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eval: Add taylor series evaluation support.

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Signed-off-by: Michael Niedermayer <michaelni@gmx.at>
This commit is contained in:
Michael Niedermayer 2012-02-21 20:47:18 +01:00
parent f16c950f32
commit 43b1943a55
3 changed files with 34 additions and 1 deletions
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7
doc/eval.texi
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@ -106,6 +106,13 @@ the evaluation of @var{y}, return 0 otherwise.
@item ifnot(x, y)
Evaluate @var{x}, and if the result is zero return the result of the
evaluation of @var{y}, return 0 otherwise.
@item taylor(expr, x)
Evaluate a taylor series at x.
expr represents the LD(0)-th derivates of f(x) at 0.
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.
@end table
The following constants are available:

22
libavutil/eval.c
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@ -134,7 +134,7 @@ 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_floor, e_ceil, e_trunc,
e_last, e_st, e_while, e_taylor, e_floor, e_ceil, e_trunc,
e_sqrt, e_not, e_random, e_hypot, e_gcd,
e_if, e_ifnot,
} type;
@ -181,6 +181,23 @@ static double eval_expr(Parser *p, AVExpr *e)
d=eval_expr(p, e->param[1]);
return d;
}
case e_taylor: {
double t = 1, d = 0, v;
double x = eval_expr(p, e->param[1]);
int i;
double var0 = p->var[0];
for(i=0; i<1000; i++) {
double ld = d;
p->var[0] = i;
v = eval_expr(p, e->param[0]);
d += t*v;
if(ld==d && v)
break;
t *= x / (i+1);
}
p->var[0] = var0;
return d;
}
default: {
double d = eval_expr(p, e->param[0]);
double d2 = eval_expr(p, e->param[1]);
@ -318,6 +335,7 @@ static int parse_primary(AVExpr **e, Parser *p)
else if (strmatch(next, "isnan" )) d->type = e_isnan;
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, "floor" )) d->type = e_floor;
else if (strmatch(next, "ceil" )) d->type = e_ceil;
else if (strmatch(next, "trunc" )) d->type = e_trunc;
@ -698,6 +716,8 @@ int main(int argc, char **argv)
"if(1, 2)",
"ifnot(0, 23)",
"ifnot(1, NaN) + if(0, 1)",
"taylor(1, 1)",
"taylor(eq(mod(ld(0),4),1)-eq(mod(ld(0),4),3), PI/2)",
NULL
};

6
tests/ref/fate/eval
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@ -169,5 +169,11 @@ Evaluating 'ifnot(0, 23)'
Evaluating 'ifnot(1, NaN) + if(0, 1)'
'ifnot(1, NaN) + if(0, 1)' -> 0.000000
Evaluating 'taylor(1, 1)'
'taylor(1, 1)' -> 2.718282
Evaluating 'taylor(eq(mod(ld(0),4),1)-eq(mod(ld(0),4),3), PI/2)'
'taylor(eq(mod(ld(0),4),1)-eq(mod(ld(0),4),3), PI/2)' -> 1.000000
12.700000 == 12.7
0.931323 == 0.931322575