/* Defines a target function F for bbopt2.c */
/* Last edited on 2003-09-21 16:47:58 by stolfi */
  
#include <ia.h>
#include <bbgoal.h>

int F_dim = 2;
char *F_name = "F1-IA";
char *F_descr = "(IA) u = x - 2/7; v = y - 3/7; u^2 + v^2 + u*v + 1";

#define F_XMINN (2.0)
#define F_XMIND (7.0)
#define F_XMIN (F_XMINN/F_XMIND)

#define F_YMINN (3.0)
#define F_YMIND (7.0)
#define F_YMIN (F_YMINN/F_YMIND)

Float F(Float *x) 
  { Float dx = x[0] - F_XMIN;
    Float dy = x[0] - F_YMIN;
    Float xx = dx*dx, xy = dx*dy, yy = dy*dy;
    return xx+xy+yy + 1.0;
  }

Interval F_ia(Interval *xr) 
  { Interval x = xr[0];
    Interval y = xr[1];
    
    Interval dx = ia_shift(x, -2.0/7.0);
    Interval dy = ia_shift(y, -3.0/7.0);

    Interval xx = ia_sqr(dx);
    Interval yy = ia_sqr(dy);
    Interval xy = ia_mul(dx, dy);

    Interval f = ia_shift(ia_add(ia_add(xx, yy), xy), +1.0);
    
    return f;
  }

void F_sol(Interval *xr, Interval *sr)
  { /* Should take `xr' into account... */
    Interval mr[2];
    mr[0] = ia_scale(ia_const(One, Zero), F_XMINN, F_XMIND);
    mr[1] = ia_scale(ia_const(One, Zero), F_YMINN, F_YMIND);
    int i;
    for (i = 0; i < F_dim; i++)
      { Float mlo = mr[i].lo, mhi = mr[i].hi;
        Float xlo = xr[i].lo, xhi = xr[i].hi;
        Float slo, shi;
        if (mhi <= xlo)
          { slo = shi = xlo; }
        else if (mlo >= xhi)
          { slo = shi = xhi; }
        else
          { slo = (mlo < xlo ? xlo : mlo);
            shi = (mhi > xhi ? xhi : mhi);
          }
        sr[i] = (Interval) { slo, shi };
      }
  }