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eval: add root() to solve f(x)=0

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Signed-off-by: Michael Niedermayer <michaelni@gmx.at>
This commit is contained in:
Michael Niedermayer 2012-02-21 22:30:35 +01:00
parent 8c5ee45d13
commit 59affed23c
3 changed files with 57 additions and 1 deletions
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4
doc/eval.texi
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@ -114,6 +114,10 @@ then 0 is assumed.
note, when you have the derivatives at y instead of 0
taylor(expr, x-y) can be used
When the series does not converge the results are undefined.
@item root(expr, max)
Finds x where f(x)=0 in the interval 0..max.
f() must be continuous or the result is undefined.
@end table
The following constants are available:

48
libavutil/eval.c
View File

@ -26,6 +26,7 @@
* see http://joe.hotchkiss.com/programming/eval/eval.html
*/
#include <float.h>
#include "avutil.h"
#include "eval.h"
#include "log.h"
@ -134,7 +135,7 @@ struct AVExpr {
e_squish, e_gauss, e_ld, e_isnan,
e_mod, e_max, e_min, e_eq, e_gt, e_gte,
e_pow, e_mul, e_div, e_add,
e_last, e_st, e_while, e_taylor, e_floor, e_ceil, e_trunc,
e_last, e_st, e_while, e_taylor, e_root, e_floor, e_ceil, e_trunc,
e_sqrt, e_not, e_random, e_hypot, e_gcd,
e_if, e_ifnot,
} type;
@ -199,6 +200,48 @@ static double eval_expr(Parser *p, AVExpr *e)
p->var[id] = var0;
return d;
}
case e_root: {
int i;
double low = -1, high = -1, v, low_v = -DBL_MAX, high_v = DBL_MAX;
double var0 = p->var[0];
double x_max = eval_expr(p, e->param[1]);
for(i=-1; i<1024; i++) {
if(i<255) {
p->var[0] = av_reverse[i&255]*x_max/255;
} else {
p->var[0] = x_max*pow(0.9, i-255);
if (i&1) p->var[0] *= -1;
if (i&2) p->var[0] += low;
else p->var[0] += high;
}
v = eval_expr(p, e->param[0]);
if (v<=0 && v>low_v) {
low = p->var[0];
low_v = v;
}
if (v>=0 && v<high_v) {
high = p->var[0];
high_v = v;
}
if (low>=0 && high>=0){
while (1) {
p->var[0] = (low+high)*0.5;
if (low == p->var[0] || high == p->var[0])
break;
v = eval_expr(p, e->param[0]);
if (v<=0) low = p->var[0];
if (v>=0) high= p->var[0];
if (isnan(v)) {
low = high = v;
break;
}
}
break;
}
}
p->var[0] = var0;
return -low_v<high_v ? low : high;
}
default: {
double d = eval_expr(p, e->param[0]);
double d2 = eval_expr(p, e->param[1]);
@ -342,6 +385,7 @@ static int parse_primary(AVExpr **e, Parser *p)
else if (strmatch(next, "st" )) d->type = e_st;
else if (strmatch(next, "while" )) d->type = e_while;
else if (strmatch(next, "taylor")) d->type = e_taylor;
else if (strmatch(next, "root" )) d->type = e_root;
else if (strmatch(next, "floor" )) d->type = e_floor;
else if (strmatch(next, "ceil" )) d->type = e_ceil;
else if (strmatch(next, "trunc" )) d->type = e_trunc;
@ -727,6 +771,8 @@ int main(int argc, char **argv)
"ifnot(1, NaN) + if(0, 1)",
"taylor(1, 1)",
"taylor(eq(mod(ld(1),4),1)-eq(mod(ld(1),4),3), PI/2, 1)",
"root(sin(ld(0))-1, 2)",
"root(sin(ld(0))+6+sin(ld(0)/12)-log(ld(0)), 100)",
NULL
};

6
tests/ref/fate/eval
View File

@ -175,5 +175,11 @@ Evaluating 'taylor(1, 1)'
Evaluating 'taylor(eq(mod(ld(1),4),1)-eq(mod(ld(1),4),3), PI/2, 1)'
'taylor(eq(mod(ld(1),4),1)-eq(mod(ld(1),4),3), PI/2, 1)' -> 1.000000
Evaluating 'root(sin(ld(0))-1, 2)'
'root(sin(ld(0))-1, 2)' -> 1.570796
Evaluating 'root(sin(ld(0))+6+sin(ld(0)/12)-log(ld(0)), 100)'
'root(sin(ld(0))+6+sin(ld(0)/12)-log(ld(0)), 100)' -> 60.965601
12.700000 == 12.7
0.931323 == 0.931322575