mpfr-2.4.1/acos.c

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

Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao projects, INRIA.

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

The GNU 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 GNU 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 GNU MPFR Library; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */

#include "mpfr-impl.h"

int
mpfr_acos (mpfr_ptr acos, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
  mpfr_t xp, arcc, tmp;
  mp_exp_t supplement;
  mp_prec_t prec;
  int sign, compared, inexact;
  MPFR_SAVE_EXPO_DECL (expo);
  MPFR_ZIV_DECL (loop);

  MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode),
                 ("acos[%#R]=%R inexact=%d", acos, acos, inexact));

  /* Singular 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_div_2ui (acos, acos, 1, rnd_mode); /* exact */
          MPFR_RET (inexact);
        }
    }

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

  compared = mpfr_cmp_ui (xp, 1);

  if (MPFR_UNLIKELY (compared >= 0))
    {
      mpfr_clear (xp);
      if (compared > 0) /* acos(x) = NaN for x > 1 */
        {
          MPFR_SET_NAN(acos);
          MPFR_RET_NAN;
        }
      else
        {
          if (MPFR_IS_POS_SIGN (sign)) /* acos(+1) = 0 */
            return mpfr_set_ui (acos, 0, rnd_mode);
          else /* acos(-1) = Pi */
            return mpfr_const_pi (acos, rnd_mode);
        }
    }

  MPFR_SAVE_EXPO_MARK (expo);

  /* Compute the supplement */
  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);
  mpfr_clear (xp);

  prec = MPFR_PREC (acos) + 10 + supplement;

  /* VL: The following change concerning prec comes from r3145
     "Optimize mpfr_acos by choosing a better initial precision."
     but it doesn't seem to be correct and leads to problems (assertion
     failure or very important inefficiency) with tiny arguments.
     Therefore, I've disabled it. */
  /* If x ~ 2^-N, acos(x) ~ PI/2 - x - x^3/6
     If Prec < 2*N, we can't round since x^3/6 won't be counted. */
#if 0
  if (MPFR_PREC (acos) >= MPFR_PREC (x) && MPFR_GET_EXP (x) < 0)
    {
      mpfr_uexp_t pmin = (mpfr_uexp_t) (-2 * MPFR_GET_EXP (x)) + 5;
      MPFR_ASSERTN (pmin <= MPFR_PREC_MAX);
      if (prec < pmin)
        prec = pmin;
    }
#endif

  mpfr_init2 (tmp, prec);
  mpfr_init2 (arcc, prec);

  MPFR_ZIV_INIT (loop, prec);
  for (;;)
    {
      /* acos(x) = Pi/2 - asin(x) = Pi/2 - atan(x/sqrt(1-x^2)) */
      mpfr_sqr (tmp, 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_LIKELY (MPFR_CAN_ROUND (arcc, prec-supplement,
                                       MPFR_PREC (acos), rnd_mode)))
        break;
      MPFR_ZIV_NEXT (loop, prec);
      mpfr_set_prec (tmp, prec);
      mpfr_set_prec (arcc, prec);
    }
  MPFR_ZIV_FREE (loop);

  inexact = mpfr_set (acos, arcc, rnd_mode);
  mpfr_clear (tmp);
  mpfr_clear (arcc);

  MPFR_SAVE_EXPO_FREE (expo);
  return mpfr_check_range (acos, inexact, rnd_mode);
}