/****************************************************************************/
/* (C) Copyright 1993 Universidade Estadual de Campinas (UNICAMP)           */
/*                    Campinas, SP, Brazil                                  */
/*                                                                          */
/* This file can be freely distributed, modified, and used for any          */
/*   non-commercial purpose, provided that this copyright and authorship    */
/*   notice be included in any copy or derived version of this file.        */
/*                                                                          */
/* DISCLAIMER: This software is offered ``as is'', without any guarantee    */
/*   as to fitness for any particular purpose.  Neither the copyright       */
/*   holder nor the authors or their employers can be held responsible for  */
/*   any damages that may result from its use.                              */
/****************************************************************************/

char *aat_gtag = "g5";
char *aat_gname = 
  "u = 3(x-1)/4; v = 3x/2; r2 = u^2 + v^2;\nm2 = (u^2 - 3*v^2)^2;\ns = u*m2 - r2^2;\nt = (1/8)/(2 + r2);\ng = s + t";

Float aat_g_flt (Float x)
  {
    ROUND_NEAR;
    {
      Float u = Three*Quarter * (x - One);
      Float v = Three*Half * x;
      Float u2 = u*u;
      Float v2 = v*v;
      Float r2 = u2 + v2;
      Float m2 = u2 - Three * v2;
      Float s = u*m2 + r2*r2;
      Float t = (1.0/8.0)/(2.0 + r2);
      Float res = s + t;
      return (res);
    }
  }

Interval aat_g_ia (Interval x)
  {
    Float Eighth = Half*Quarter;
    Interval u = ia_affine(x, Three, Four, -Three*Quarter, Zero);
    Interval v = ia_scale(x, Three, Two);
    Interval u2 = ia_sqr(u);
    Interval v2 = ia_sqr(v);
    Interval r2 = ia_add(u2, v2);
    Interval m2 = ia_sub(u2, ia_scale(v2, Three, One));
    Interval s = ia_add(ia_mul(u, m2), ia_sqr(r2));
    Interval t = ia_scale(ia_inv(ia_shift(r2, Two)), Eighth, One);
    Interval res = ia_add(s, t);
    return (res);
  }

AAP aat_g_aa (AAP x)
  {
    MemP frame = aa_top();
    Float Eighth = Half*Quarter;
    AAP u = aa_affine(x, Three, Four, -Three*Quarter, Zero);
    AAP v = aa_scale(x, Three, Two);
    AAP u2 = aa_sqr(u);
    AAP v2 = aa_sqr(v);
    AAP r2 = aa_add(u2, v2);
    AAP m2 = aa_sub(u2, aa_scale(v2, Three, One));
    AAP s = aa_add(aa_mul(u, m2), aa_sqr(r2));
    AAP t = aa_scale(aa_inv(aa_shift(r2, Two)), Eighth, One);
    AAP res = aa_add(s, t);
    return (aa_return(frame, res));
  }

Interval aat_gxd = {-One, One};
Interval aat_gyd = {-One, One};

int aat_gn = 16;