@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:
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;
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]);
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;
"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
};
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