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) };
64 } si_prefixes['z' - 'E' + 1] = {
65 ['y'-'E']= { 8.271806125530276749e-25, 1e-24, -24 },
66 ['z'-'E']= { 8.4703294725430034e-22, 1e-21, -21 },
67 ['a'-'E']= { 8.6736173798840355e-19, 1e-18, -18 },
68 ['f'-'E']= { 8.8817841970012523e-16, 1e-15, -15 },
69 ['p'-'E']= { 9.0949470177292824e-13, 1e-12, -12 },
70 ['n'-'E']= { 9.3132257461547852e-10, 1e-9, -9 },
71 ['u'-'E']= { 9.5367431640625e-7, 1e-6, -6 },
72 ['m'-'E']= { 9.765625e-4, 1e-3, -3 },
73 ['c'-'E']= { 9.8431332023036951e-3, 1e-2, -2 },
74 ['d'-'E']= { 9.921256574801246e-2, 1e-1, -1 },
75 ['h'-'E']= { 1.0159366732596479e2, 1e2, 2 },
76 ['k'-'E']= { 1.024e3, 1e3, 3 },
77 ['K'-'E']= { 1.024e3, 1e3, 3 },
78 ['M'-'E']= { 1.048576e6, 1e6, 6 },
79 ['G'-'E']= { 1.073741824e9, 1e9, 9 },
80 ['T'-'E']= { 1.099511627776e12, 1e12, 12 },
81 ['P'-'E']= { 1.125899906842624e15, 1e15, 15 },
82 ['E'-'E']= { 1.152921504606847e18, 1e18, 18 },
83 ['Z'-'E']= { 1.1805916207174113e21, 1e21, 21 },
84 ['Y'-'E']= { 1.2089258196146292e24, 1e24, 24 },
94 { "QP2LAMBDA", FF_QP2LAMBDA },
97 double av_strtod(const char *numstr, char **tail)
101 if(numstr[0]=='0' && (numstr[1]|0x20)=='x') {
102 d = strtoul(numstr, &next, 16);
104 d = strtod(numstr, &next);
105 /* if parsing succeeded, check for and interpret postfixes */
107 if (next[0] == 'd' && next[1] == 'B') {
108 /* treat dB as decibels instead of decibytes */
109 d = ff_exp10(d / 20);
111 } else if (*next >= 'E' && *next <= 'z') {
112 int e= si_prefixes[*next - 'E'].exp;
114 if (next[1] == 'i') {
115 d*= si_prefixes[*next - 'E'].bin_val;
118 d*= si_prefixes[*next - 'E'].dec_val;
129 /* if requested, fill in tail with the position after the last parsed
136 #define IS_IDENTIFIER_CHAR(c) ((c) - '0' <= 9U || (c) - 'a' <= 25U || (c) - 'A' <= 25U || (c) == '_')
138 static int strmatch(const char *s, const char *prefix)
141 for (i=0; prefix[i]; i++) {
142 if (prefix[i] != s[i]) return 0;
144 /* return 1 only if the s identifier is terminated */
145 return !IS_IDENTIFIER_CHAR(s[i]);
150 e_value, e_const, e_func0, e_func1, e_func2,
151 e_squish, e_gauss, e_ld, e_isnan, e_isinf,
152 e_mod, e_max, e_min, e_eq, e_gt, e_gte, e_lte, e_lt,
153 e_pow, e_mul, e_div, e_add,
154 e_last, e_st, e_while, e_taylor, e_root, e_floor, e_ceil, e_trunc,
155 e_sqrt, e_not, e_random, e_hypot, e_gcd,
156 e_if, e_ifnot, e_print, e_bitand, e_bitor, e_between, e_clip
158 double value; // is sign in other types
161 double (*func0)(double);
162 double (*func1)(void *, double);
163 double (*func2)(void *, double, double);
165 struct AVExpr *param[3];
169 static double etime(double v)
171 return av_gettime() * 0.000001;
174 static double eval_expr(Parser *p, AVExpr *e)
177 case e_value: return e->value;
178 case e_const: return e->value * p->const_values[e->a.const_index];
179 case e_func0: return e->value * e->a.func0(eval_expr(p, e->param[0]));
180 case e_func1: return e->value * e->a.func1(p->opaque, eval_expr(p, e->param[0]));
181 case e_func2: return e->value * e->a.func2(p->opaque, eval_expr(p, e->param[0]), eval_expr(p, e->param[1]));
182 case e_squish: return 1/(1+exp(4*eval_expr(p, e->param[0])));
183 case e_gauss: { double d = eval_expr(p, e->param[0]); return exp(-d*d/2)/sqrt(2*M_PI); }
184 case e_ld: return e->value * p->var[av_clip(eval_expr(p, e->param[0]), 0, VARS-1)];
185 case e_isnan: return e->value * !!isnan(eval_expr(p, e->param[0]));
