/*
 * The Spar Library - modular math parser
 * Copyright (C) 2000,2001 Davide Angelocola <davide178@inwind.it>
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the
 * Free Software Foundation, Inc., 59 Temple Place - Suite 330,
 * Boston, MA  02111-1307, USA.
 *
 */

#include <spar/sl_math_library.h>
#include <spar/sl_complex.h>

sl_complex
sl_complex_def (double x, double y)
{
  SL_COMPLEX (z, x, y);
  return z;
}

/*
 *  Standard functions
 * 
 *  missing: cos, log, exp, tanh, atan, asinh...
 */
sl_complex
sl_complex_conjugate (sl_complex x)
{
  return sl_complex_def (SL_COMPLEX_RE (x), SL_COMPLEX_IM (x) * (-1));
}

sl_complex
sl_complex_negative (sl_complex x)
{
  return sl_complex_def (SL_COMPLEX_RE (x) * (-1), SL_COMPLEX_IM (x) * (-1));
}

double
sl_complex_abs (sl_complex x)
{
  return sl_hypot (SL_COMPLEX_RE (x), SL_COMPLEX_IM (x));
}

double
sl_complex_abs_2 (sl_complex x)
{
  return (SL_COMPLEX_RE (x) * SL_COMPLEX_RE (x)) +
    (SL_COMPLEX_IM (x) * SL_COMPLEX_IM (x));
}

double
sl_complex_arg (sl_complex x)
{
  return sl_arctan (SL_COMPLEX_IM (x) / SL_COMPLEX_RE (x));
}

sl_complex
sl_complex_polar (double r, double theta)
{
  return sl_complex_def (r * sl_cos (theta), r * sl_sin (theta));
}

/*
 *   ADD complex operator
 */
sl_complex
sl_complex_add (sl_complex x, sl_complex y)
{
  return sl_complex_def (SL_COMPLEX_RE (x) + SL_COMPLEX_RE (y),
			 SL_COMPLEX_IM (x) + SL_COMPLEX_IM (y));
}

sl_complex
sl_complex_add_real (sl_complex x, double r)
{
  return sl_complex_def (SL_COMPLEX_RE (x) + r, SL_COMPLEX_IM (x));
}

sl_complex
sl_complex_add_imag (sl_complex x, double i)
{
  return sl_complex_def (SL_COMPLEX_RE (x), SL_COMPLEX_IM (x) + i);
}

/*
 *  SUB complex operator
 */
sl_complex
sl_complex_sub (sl_complex x, sl_complex y)
{
  return sl_complex_def (SL_COMPLEX_RE (x) - SL_COMPLEX_RE (y),
			 SL_COMPLEX_IM (x) - SL_COMPLEX_IM (y));
}

sl_complex
sl_complex_sub_real (sl_complex x, double r)
{
  return sl_complex_def (SL_COMPLEX_RE (x) - r, SL_COMPLEX_IM (x));
}

sl_complex
sl_complex_sub_imag (sl_complex x, double i)
{
  return sl_complex_def (SL_COMPLEX_RE (x), SL_COMPLEX_IM (x) - i);
}

/*
 *  MUL complex operator
 */
sl_complex
sl_complex_mul (sl_complex x, sl_complex y)
{
  return sl_complex_def ((SL_COMPLEX_RE (x) * SL_COMPLEX_RE (y) -
			  SL_COMPLEX_IM (x) * SL_COMPLEX_IM (y)),
			 (SL_COMPLEX_RE (x) * SL_COMPLEX_IM (y) +
			  SL_COMPLEX_IM (x) * SL_COMPLEX_RE (y)));
}

sl_complex
sl_complex_mul_real (sl_complex x, double r)
{
  return sl_complex_def (SL_COMPLEX_RE (x) * r, SL_COMPLEX_IM (x) * r);
}

sl_complex
sl_complex_mul_imag (sl_complex x, double i)
{
  return sl_complex_def (-i * SL_COMPLEX_IM (x), SL_COMPLEX_RE (x) * i);
}

sl_complex
sl_complex_div (sl_complex x, sl_complex y)
{
  double arg_x = sl_complex_arg (x);
  double arg_y = sl_complex_arg (y);
  double mod_x = sl_complex_abs (x);
  double mod_y = sl_complex_abs (y);

  return sl_complex_def ((mod_x / mod_y), (arg_x - arg_y));
}