/****************************************************************************/
/* (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 = "g12";
char *aat_gname = 
  "y = [x]+2;\nd = x-y;\nt = d(1-d^2)/4; h = t/(1+t^2);\nu = x+h; v = x+h;\nm = u^2 + v^2 + 2uv; f = m - 1/4\ng=m";

Float aat_f_flt (Float x, Float y);
Interval aat_f_ia (Interval x, Interval y);
AAP aat_f_aa (AAP x, AAP y);

Float aat_f_flt (Float x, Float y)
  {
    ROUND_NEAR;
    {
      Float d = x - y;
      Float t = Quarter * d * (One - d*d);
      Float h = t / (1 + t*t);
      Float u = x + h;
      Float v = y + h;
      Float u2 = u*u;
      Float v2 = v*v;
      Float uv = u*v;
      Float m = u2 + v2 + uv + uv;
      Float res = m - Quarter;
      return (res);
    }
  }
  
Float aat_g_flt (Float x)
  {
    ROUND_NEAR;
    {
      Float y = x + Two;
      Float res = aat_f_flt(x, y);
      return (res);
    }
  }
    
Interval aat_f_ia (Interval x, Interval y)
  {
    Interval d = ia_sub(x, y);
    Interval t = ia_mul(d, ia_affine(ia_sqr(d), -One, Four, Quarter, Zero));
    Interval h = ia_div(t, ia_shift(ia_sqr(t), One));
    Interval u = ia_add(x, h);
    Interval v = ia_add(y, h);
    Interval u2 = ia_sqr(u);
    Interval v2 = ia_sqr(v);
    Interval uv = ia_mul(u, v);
    Interval m = ia_add(ia_add(u2, v2), ia_add(uv, uv));
    Interval res = ia_shift(m, -Quarter);
    return (res);
  }
  
Interval aat_g_ia (Interval x)
  {
    Interval y = ia_shift(x, Two);
    Interval res = aat_f_ia(x, y);
    return (res);
  }

AAP aat_f_aa (AAP x, AAP y)
  {
    AAP d = aa_sub(x, y);
    AAP t = aa_mul(d, aa_affine(aa_sqr(d), -One, Four, Quarter, Zero));
    AAP h = aa_div(t, aa_shift(aa_sqr(t), One));
    AAP u = aa_add(x, h);
    AAP v = aa_add(y, h);
    AAP u2 = aa_sqr(u);
    AAP v2 = aa_sqr(v);
    AAP uv = aa_mul(u, v);
    AAP m = aa_add(aa_add(u2, v2), aa_add(uv, uv));
    AAP res = aa_shift(m, -Quarter);
    return (res);
  }

AAP aat_g_aa (AAP x)
  {
    MemP frame = aa_top();
    AAP y = aa_shift(aa_from_interval(aa_range(x)), Two);
    AAP res = aat_f_aa(x, y);
    return (aa_return(frame, res));
  }

Interval aat_gxd = {-Four, Four};
Interval aat_gyd = {-2.0, 6.0};

int aat_gn = 8;