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"
36 typedef struct Parser {
40 const double *const_values;
41 const char * const *const_names; // NULL terminated
42 double (* const *funcs1)(void *, double a); // NULL terminated
43 const char * const *func1_names; // NULL terminated
44 double (* const *funcs2)(void *, double a, double b); // NULL terminated
45 const char * const *func2_names; // NULL terminated
53 static const AVClass class = { "Eval", av_default_item_name, NULL, LIBAVUTIL_VERSION_INT, offsetof(Parser,log_offset), offsetof(Parser,log_ctx) };
55 static const int8_t si_prefixes['z' - 'E' + 1] = {
87 double av_strtod(const char *numstr, char **tail)
91 if(numstr[0]=='0' && (numstr[1]|0x20)=='x') {
92 d = strtoul(numstr, &next, 16);
94 d = strtod(numstr, &next);
95 /* if parsing succeeded, check for and interpret postfixes */
97 if (next[0] == 'd' && next[1] == 'B') {
98 /* treat dB as decibels instead of decibytes */
101 } else if (*next >= 'E' && *next <= 'z') {
102 int e= si_prefixes[*next - 'E'];
104 if (next[1] == 'i') {
119 /* if requested, fill in tail with the position after the last parsed
126 #define IS_IDENTIFIER_CHAR(c) ((c) - '0' <= 9U || (c) - 'a' <= 25U || (c) - 'A' <= 25U || (c) == '_')
128 static int strmatch(const char *s, const char *prefix)
131 for (i=0; prefix[i]; i++) {
132 if (prefix[i] != s[i]) return 0;
134 /* return 1 only if the s identifier is terminated */
135 return !IS_IDENTIFIER_CHAR(s[i]);
140 e_value, e_const, e_func0, e_func1, e_func2,
141 e_squish, e_gauss, e_ld, e_isnan, e_isinf,
142 e_mod, e_max, e_min, e_eq, e_gt, e_gte,
143 e_pow, e_mul, e_div, e_add,
144 e_last, e_st, e_while, e_taylor, e_root, e_floor, e_ceil, e_trunc,
145 e_sqrt, e_not, e_random, e_hypot, e_gcd,
148 double value; // is sign in other types
151 double (*func0)(double);
152 double (*func1)(void *, double);
153 double (*func2)(void *, double, double);
155 struct AVExpr *param[3];
159 static double eval_expr(Parser *p, AVExpr *e)
162 case e_value: return e->value;
163 case e_const: return e->value * p->const_values[e->a.const_index];
164 case e_func0: return e->value * e->a.func0(eval_expr(p, e->param[0]));
165 case e_func1: return e->value * e->a.func1(p->opaque, eval_expr(p, e->param[0]));
166 case e_func2: return e->value * e->a.func2(p->opaque, eval_expr(p, e->param[0]), eval_expr(p, e->param[1]));
167 case e_squish: return 1/(1+exp(4*eval_expr(p, e->param[0])));
168 case e_gauss: { double d = eval_expr(p, e->param[0]); return exp(-d*d/2)/sqrt(2*M_PI); }
169 case e_ld: return e->value * p->var[av_clip(eval_expr(p, e->param[0]), 0, VARS-1)];
170 case e_isnan: return e->value * !!isnan(eval_expr(p, e->param[0]));
171 case e_isinf: return e->value * !!isinf(eval_expr(p, e->param[0]));
172 case e_floor: return e->value * floor(eval_expr(p, e->param[0]));
173 case e_ceil : return e->value * ceil (eval_expr(p, e->param[0]));
174 case e_trunc: return e->value * trunc(eval_expr(p, e->param[0]));
175 case e_sqrt: return e->value * sqrt (eval_expr(p, e->param[0]));
176 case e_not: return e->value * (eval_expr(p, e->param[0]) == 0);
177 case e_if: return e->value * ( eval_expr(p, e->param[0]) ? eval_expr(p, e->param[1]) : 0);
178 case e_ifnot: return e->value * (!eval_expr(p, e->param[0]) ? eval_expr(p, e->param[1]) : 0);
180 int idx= av_clip(eval_expr(p, e->param[0]), 0, VARS-1);
181 uint64_t r= isnan(p->var[idx]) ? 0 : p->var[idx];
182 r= r*1664525+1013904223;
184 return e->value * (r * (1.0/UINT64_MAX));
188 while (eval_expr(p, e->param[0]))
189 d=eval_expr(p, e->param[1]);
193 double t = 1, d = 0, v;
194 double x = eval_expr(p, e->param[1]);
195 int id = e->param[2] ? av_clip(eval_expr(p, e->param[2]), 0, VARS-1) : 0;
