/* See {fn2_f1.h}. */
/* Last edited on 2005-09-25 14:22:05 by stolfi */
 
#include <fn2_f1.h>
#include <aa.h>
#include <ia.h>
#include <flt.h>
#include <fn2_functions.h>
 
Float fn2_f1_eval_fp (Float x, Float y);
Interval fn2_f1_eval_ia (Interval x, Interval y);
AAP fn2_f1_eval_aa (AAP x, AAP y);
 
char *fn2_f1_tag = "f1";
char *fn2_f1_descr = "f = x^2 + y^2 + x*y - (x*y)^2/2 - 1/4";

Float fn2_f1_eval_fp (Float x, Float y)
  {
    ROUND_NEAR;
    return (x*x + y*y + x*y - (x*y)*(x*y)*Half - Quarter);
  }

Interval fn2_f1_eval_ia (Interval x, Interval y)
  {
    Interval x2 = ia_sqr(x);
    Interval y2 = ia_sqr(y);
    Interval xy = ia_mul(x, y);
    Interval x2y2d2 = ia_scale(ia_sqr(xy), One, Two);
    Interval sum = ia_add(ia_add(ia_add(x2, y2), xy), ia_neg(x2y2d2));
    Interval res = ia_shift(sum, -Quarter);
    return (res);
  }

AAP fn2_f1_eval_aa (AAP x, AAP y)
  {
    MemP frame = aa_top();
    AAP x2  = aa_sqr(x);
    AAP y2  = aa_sqr(y);
    AAP xy  = aa_mul(x, y);
    AAP x2y2d2 = aa_scale(aa_sqr(xy), One, Two);
    AAP sum = aa_add(aa_add(aa_add(x2, y2), xy), aa_neg(x2y2d2));
    AAP res = aa_shift(sum, -Quarter);
    return (aa_return(frame, res));
  }

Interval fn2_f1_xd = {-Two, Two};
Interval fn2_f1_yd = {-Two, Two};

int fn2_f1_fn = 32;
 
fn2_data_t fn2_f1_get_data(void)
  { 
    fn2_data_t f;
    f.tag = fn2_f1_tag;
    f.descr = fn2_f1_descr;
    f.eval_fp = &fn2_f1_eval_fp;
    f.eval_ia = &fn2_f1_eval_ia;
    f.eval_aa = &fn2_f1_eval_aa;
    f.xd = fn2_f1_xd;
    f.yd = fn2_f1_yd;
    return f;
  }