/* mpfr_acosh -- inverse hyperbolic cosine

Copyright 2001, 2002, 2003, 2004, 2005, 2006 Free Software Foundation, Inc.

This file is part of the MPFR Library.

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., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */

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

/* The computation of acosh is done by   *
 *  acosh= ln(x + sqrt(x^2-1))           */

int
mpfr_acosh (mpfr_ptr y, mpfr_srcptr x , mp_rnd_t rnd_mode)
{
  MPFR_SAVE_EXPO_DECL (expo);
  int inexact;
  int comp;

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

  /* Deal with special cases */
  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
    {
      /* Nan, or zero or -Inf */
      if (MPFR_IS_INF (x) && MPFR_IS_POS (x))
        {
          MPFR_SET_INF (y);
          MPFR_SET_POS (y);
          MPFR_RET (0);
        }
      else /* Nan, or zero or -Inf */
        {
          MPFR_SET_NAN (y);
          MPFR_RET_NAN;
        }
    }
  comp = mpfr_cmp_ui (x, 1);
  if (MPFR_UNLIKELY (comp < 0))
    {
      MPFR_SET_NAN (y);
      MPFR_RET_NAN;
    }
  else if (MPFR_UNLIKELY (comp == 0))
    {
      MPFR_SET_ZERO (y); /* acosh(1) = 0 */
      MPFR_SET_POS (y);
      MPFR_RET (0);
    }
  MPFR_SAVE_EXPO_MARK (expo);

  /* General case */
  {
    /* Declaration of the intermediary variables */
    mpfr_t t;
    /* Declaration of the size variables */
    mp_prec_t Ny = MPFR_PREC(y);   /* Precision of output variable */
    mp_prec_t Nt;                  /* Precision of the intermediary variable */
    mp_exp_t  err, exp_te, exp_ti; /* Precision of error */
    MPFR_ZIV_DECL (loop);

    /* compute the precision of intermediary variable */
    /* the optimal number of bits : see algorithms.tex */
    Nt = Ny + 4 + MPFR_INT_CEIL_LOG2 (Ny);

    /* initialization of intermediary variables */
    mpfr_init2 (t, Nt);

    /* First computation of acosh */
    MPFR_ZIV_INIT (loop, Nt);
    for (;;)
      {
        /* compute acosh */
        mpfr_mul (t, x, x, GMP_RNDD);      /* x^2 */
        exp_te = MPFR_GET_EXP (t);
        mpfr_sub_ui (t, t, 1, GMP_RNDD);   /* x^2-1 */
        exp_ti = MPFR_GET_EXP (t);
        mpfr_sqrt (t, t, GMP_RNDN);        /* sqrt(x^2-1) */
        mpfr_add (t, t, x, GMP_RNDN);      /* sqrt(x^2-1)+x */
        mpfr_log (t, t, GMP_RNDN);         /* ln(sqrt(x^2-1)+x)*/

        /* error estimate -- see algorithms.tex */
        err = 2 + MAX (1, exp_te - exp_ti) - MPFR_GET_EXP(t);
        /* error is bounded by 1/2 + 2^err <= 2^(1+max(-1,err)) */
        err = 1 + MAX (-1, err);
        if (MPFR_LIKELY (MPFR_CAN_ROUND (t, Nt - err, Ny, rnd_mode)))
          break;

        /* reactualisation of the precision */
        MPFR_ZIV_NEXT (loop, Nt);
        mpfr_set_prec (t, Nt);
      }
    MPFR_ZIV_FREE (loop);

    inexact = mpfr_set (y, t, rnd_mode);

    mpfr_clear (t);
  }

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