197 double var0 = p->var[id];
198 for(i=0; i<1000; i++) {
201 v = eval_expr(p, e->param[0]);
212 double low = -1, high = -1, v, low_v = -DBL_MAX, high_v = DBL_MAX;
213 double var0 = p->var[0];
214 double x_max = eval_expr(p, e->param[1]);
215 for(i=-1; i<1024; i++) {
217 p->var[0] = av_reverse[i&255]*x_max/255;
219 p->var[0] = x_max*pow(0.9, i-255);
220 if (i&1) p->var[0] *= -1;
221 if (i&2) p->var[0] += low;
222 else p->var[0] += high;
224 v = eval_expr(p, e->param[0]);
225 if (v<=0 && v>low_v) {
229 if (v>=0 && v<high_v) {
233 if (low>=0 && high>=0){
234 for (j=0; j<1000; j++) {
235 p->var[0] = (low+high)*0.5;
236 if (low == p->var[0] || high == p->var[0])
238 v = eval_expr(p, e->param[0]);
239 if (v<=0) low = p->var[0];
240 if (v>=0) high= p->var[0];
250 return -low_v<high_v ? low : high;
253 double d = eval_expr(p, e->param[0]);
254 double d2 = eval_expr(p, e->param[1]);
256 case e_mod: return e->value * (d - floor(d/d2)*d2);
257 case e_gcd: return e->value * av_gcd(d,d2);
258 case e_max: return e->value * (d > d2 ? d : d2);
259 case e_min: return e->value * (d < d2 ? d : d2);
260 case e_eq: return e->value * (d == d2 ? 1.0 : 0.0);
261 case e_gt: return e->value * (d > d2 ? 1.0 : 0.0);
262 case e_gte: return e->value * (d >= d2 ? 1.0 : 0.0);
263 case e_pow: return e->value * pow(d, d2);
264 case e_mul: return e->value * (d * d2);
265 case e_div: return e->value * ((!CONFIG_FTRAPV || d2 ) ? (d / d2) : d * INFINITY);
266 case e_add: return e->value * (d + d2);
267 case e_last:return e->value * d2;
268 case e_st : return e->value * (p->var[av_clip(d, 0, VARS-1)]= d2);
269 case e_hypot:return e->value * (sqrt(d*d + d2*d2));
276 static int parse_expr(AVExpr **e, Parser *p);
278 void av_expr_free(AVExpr *e)
281 av_expr_free(e->param[0]);
282 av_expr_free(e->param[1]);
283 av_expr_free(e->param[2]);
288 static int parse_primary(AVExpr **e, Parser *p)
290 AVExpr *d = av_mallocz(sizeof(AVExpr));
291 char *next = p->s, *s0 = p->s;
295 return AVERROR(ENOMEM);
298 d->value = av_strtod(p->s, &next);
307 /* named constants */
308 for (i=0; p->const_names && p->const_names[i]; i++) {
309 if (strmatch(p->s, p->const_names[i])) {
310 p->s+= strlen(p->const_names[i]);
312 d->a.const_index = i;
317 for (i = 0; i < FF_ARRAY_ELEMS(constants); i++) {
318 if (strmatch(p->s, constants[i].name)) {
319 p->s += strlen(constants[i].name);
321 d->value = constants[i].value;
327 p->s= strchr(p->s, '(');
329 av_log(p, AV_LOG_ERROR, "Undefined constant or missing '(' in '%s'\n", s0);
332 return AVERROR(EINVAL);
335 if (*next == '(') { // special case do-nothing
337 if ((ret = parse_expr(&d, p)) < 0)
339 if (p->s[0] != ')') {
340 av_log(p, AV_LOG_ERROR, "Missing ')' in '%s'\n", s0);
342 return AVERROR(EINVAL);
348 if ((ret = parse_expr(&(d->param[0]), p)) < 0) {
354 parse_expr(&d->param[1], p);
358 parse_expr(&d->param[2], p);
360 if (p->s[0] != ')') {
361 av_log(p, AV_LOG_ERROR, "Missing ')' or too many args in '%s'\n", s0);
363 return AVERROR(EINVAL);
368 if (strmatch(next, "sinh" )) d->a.func0 = sinh;
369 else if (strmatch(next, "cosh" )) d->a.func0 = cosh;
370 else if (strmatch(next, "tanh" )) d->a.func0 = tanh;
371 else if (strmatch(next, "sin" )) d->a.func0 = sin;
372 else if (strmatch(next, "cos" )) d->a.func0 = cos;
373 else if (strmatch(next, "tan" )) d->a.func0 = tan;
374 else if (strmatch(next, "atan" )) d->a.func0 = atan;
375 else if (strmatch(next, "asin" )) d->a.func0 = asin;
376 else if (strmatch(next, "acos" )) d->a.func0 = acos;
377 else if (strmatch(next, "exp" )) d->a.func0 = exp;
378 else if (strmatch(next, "log" )) d->a.func0 = log;
379 else if (strmatch(next, "abs" )) d->a.func0 = fabs;