186 case e_isinf: return e->value * !!isinf(eval_expr(p, e->param[0]));
187 case e_floor: return e->value * floor(eval_expr(p, e->param[0]));
188 case e_ceil : return e->value * ceil (eval_expr(p, e->param[0]));
189 case e_trunc: return e->value * trunc(eval_expr(p, e->param[0]));
190 case e_sqrt: return e->value * sqrt (eval_expr(p, e->param[0]));
191 case e_not: return e->value * (eval_expr(p, e->param[0]) == 0);
192 case e_if: return e->value * (eval_expr(p, e->param[0]) ? eval_expr(p, e->param[1]) :
193 e->param[2] ? eval_expr(p, e->param[2]) : 0);
194 case e_ifnot: return e->value * (!eval_expr(p, e->param[0]) ? eval_expr(p, e->param[1]) :
195 e->param[2] ? eval_expr(p, e->param[2]) : 0);
197 double x = eval_expr(p, e->param[0]);
198 double min = eval_expr(p, e->param[1]), max = eval_expr(p, e->param[2]);
199 if (isnan(min) || isnan(max) || isnan(x) || min > max)
201 return e->value * av_clipd(eval_expr(p, e->param[0]), min, max);
204 double d = eval_expr(p, e->param[0]);
205 return e->value * (d >= eval_expr(p, e->param[1]) &&
206 d <= eval_expr(p, e->param[2]));
209 double x = eval_expr(p, e->param[0]);
210 int level = e->param[1] ? av_clip(eval_expr(p, e->param[1]), INT_MIN, INT_MAX) : AV_LOG_INFO;
211 av_log(p, level, "%f\n", x);
215 int idx= av_clip(eval_expr(p, e->param[0]), 0, VARS-1);
216 uint64_t r= isnan(p->var[idx]) ? 0 : p->var[idx];
217 r= r*1664525+1013904223;
219 return e->value * (r * (1.0/UINT64_MAX));
223 while (eval_expr(p, e->param[0]))
224 d=eval_expr(p, e->param[1]);
228 double t = 1, d = 0, v;
229 double x = eval_expr(p, e->param[1]);
230 int id = e->param[2] ? av_clip(eval_expr(p, e->param[2]), 0, VARS-1) : 0;
232 double var0 = p->var[id];
233 for(i=0; i<1000; i++) {
236 v = eval_expr(p, e->param[0]);
247 double low = -1, high = -1, v, low_v = -DBL_MAX, high_v = DBL_MAX;
248 double var0 = p->var[0];
249 double x_max = eval_expr(p, e->param[1]);
250 for(i=-1; i<1024; i++) {
252 p->var[0] = ff_reverse[i&255]*x_max/255;
254 p->var[0] = x_max*pow(0.9, i-255);
255 if (i&1) p->var[0] *= -1;
256 if (i&2) p->var[0] += low;
257 else p->var[0] += high;
259 v = eval_expr(p, e->param[0]);
260 if (v<=0 && v>low_v) {
264 if (v>=0 && v<high_v) {
268 if (low>=0 && high>=0){
269 for (j=0; j<1000; j++) {
270 p->var[0] = (low+high)*0.5;
271 if (low == p->var[0] || high == p->var[0])
273 v = eval_expr(p, e->param[0]);
274 if (v<=0) low = p->var[0];
275 if (v>=0) high= p->var[0];
285 return -low_v<high_v ? low : high;
288 double d = eval_expr(p, e->param[0]);
289 double d2 = eval_expr(p, e->param[1]);
291 case e_mod: return e->value * (d - floor((!CONFIG_FTRAPV || d2) ? d / d2 : d * INFINITY) * d2);
292 case e_gcd: return e->value * av_gcd(d,d2);
293 case e_max: return e->value * (d > d2 ? d : d2);
294 case e_min: return e->value * (d < d2 ? d : d2);
295 case e_eq: return e->value * (d == d2 ? 1.0 : 0.0);
296 case e_gt: return e->value * (d > d2 ? 1.0 : 0.0);
297 case e_gte: return e->value * (d >= d2 ? 1.0 : 0.0);
298 case e_lt: return e->value * (d < d2 ? 1.0 : 0.0);
299 case e_lte: return e->value * (d <= d2 ? 1.0 : 0.0);
300 case e_pow: return e->value * pow(d, d2);
301 case e_mul: return e->value * (d * d2);
302 case e_div: return e->value * ((!CONFIG_FTRAPV || d2 ) ? (d / d2) : d * INFINITY);
303 case e_add: return e->value * (d + d2);
304 case e_last:return e->value * d2;
305 case e_st : return e->value * (p->var[av_clip(d, 0, VARS-1)]= d2);
