * av_gcd(d,d2);
273 case e_max: return e->value * (d > d2 ? d : d2);
274 case e_min: return e->value * (d < d2 ? d : d2);
275 case e_eq: return e->value * (d == d2 ? 1.0 : 0.0);
276 case e_gt: return e->value * (d > d2 ? 1.0 : 0.0);
277 case e_gte: return e->value * (d >= d2 ? 1.0 : 0.0);
278 case e_lt: return e->value * (d < d2 ? 1.0 : 0.0);
279 case e_lte: return e->value * (d <= d2 ? 1.0 : 0.0);
280 case e_pow: return e->value * pow(d, d2);
281 case e_mul: return e->value * (d * d2);
282 case e_div: return e->value * ((!CONFIG_FTRAPV || d2 ) ? (d / d2) : d * INFINITY);
283 case e_add: return e->value * (d + d2);
284 case e_last:return e->value * d2;
285 case e_st : return e->value * (p->var[av_clip(d, 0, VARS-1)]= d2);
286 case e_hypot:return e->value * (sqrt(d*d + d2*d2));
293 static int parse_expr(AVExpr **e, Parser *p);
295 void av_expr_free(AVExpr *e)
298 av_expr_free(e->param[0]);
299 av_expr_free(e->param[1]);
300 av_expr_free(e->param[2]);
305 static int parse_primary(AVExpr **e, Parser *p)
307 AVExpr *d = av_mallocz(sizeof(AVExpr));
308 char *next = p->s, *s0 = p->s;
312 return AVERROR(ENOMEM);
315 d->value = av_strtod(p->s, &next);
324 /* named constants */
325 for (i=0; p->const_names && p->const_names[i]; i++) {
326 if (strmatch(p->s, p->const_names[i])) {
327 p->s+= strlen(p->const_names[i]);
329 d->a.const_index = i;
334 for (i = 0; i < FF_ARRAY_ELEMS(constants); i++) {
335 if (strmatch(p->s, constants[i].name)) {
336 p->s += strlen(constants[i].name);
338 d->value = constants[i].value;
344 p->s= strchr(p->s, '(');
346 av_log(p, AV_LOG_ERROR, "Undefined constant or missing '(' in '%s'\n", s0);
349 return AVERROR(EINVAL);
352 if (*next == '(') { // special case do-nothing
354 if ((ret = parse_expr(&d, p)) < 0)
356 if (p->s[0] != ')') {
357 av_log(p, AV_LOG_ERROR, "Missing ')' in '%s'\n", s0);
359 return AVERROR(EINVAL);
365 if ((ret = parse_expr(&(d->param[0]), p)) < 0) {
371 parse_expr(&d->param[1], p);
375 parse_expr(&d->param[2], p);
377 if (p->s[0] != ')') {
378 av_log(p, AV_LOG_ERROR, "Missing ')' or too many args in '%s'\n", s0);
380 return AVERROR(EINVAL);
385 if (strmatch(next, "sinh" )) d->a.func0 = sinh;
386 else if (strmatch(next, "cosh" )) d->a.func0 = cosh;
387 else if (strmatch(next, "tanh" )) d->a.func0 = tanh;
388 else if (strmatch(next, "sin" )) d->a.func0 = sin;
389 else if (strmatch(next, "cos" )) d->a.func0 = cos;
390 else if (strmatch(next, "tan" )) d->a.func0 = tan;
391 else if (strmatch(next, "atan" )) d->a.func0 = atan;
392 else if (strmatch(next, "asin" )) d->a.func0 = asin;
393 else if (strmatch(next, "acos" )) d->a.func0 = acos;
394 else if (strmatch(next, "exp" )) d->a.func0 = exp;
395 else if (strmatch(next, "log" )) d->a.func0 = log;
396 else if (strmatch(next, "abs" )) d->a.func0 = fabs;
397 else if (strmatch(next, "time" )) d->a.func0 = etime;
398 else if (strmatch(next, "squish")) d->type = e_squish;
399 else if (strmatch(next, "gauss" )) d->type = e_gauss;
400 else if (strmatch(next, "mod" )) d->type = e_mod;
401 else if (strmatch(next, "max" )) d->type = e_max;
402 else if (strmatch(next, "min" )) d->type = e_min;
403 else if (strmatch(next, "eq" )) d->type = e_eq;
404 else if (strmatch(next, "gte" )) d->type = e_gte;
405 else if (strmatch(next, "gt" )) d->type = e_gt;
406 else if (strmatch(next, "lte" )) d->type = e_lte;
407 else if (strmatch(next, "lt" )) d->type = e_lt;
408 else if (strmatch(next, "ld" )) d->type = e_ld;