380 else if (strmatch(next, "squish")) d->type = e_squish;
381 else if (strmatch(next, "gauss" )) d->type = e_gauss;
382 else if (strmatch(next, "mod" )) d->type = e_mod;
383 else if (strmatch(next, "max" )) d->type = e_max;
384 else if (strmatch(next, "min" )) d->type = e_min;
385 else if (strmatch(next, "eq" )) d->type = e_eq;
386 else if (strmatch(next, "gte" )) d->type = e_gte;
387 else if (strmatch(next, "gt" )) d->type = e_gt;
388 else if (strmatch(next, "lte" )) { AVExpr *tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gte; }
389 else if (strmatch(next, "lt" )) { AVExpr *tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gt; }
390 else if (strmatch(next, "ld" )) d->type = e_ld;
391 else if (strmatch(next, "isnan" )) d->type = e_isnan;
392 else if (strmatch(next, "isinf" )) d->type = e_isinf;
393 else if (strmatch(next, "st" )) d->type = e_st;
394 else if (strmatch(next, "while" )) d->type = e_while;
395 else if (strmatch(next, "taylor")) d->type = e_taylor;
396 else if (strmatch(next, "root" )) d->type = e_root;
397 else if (strmatch(next, "floor" )) d->type = e_floor;
398 else if (strmatch(next, "ceil" )) d->type = e_ceil;
399 else if (strmatch(next, "trunc" )) d->type = e_trunc;
400 else if (strmatch(next, "sqrt" )) d->type = e_sqrt;
401 else if (strmatch(next, "not" )) d->type = e_not;
402 else if (strmatch(next, "pow" )) d->type = e_pow;
403 else if (strmatch(next, "random")) d->type = e_random;
404 else if (strmatch(next, "hypot" )) d->type = e_hypot;
405 else if (strmatch(next, "gcd" )) d->type = e_gcd;
406 else if (strmatch(next, "if" )) d->type = e_if;
407 else if (strmatch(next, "ifnot" )) d->type = e_ifnot;
409 for (i=0; p->func1_names && p->func1_names[i]; i++) {
410 if (strmatch(next, p->func1_names[i])) {
411 d->a.func1 = p->funcs1[i];
418 for (i=0; p->func2_names && p->func2_names[i]; i++) {
419 if (strmatch(next, p->func2_names[i])) {
420 d->a.func2 = p->funcs2[i];
427 av_log(p, AV_LOG_ERROR, "Unknown function in '%s'\n", s0);
429 return AVERROR(EINVAL);
436 static AVExpr *new_eval_expr(int type, int value, AVExpr *p0, AVExpr *p1)
438 AVExpr *e = av_mallocz(sizeof(AVExpr));
448 static int parse_pow(AVExpr **e, Parser *p, int *sign)
450 *sign= (*p->s == '+') - (*p->s == '-');
452 return parse_primary(e, p);
455 static int parse_dB(AVExpr **e, Parser *p, int *sign)
457 /* do not filter out the negative sign when parsing a dB value.
458 for example, -3dB is not the same as -(3dB) */
462 if (next != p->s && next[0] == 'd' && next[1] == 'B') {
464 return parse_primary(e, p);
467 return parse_pow(e, p, sign);
470 static int parse_factor(AVExpr **e, Parser *p)
472 int sign, sign2, ret;
473 AVExpr *e0, *e1, *e2;
474 if ((ret = parse_dB(&e0, p, &sign)) < 0)
479 if ((ret = parse_dB(&e2, p, &sign2)) < 0) {
483 e0 = new_eval_expr(e_pow, 1, e1, e2);
487 return AVERROR(ENOMEM);
489 if (e0->param[1]) e0->param[1]->value *= (sign2|1);
491 if (e0) e0->value *= (sign|1);
497 static int parse_term(AVExpr **e, Parser *p)
500 AVExpr *e0, *e1, *e2;
501 if ((ret = parse_factor(&e0, p)) < 0)
503 while (p->s[0]=='*' || p->s[0]=='/') {
506 if ((ret = parse_factor(&e2, p)) < 0) {
510 e0 = new_eval_expr(c == '*' ? e_mul : e_div, 1, e1, e2);
514 return AVERROR(ENOMEM);
521 static int parse_subexpr(AVExpr **e, Parser *p)
524 AVExpr *e0, *e1, *e2;
525 if ((ret = parse_term(&e0, p)) < 0)
527 while (*p->s == '+' || *p->s == '-') {
529 if ((ret = parse_term(&e2, p)) < 0) {
533 e0 = new_eval_expr(e_add, 1, e1, e2);
537 return AVERROR(ENOMEM);
545 static int parse_expr(AVExpr **e, Parser *p)
548 AVExpr *e0, *e1, *e2;
549 if (p->stack_index <= 0) //protect against stack overflows
550 return AVERROR(EINVAL);