306 case e_hypot:return e->value * hypot(d, d2);
307 case e_bitand: return isnan(d) || isnan(d2) ? NAN : e->value * ((long int)d & (long int)d2);
308 case e_bitor: return isnan(d) || isnan(d2) ? NAN : e->value * ((long int)d | (long int)d2);
315 static int parse_expr(AVExpr **e, Parser *p);
317 void av_expr_free(AVExpr *e)
320 av_expr_free(e->param[0]);
321 av_expr_free(e->param[1]);
322 av_expr_free(e->param[2]);
327 static int parse_primary(AVExpr **e, Parser *p)
329 AVExpr *d = av_mallocz(sizeof(AVExpr));
330 char *next = p->s, *s0 = p->s;
334 return AVERROR(ENOMEM);
337 d->value = av_strtod(p->s, &next);
346 /* named constants */
347 for (i=0; p->const_names && p->const_names[i]; i++) {
348 if (strmatch(p->s, p->const_names[i])) {
349 p->s+= strlen(p->const_names[i]);
351 d->a.const_index = i;
356 for (i = 0; i < FF_ARRAY_ELEMS(constants); i++) {
357 if (strmatch(p->s, constants[i].name)) {
358 p->s += strlen(constants[i].name);
360 d->value = constants[i].value;
366 p->s= strchr(p->s, '(');
368 av_log(p, AV_LOG_ERROR, "Undefined constant or missing '(' in '%s'\n", s0);
371 return AVERROR(EINVAL);
374 if (*next == '(') { // special case do-nothing
376 if ((ret = parse_expr(&d, p)) < 0)
378 if (p->s[0] != ')') {
379 av_log(p, AV_LOG_ERROR, "Missing ')' in '%s'\n", s0);
381 return AVERROR(EINVAL);
387 if ((ret = parse_expr(&(d->param[0]), p)) < 0) {
393 parse_expr(&d->param[1], p);
397 parse_expr(&d->param[2], p);
399 if (p->s[0] != ')') {
400 av_log(p, AV_LOG_ERROR, "Missing ')' or too many args in '%s'\n", s0);
402 return AVERROR(EINVAL);
407 if (strmatch(next, "sinh" )) d->a.func0 = sinh;
408 else if (strmatch(next, "cosh" )) d->a.func0 = cosh;
409 else if (strmatch(next, "tanh" )) d->a.func0 = tanh;
410 else if (strmatch(next, "sin" )) d->a.func0 = sin;
411 else if (strmatch(next, "cos" )) d->a.func0 = cos;
412 else if (strmatch(next, "tan" )) d->a.func0 = tan;
413 else if (strmatch(next, "atan" )) d->a.func0 = atan;
414 else if (strmatch(next, "asin" )) d->a.func0 = asin;
415 else if (strmatch(next, "acos" )) d->a.func0 = acos;
416 else if (strmatch(next, "exp" )) d->a.func0 = exp;
417 else if (strmatch(next, "log" )) d->a.func0 = log;
418 else if (strmatch(next, "abs" )) d->a.func0 = fabs;
419 else if (strmatch(next, "time" )) d->a.func0 = etime;
420 else if (strmatch(next, "squish")) d->type = e_squish;
421 else if (strmatch(next, "gauss" )) d->type = e_gauss;
422 else if (strmatch(next, "mod" )) d->type = e_mod;
423 else if (strmatch(next, "max" )) d->type = e_max;
424 else if (strmatch(next, "min" )) d->type = e_min;
425 else if (strmatch(next, "eq" )) d->type = e_eq;
426 else if (strmatch(next, "gte" )) d->type = e_gte;
427 else if (strmatch(next, "gt" )) d->type = e_gt;
428 else if (strmatch(next, "lte" )) d->type = e_lte;
429 else if (strmatch(next, "lt" )) d->type = e_lt;
430 else if (strmatch(next, "ld" )) d->type = e_ld;
431 else if (strmatch(next, "isnan" )) d->type = e_isnan;
432 else if (strmatch(next, "isinf" )) d->type = e_isinf;
433 else if (strmatch(next, "st" )) d->type = e_st;
434 else if (strmatch(next, "while" )) d->type = e_while;
435 else if (strmatch(next, "taylor")) d->type = e_taylor;
436 else if (strmatch(next, "root" )) d->type = e_root;
437 else if (strmatch(next, "floor" )) d->type = e_floor;
438 else if (strmatch(next, "ceil" )) d->type = e_ceil;
439 else if (strmatch(next, "trunc" )) d->type = e_trunc;