409 else if (strmatch(next, "isnan" )) d->type = e_isnan;
410 else if (strmatch(next, "isinf" )) d->type = e_isinf;
411 else if (strmatch(next, "st" )) d->type = e_st;
412 else if (strmatch(next, "while" )) d->type = e_while;
413 else if (strmatch(next, "taylor")) d->type = e_taylor;
414 else if (strmatch(next, "root" )) d->type = e_root;
415 else if (strmatch(next, "floor" )) d->type = e_floor;
416 else if (strmatch(next, "ceil" )) d->type = e_ceil;
417 else if (strmatch(next, "trunc" )) d->type = e_trunc;
418 else if (strmatch(next, "sqrt" )) d->type = e_sqrt;
419 else if (strmatch(next, "not" )) d->type = e_not;
420 else if (strmatch(next, "pow" )) d->type = e_pow;
421 else if (strmatch(next, "print" )) d->type = e_print;
422 else if (strmatch(next, "random")) d->type = e_random;
423 else if (strmatch(next, "hypot" )) d->type = e_hypot;
424 else if (strmatch(next, "gcd" )) d->type = e_gcd;
425 else if (strmatch(next, "if" )) d->type = e_if;
426 else if (strmatch(next, "ifnot" )) d->type = e_ifnot;
428 for (i=0; p->func1_names && p->func1_names[i]; i++) {
429 if (strmatch(next, p->func1_names[i])) {
430 d->a.func1 = p->funcs1[i];
437 for (i=0; p->func2_names && p->func2_names[i]; i++) {
438 if (strmatch(next, p->func2_names[i])) {
439 d->a.func2 = p->funcs2[i];
446 av_log(p, AV_LOG_ERROR, "Unknown function in '%s'\n", s0);
448 return AVERROR(EINVAL);
455 static AVExpr *new_eval_expr(int type, int value, AVExpr *p0, AVExpr *p1)
457 AVExpr *e = av_mallocz(sizeof(AVExpr));
467 static int parse_pow(AVExpr **e, Parser *p, int *sign)
469 *sign= (*p->s == '+') - (*p->s == '-');
471 return parse_primary(e, p);
474 static int parse_dB(AVExpr **e, Parser *p, int *sign)
476 /* do not filter out the negative sign when parsing a dB value.
477 for example, -3dB is not the same as -(3dB) */
480 double av_unused v = strtod(p->s, &next);
481 if (next != p->s && next[0] == 'd' && next[1] == 'B') {
483 return parse_primary(e, p);
486 return parse_pow(e, p, sign);
489 static int parse_factor(AVExpr **e, Parser *p)
491 int sign, sign2, ret;
492 AVExpr *e0, *e1, *e2;
493 if ((ret = parse_dB(&e0, p, &sign)) < 0)
498 if ((ret = parse_dB(&e2, p, &sign2)) < 0) {
502 e0 = new_eval_expr(e_pow, 1, e1, e2);
506 return AVERROR(ENOMEM);
508 if (e0->param[1]) e0->param[1]->value *= (sign2|1);
510 if (e0) e0->value *= (sign|1);
516 static int parse_term(AVExpr **e, Parser *p)
519 AVExpr *e0, *e1, *e2;
520 if ((ret = parse_factor(&e0, p)) < 0)
522 while (p->s[0]=='*' || p->s[0]=='/') {
525 if ((ret = parse_factor(&e2, p)) < 0) {
529 e0 = new_eval_expr(c == '*' ? e_mul : e_div, 1, e1, e2);
533 return AVERROR(ENOMEM);
540 static int parse_subexpr(AVExpr **e, Parser *p)
543 AVExpr *e0, *e1, *e2;
544 if ((ret = parse_term(&e0, p)) < 0)
546 while (*p->s == '+' || *p->s == '-') {
548 if ((ret = parse_term(&e2, p)) < 0) {
552 e0 = new_eval_expr(e_add, 1, e1, e2);
556 return AVERROR(ENOMEM);
564 static int parse_expr(AVExpr **e, Parser *p)
567 AVExpr *e0, *e1, *e2;
568 if (p->stack_index <= 0) //protect against stack overflows
569 return AVERROR(EINVAL);
572 if ((ret = parse_subexpr(&e0, p)) < 0)
574 while (*p->s == ';') {
577 if ((ret = parse_subexpr(&e2, p)) < 0) {
581 e0 = new_eval_expr(e_last, 1, e1, e2);
585 return AVERROR(ENOMEM);
594 static int verify_expr(AVExpr *e)
599 case e_const: return 1;
613 return verify_expr(e->param[0]) && !e->param[1];
615 return verify_expr(e->param[0])
