/* mpfr_acos -- arc-cosinus of a floating-point number

Copyright 2001, 2002, 2003, 2004 Free Software Foundation.

This file is part of the MPFR Library, and was contributed by Mathieu Dutour.

The MPFR 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, or (at your
option) any later version.

The MPFR 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 the MPFR Library; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */

#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"

int
mpfr_acos (mpfr_ptr acos, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
  mpfr_t xp;
  mpfr_t arcc;

  int sign, supplement;

  mpfr_t tmp;
  int Prec;
  int prec_acos;
  int good = 0;
  int realprec;
  int compared;
  int inexact = 0;
  MPFR_SAVE_EXPO_DECL (expo);

  /* Special cases */
  if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(x) ))
    {
      if (MPFR_IS_NAN(x) || MPFR_IS_INF(x))
	{
	  MPFR_SET_NAN(acos);
	  MPFR_RET_NAN;
	}
      else /* necessarily x=0 */
	{
          MPFR_ASSERTD(MPFR_IS_ZERO(x));
	  /* acos(0)=Pi/2 */
	  inexact = mpfr_const_pi (acos, rnd_mode);
	  MPFR_SET_EXP (acos, MPFR_GET_EXP (acos) - 1);
	  return mpfr_check_range (acos, inexact, rnd_mode);
	}
    }
  MPFR_CLEAR_FLAGS(x);

  /* Set x_p=|x| */
  sign = MPFR_SIGN(x);
  mpfr_init2 (xp, MPFR_PREC(x));
  mpfr_abs (xp, x, rnd_mode);

  compared = mpfr_cmp_ui (xp, 1);

  if (compared > 0) /* acos(x) = NaN for x > 1 */
    {
      mpfr_clear (xp);
      MPFR_SET_NAN(acos);
      MPFR_RET_NAN;
    }

  if (compared == 0)
    {
      mpfr_clear (xp);
      if (MPFR_IS_POS_SIGN(sign)) /* acos(+1) = 0 */
	return mpfr_set_ui (acos, 0, rnd_mode);
      else /* acos(-1) = Pi */
        {
          mpfr_const_pi (acos, rnd_mode);
          return 1; /* inexact */
        }
    }

  MPFR_SAVE_EXPO_MARK (expo);

  prec_acos = MPFR_PREC(acos);
  mpfr_ui_sub (xp, 1, xp, GMP_RNDD);

  if (MPFR_IS_POS_SIGN(sign))
    supplement = 2 - 2 * MPFR_GET_EXP (xp);
  else
    supplement = 2 - MPFR_GET_EXP(xp);

  realprec = prec_acos + 10;

  while (!good)
    {
      Prec = realprec + supplement;

      /* Initialisation    */
      mpfr_init2 (tmp, Prec);
      mpfr_init2 (arcc, Prec);

      /* acos(x) = Pi/2 - asin(x) = Pi/2 - atan(x/sqrt(1-x^2)) */
      mpfr_mul (tmp, x, x, GMP_RNDN);
      mpfr_ui_sub (tmp, 1, tmp, GMP_RNDN);
      mpfr_sqrt (tmp, tmp, GMP_RNDN);
      mpfr_div (tmp, x, tmp, GMP_RNDN);
      mpfr_atan (arcc, tmp, GMP_RNDN);
      mpfr_const_pi (tmp, GMP_RNDN);
      mpfr_div_2ui (tmp, tmp, 1, GMP_RNDN);
      mpfr_sub (arcc, tmp, arcc, GMP_RNDN);

      if (mpfr_can_round (arcc, realprec, GMP_RNDN, GMP_RNDZ,
                          MPFR_PREC(acos) + (rnd_mode == GMP_RNDN)))
        {
          inexact = mpfr_set (acos, arcc, rnd_mode);
          good = 1;
        }
      else
        realprec +=  MPFR_INT_CEIL_LOG2 (realprec);

      mpfr_clear (tmp);
      mpfr_clear (arcc);
    }
  
  mpfr_clear (xp);
  MPFR_SAVE_EXPO_FREE (expo);
  return mpfr_check_range (acos, inexact, rnd_mode);
}