553 if ((ret = parse_subexpr(&e0, p)) < 0)
555 while (*p->s == ';') {
558 if ((ret = parse_subexpr(&e2, p)) < 0) {
562 e0 = new_eval_expr(e_last, 1, e1, e2);
566 return AVERROR(ENOMEM);
575 static int verify_expr(AVExpr *e)
580 case e_const: return 1;
594 return verify_expr(e->param[0]) && !e->param[1];
596 return verify_expr(e->param[0]) && verify_expr(e->param[1])
597 && (!e->param[2] || verify_expr(e->param[2]));
598 default: return verify_expr(e->param[0]) && verify_expr(e->param[1]) && !e->param[2];
602 int av_expr_parse(AVExpr **expr, const char *s,
603 const char * const *const_names,
604 const char * const *func1_names, double (* const *funcs1)(void *, double),
605 const char * const *func2_names, double (* const *funcs2)(void *, double, double),
606 int log_offset, void *log_ctx)
610 char *w = av_malloc(strlen(s) + 1);
616 return AVERROR(ENOMEM);
619 if (!isspace(*s++)) *wp++ = s[-1];
625 p.const_names = const_names;
627 p.func1_names = func1_names;
629 p.func2_names = func2_names;
630 p.log_offset = log_offset;
633 if ((ret = parse_expr(&e, &p)) < 0)
637 av_log(&p, AV_LOG_ERROR, "Invalid chars '%s' at the end of expression '%s'\n", p.s, s0);
638 ret = AVERROR(EINVAL);
641 if (!verify_expr(e)) {
643 ret = AVERROR(EINVAL);
646 e->var= av_mallocz(sizeof(double) *VARS);
653 double av_expr_eval(AVExpr *e, const double *const_values, void *opaque)
658 p.const_values = const_values;
660 return eval_expr(&p, e);
663 int av_expr_parse_and_eval(double *d, const char *s,
664 const char * const *const_names, const double *const_values,
665 const char * const *func1_names, double (* const *funcs1)(void *, double),
666 const char * const *func2_names, double (* const *funcs2)(void *, double, double),
667 void *opaque, int log_offset, void *log_ctx)
670 int ret = av_expr_parse(&e, s, const_names, func1_names, funcs1, func2_names, funcs2, log_offset, log_ctx);
676 *d = av_expr_eval(e, const_values, opaque);
678 return isnan(*d) ? AVERROR(EINVAL) : 0;
684 static const double const_values[] = {
690 static const char *const const_names[] = {
696 int main(int argc, char **argv)
700 const char *const *expr;
701 static const char *const exprs[] = {
707 "1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)",
728 "bar + PI + E + 100f*2 + foo",
729 "13k + 12f - foo(1, 2)",
742 /* compute 1+2+...+N */
743 "st(0, 1); while(lte(ld(0), 100), st(1, ld(1)+ld(0));st(0, ld(0)+1)); ld(1)",
745 "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)",
747 "st(0, 1); while(lte(ld(0),100), st(1, ld(1)+ld(0)); st(0, ld(0)+1))",
774 "ifnot(1, NaN) + if(0, 1)",
776 "taylor(eq(mod(ld(1),4),1)-eq(mod(ld(1),4),3), PI/2, 1)",
777 "root(sin(ld(0))-1, 2)",
778 "root(sin(ld(0))+6+sin(ld(0)/12)-log(ld(0)), 100)",
779 "7000000B*random(0)",
783 "gcd(30,55)*min(9,1)",
787 for (expr = exprs; *expr; expr++) {
788 printf("Evaluating '%s'\n", *expr);
789 av_expr_parse_and_eval(&d, *expr,
790 const_names, const_values,
791 NULL, NULL, NULL, NULL, NULL, 0, NULL);
793 printf("'%s' -> nan\n\n", *expr);
795 printf("'%s' -> %f\n\n", *expr, d);
798 av_expr_parse_and_eval(&d, "1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)",
799 const_names, const_values,
800 NULL, NULL, NULL, NULL, NULL, 0, NULL);
801 printf("%f == 12.7\n", d);
802 av_expr_parse_and_eval(&d, "80G/80Gi",
803 const_names, const_values,
804 NULL, NULL, NULL, NULL, NULL, 0, NULL);
805 printf("%f == 0.931322575\n", d);
807 if (argc > 1 && !strcmp(argv[1], "-t")) {
808 for (i = 0; i < 1050; i++) {
810 av_expr_parse_and_eval(&d, "1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)",
811 const_names, const_values,
812 NULL, NULL, NULL, NULL, NULL, 0, NULL);
813 STOP_TIMER("av_expr_parse_and_eval");