616 && (!e->param[1] || verify_expr(e->param[1]));
620 return verify_expr(e->param[0]) && verify_expr(e->param[1])
621 && (!e->param[2] || verify_expr(e->param[2]));
622 default: return verify_expr(e->param[0]) && verify_expr(e->param[1]) && !e->param[2];
626 int av_expr_parse(AVExpr **expr, const char *s,
627 const char * const *const_names,
628 const char * const *func1_names, double (* const *funcs1)(void *, double),
629 const char * const *func2_names, double (* const *funcs2)(void *, double, double),
630 int log_offset, void *log_ctx)
634 char *w = av_malloc(strlen(s) + 1);
640 return AVERROR(ENOMEM);
643 if (!av_isspace(*s++)) *wp++ = s[-1];
649 p.const_names = const_names;
651 p.func1_names = func1_names;
653 p.func2_names = func2_names;
654 p.log_offset = log_offset;
657 if ((ret = parse_expr(&e, &p)) < 0)
661 av_log(&p, AV_LOG_ERROR, "Invalid chars '%s' at the end of expression '%s'\n", p.s, s0);
662 ret = AVERROR(EINVAL);
665 if (!verify_expr(e)) {
667 ret = AVERROR(EINVAL);
670 e->var= av_mallocz(sizeof(double) *VARS);
677 double av_expr_eval(AVExpr *e, const double *const_values, void *opaque)
682 p.const_values = const_values;
684 return eval_expr(&p, e);
687 int av_expr_parse_and_eval(double *d, const char *s,
688 const char * const *const_names, const double *const_values,
689 const char * const *func1_names, double (* const *funcs1)(void *, double),
690 const char * const *func2_names, double (* const *funcs2)(void *, double, double),
691 void *opaque, int log_offset, void *log_ctx)
694 int ret = av_expr_parse(&e, s, const_names, func1_names, funcs1, func2_names, funcs2, log_offset, log_ctx);
700 *d = av_expr_eval(e, const_values, opaque);
702 return isnan(*d) ? AVERROR(EINVAL) : 0;
708 static const double const_values[] = {
714 static const char *const const_names[] = {
720 int main(int argc, char **argv)
724 const char *const *expr;
725 static const char *const exprs[] = {
731 "1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)",
752 "bar + PI + E + 100f*2 + foo",
753 "13k + 12f - foo(1, 2)",
766 /* compute 1+2+...+N */
767 "st(0, 1); while(lte(ld(0), 100), st(1, ld(1)+ld(0));st(0, ld(0)+1)); ld(1)",
769 "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)",
771 "st(0, 1); while(lte(ld(0),100), st(1, ld(1)+ld(0)); st(0, ld(0)+1))",
800 "ifnot(1, NaN) + if(0, 1)",
804 "taylor(eq(mod(ld(1),4),1)-eq(mod(ld(1),4),3), PI/2, 1)",
805 "root(sin(ld(0))-1, 2)",
806 "root(sin(ld(0))+6+sin(ld(0)/12)-log(ld(0)), 100)",
807 "7000000B*random(0)",
811 "gcd(30,55)*print(min(9,1))",
815 for (expr = exprs; *expr; expr++) {
816 printf("Evaluating '%s'\n", *expr);
817 av_expr_parse_and_eval(&d, *expr,
818 const_names, const_values,
819 NULL, NULL, NULL, NULL, NULL, 0, NULL);
821 printf("'%s' -> nan\n\n", *expr);
823 printf("'%s' -> %f\n\n", *expr, d);
826 av_expr_parse_and_eval(&d, "1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)",
827 const_names, const_values,
828 NULL, NULL, NULL, NULL, NULL, 0, NULL);
829 printf("%f == 12.7\n", d);
830 av_expr_parse_and_eval(&d, "80G/80Gi",
831 const_names, const_values,
832 NULL, NULL, NULL, NULL, NULL, 0, NULL);
833 printf("%f == 0.931322575\n", d);
835 if (argc > 1 && !strcmp(argv[1], "-t")) {
836 for (i = 0; i < 1050; i++) {
838 av_expr_parse_and_eval(&d, "1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)",
839 const_names, const_values,
840 NULL, NULL, NULL, NULL, NULL, 0, NULL);
841 STOP_TIMER("av_expr_parse_and_eval");