440 else if (strmatch(next, "sqrt" )) d->type = e_sqrt;
441 else if (strmatch(next, "not" )) d->type = e_not;
442 else if (strmatch(next, "pow" )) d->type = e_pow;
443 else if (strmatch(next, "print" )) d->type = e_print;
444 else if (strmatch(next, "random")) d->type = e_random;
445 else if (strmatch(next, "hypot" )) d->type = e_hypot;
446 else if (strmatch(next, "gcd" )) d->type = e_gcd;
447 else if (strmatch(next, "if" )) d->type = e_if;
448 else if (strmatch(next, "ifnot" )) d->type = e_ifnot;
449 else if (strmatch(next, "bitand")) d->type = e_bitand;
450 else if (strmatch(next, "bitor" )) d->type = e_bitor;
451 else if (strmatch(next, "between"))d->type = e_between;
452 else if (strmatch(next, "clip" )) d->type = e_clip;
454 for (i=0; p->func1_names && p->func1_names[i]; i++) {
455 if (strmatch(next, p->func1_names[i])) {
456 d->a.func1 = p->funcs1[i];
463 for (i=0; p->func2_names && p->func2_names[i]; i++) {
464 if (strmatch(next, p->func2_names[i])) {
465 d->a.func2 = p->funcs2[i];
472 av_log(p, AV_LOG_ERROR, "Unknown function in '%s'\n", s0);
474 return AVERROR(EINVAL);
481 static AVExpr *make_eval_expr(int type, int value, AVExpr *p0, AVExpr *p1)
483 AVExpr *e = av_mallocz(sizeof(AVExpr));
493 static int parse_pow(AVExpr **e, Parser *p, int *sign)
495 *sign= (*p->s == '+') - (*p->s == '-');
497 return parse_primary(e, p);
500 static int parse_dB(AVExpr **e, Parser *p, int *sign)
502 /* do not filter out the negative sign when parsing a dB value.
503 for example, -3dB is not the same as -(3dB) */
506 double av_unused ignored = strtod(p->s, &next);
507 if (next != p->s && next[0] == 'd' && next[1] == 'B') {
509 return parse_primary(e, p);
512 return parse_pow(e, p, sign);
515 static int parse_factor(AVExpr **e, Parser *p)
517 int sign, sign2, ret;
518 AVExpr *e0, *e1, *e2;
519 if ((ret = parse_dB(&e0, p, &sign)) < 0)
524 if ((ret = parse_dB(&e2, p, &sign2)) < 0) {
528 e0 = make_eval_expr(e_pow, 1, e1, e2);
532 return AVERROR(ENOMEM);
534 if (e0->param[1]) e0->param[1]->value *= (sign2|1);
536 if (e0) e0->value *= (sign|1);
542 static int parse_term(AVExpr **e, Parser *p)
545 AVExpr *e0, *e1, *e2;
546 if ((ret = parse_factor(&e0, p)) < 0)
548 while (p->s[0]=='*' || p->s[0]=='/') {
551 if ((ret = parse_factor(&e2, p)) < 0) {
555 e0 = make_eval_expr(c == '*' ? e_mul : e_div, 1, e1, e2);
559 return AVERROR(ENOMEM);
566 static int parse_subexpr(AVExpr **e, Parser *p)
569 AVExpr *e0, *e1, *e2;
570 if ((ret = parse_term(&e0, p)) < 0)
572 while (*p->s == '+' || *p->s == '-') {
574 if ((ret = parse_term(&e2, p)) < 0) {
578 e0 = make_eval_expr(e_add, 1, e1, e2);
582 return AVERROR(ENOMEM);
590 static int parse_expr(AVExpr **e, Parser *p)
593 AVExpr *e0, *e1, *e2;
594 if (p->stack_index <= 0) //protect against stack overflows
595 return AVERROR(EINVAL);
598 if ((ret = parse_subexpr(&e0, p)) < 0)
600 while (*p->s == ';') {
603 if ((ret = parse_subexpr(&e2, p)) < 0) {
607 e0 = make_eval_expr(e_last, 1, e1, e2);
611 return AVERROR(ENOMEM);
620 static int verify_expr(AVExpr *e)
625 case e_const: return 1;
639 return verify_expr(e->param[0]) && !e->param[1];
641 return verify_expr(e->param[0])
642 && (!e->param[1] || verify_expr(e->param[1]));
646 return verify_expr(e->param[0]) && verify_expr(e->param[1])
647 && (!e->param[2] || verify_expr(e->param[2]));
650 return verify_expr(e->param[0]) &&
651 verify_expr(e->param[1]) &&
