/****************************************************************************/
/* (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 = "giaboom";
char *aat_gname = "h(x) = sqrt(x^2 - x + 1/2)/sqrt(x^2 + 1/2) g(x) = h(h(x))";

Float aat_h_flt (Float x);
Interval aat_h_ia (Interval x);
AAP aat_h_aa (AAP x);

Float aat_h_flt (Float x)
  {
    ROUND_NEAR;
    return (sqrt(x*x - x + 0.50)/sqrt(x*x + 0.50));
  }

Float aat_g_flt (Float x)
  {
    ROUND_NEAR;
    return aat_h_flt(aat_h_flt(x));
  }

Interval aat_h_ia (Interval x)
  {
    Interval x2  = ia_sqr(x);
    Interval hlf = {Half, Half};
    Interval dif = ia_sub(x2, x);
    Interval sum1 = ia_add(dif, hlf);
    Interval sum2 = ia_add(x2, hlf);
    Interval res = ia_div(ia_sqrt(sum1), ia_sqrt(sum2));
    return (res);
  }

Interval aat_g_ia (Interval x)
  {
    return (aat_h_ia(aat_h_ia(x)));
  }

AAP aat_h_aa (AAP x)
  {
    AAP x2  = aa_sqr(x);
    AAP hlf = aa_const(Half, Zero);
    AAP dif = aa_sub(x2, x);
    AAP sum1 = aa_add(dif, hlf);
    AAP sum2 = aa_add(x2, hlf);
    AAP res = aa_div(aa_sqrt(sum1), aa_sqrt(sum2));
    return (res);
  }

AAP aat_g_aa (AAP x)
  {
    MemP frame = aa_top();
    AAP res = aat_h_aa(aat_h_aa(x));
    return (aa_return(frame, res));
  }

Interval aat_gxd = {-Two, Two};
Interval aat_gyd = {-Half*Quarter, Two};

int aat_gn = 16;