652 verify_expr(e->param[2]);
653 default: return verify_expr(e->param[0]) && verify_expr(e->param[1]) && !e->param[2];
657 int av_expr_parse(AVExpr **expr, const char *s,
658 const char * const *const_names,
659 const char * const *func1_names, double (* const *funcs1)(void *, double),
660 const char * const *func2_names, double (* const *funcs2)(void *, double, double),
661 int log_offset, void *log_ctx)
665 char *w = av_malloc(strlen(s) + 1);
671 return AVERROR(ENOMEM);
674 if (!av_isspace(*s++)) *wp++ = s[-1];
677 p.class = &eval_class;
680 p.const_names = const_names;
682 p.func1_names = func1_names;
684 p.func2_names = func2_names;
685 p.log_offset = log_offset;
688 if ((ret = parse_expr(&e, &p)) < 0)
691 av_log(&p, AV_LOG_ERROR, "Invalid chars '%s' at the end of expression '%s'\n", p.s, s0);
692 ret = AVERROR(EINVAL);
695 if (!verify_expr(e)) {
696 ret = AVERROR(EINVAL);
699 e->var= av_mallocz(sizeof(double) *VARS);
701 ret = AVERROR(ENOMEM);
712 double av_expr_eval(AVExpr *e, const double *const_values, void *opaque)
717 p.const_values = const_values;
719 return eval_expr(&p, e);
722 int av_expr_parse_and_eval(double *d, const char *s,
723 const char * const *const_names, const double *const_values,
724 const char * const *func1_names, double (* const *funcs1)(void *, double),
725 const char * const *func2_names, double (* const *funcs2)(void *, double, double),
726 void *opaque, int log_offset, void *log_ctx)
729 int ret = av_expr_parse(&e, s, const_names, func1_names, funcs1, func2_names, funcs2, log_offset, log_ctx);
735 *d = av_expr_eval(e, const_values, opaque);
737 return isnan(*d) ? AVERROR(EINVAL) : 0;
743 static const double const_values[] = {
749 static const char *const const_names[] = {
755 int main(int argc, char **argv)
759 const char *const *expr;
760 static const char *const exprs[] = {
766 "1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)",
787 "bar + PI + E + 100f*2 + foo",
788 "13k + 12f - foo(1, 2)",
801 /* compute 1+2+...+N */
802 "st(0, 1); while(lte(ld(0), 100), st(1, ld(1)+ld(0));st(0, ld(0)+1)); ld(1)",
804 "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)",
806 "st(0, 1); while(lte(ld(0),100), st(1, ld(1)+ld(0)); st(0, ld(0)+1))",
835 "ifnot(1, NaN) + if(0, 1)",
839 "taylor(eq(mod(ld(1),4),1)-eq(mod(ld(1),4),3), PI/2, 1)",
840 "root(sin(ld(0))-1, 2)",
841 "root(sin(ld(0))+6+sin(ld(0)/12)-log(ld(0)), 100)",
842 "7000000B*random(0)",
846 "gcd(30,55)*print(min(9,1))",
850 "between(10, -3, 10)",
851 "between(-4, -2, -1)",
859 for (expr = exprs; *expr; expr++) {
860 printf("Evaluating '%s'\n", *expr);
861 av_expr_parse_and_eval(&d, *expr,
862 const_names, const_values,
863 NULL, NULL, NULL, NULL, NULL, 0, NULL);
865 printf("'%s' -> nan\n\n", *expr);
867 printf("'%s' -> %f\n\n", *expr, d);
870 av_expr_parse_and_eval(&d, "1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)",
871 const_names, const_values,
872 NULL, NULL, NULL, NULL, NULL, 0, NULL);
873 printf("%f == 12.7\n", d);
874 av_expr_parse_and_eval(&d, "80G/80Gi",
875 const_names, const_values,
876 NULL, NULL, NULL, NULL, NULL, 0, NULL);
877 printf("%f == 0.931322575\n", d);
879 if (argc > 1 && !strcmp(argv[1], "-t")) {
880 for (i = 0; i < 1050; i++) {
882 av_expr_parse_and_eval(&d, "1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)",
883 const_names, const_values,
884 NULL, NULL, NULL, NULL, NULL, 0, NULL);
885 STOP_TIMER("av_expr_parse_and_eval");