/* mpfr_sinh -- hyperbolic sine

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 Place, Fifth Floor, Boston,
MA 02110-1301, USA. */

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

 /* The computation of sinh is done by
    sinh(x) = 1/2 [e^(x)-e^(-x)]          */

int
mpfr_sinh (mpfr_ptr y, mpfr_srcptr xt, mp_rnd_t rnd_mode)
{
  mpfr_t x;
  int inexact;

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

  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt)))
    {
      if (MPFR_IS_NAN (xt))
        {
          MPFR_SET_NAN (y);
          MPFR_RET_NAN;
        }
      else if (MPFR_IS_INF (xt))
        {
          MPFR_SET_INF (y);
          MPFR_SET_SAME_SIGN (y, xt);
          MPFR_RET (0);
        }
      else /* xt is zero */
        {
          MPFR_ASSERTD (MPFR_IS_ZERO (xt));
          MPFR_SET_ZERO (y);   /* sinh(0) = 0 */
          MPFR_SET_SAME_SIGN (y, xt);
          MPFR_RET (0);
        }
    }

  /* sinh(x) = x + x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */
  MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, xt, -2*MPFR_GET_EXP(xt)+2,1,rnd_mode, );

  MPFR_TMP_INIT_ABS (x, xt);

  {
    mpfr_t t, ti;
    mp_exp_t d;
    mp_prec_t Nt;    /* Precision of the intermediary variable */
    long int err;    /* Precision of error */
    MPFR_ZIV_DECL (loop);
    MPFR_SAVE_EXPO_DECL (expo);
    MPFR_GROUP_DECL (group);

    MPFR_SAVE_EXPO_MARK (expo);

    /* compute the precision of intermediary variable */
    Nt = MAX (MPFR_PREC (x), MPFR_PREC (y));
    /* the optimal number of bits : see algorithms.ps */
    Nt = Nt + MPFR_INT_CEIL_LOG2 (Nt) + 4;
    /* If x is near 0, exp(x) - 1/exp(x) = 2*x+x^3/3+O(x^5) */
    if (MPFR_GET_EXP (x) < 0)
      Nt -= 2*MPFR_GET_EXP (x);

    /* initialise of intermediary variables */
    MPFR_GROUP_INIT_2 (group, Nt, t, ti);

    /* First computation of sinh */
    MPFR_ZIV_INIT (loop, Nt);
    for (;;) {
      /* compute sinh */
      mpfr_clear_flags ();
      mpfr_exp (t, x, GMP_RNDD);        /* exp(x) */
      /* exp(x) can overflow! */
      /* BUG/TODO/FIXME: exp can overflow but sinh may be representable! */
      if (MPFR_UNLIKELY (mpfr_overflow_p ())) {
        inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN (xt));
        MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
        break;
      }
      d = MPFR_GET_EXP (t);
      mpfr_ui_div (ti, 1, t, GMP_RNDU); /* 1/exp(x) */
      mpfr_sub (t, t, ti, GMP_RNDN);    /* exp(x) - 1/exp(x) */
      mpfr_div_2ui (t, t, 1, GMP_RNDN);  /* 1/2(exp(x) - 1/exp(x)) */

      /* it may be that t is zero (in fact, it can only occur when te=1,
         and thus ti=1 too) */
      if (MPFR_IS_ZERO (t))
        err = Nt; /* double the precision */
      else
        {
          /* calculation of the error */
          d = d - MPFR_GET_EXP (t) + 2;
          /* error estimate: err = Nt-(__gmpfr_ceil_log2(1+pow(2,d)));*/
          err = Nt - (MAX (d, 0) + 1);
          if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, MPFR_PREC (y), rnd_mode)))
            {
              inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (xt));
              break;
            }
        }
      /* actualisation of the precision */
      Nt += err;
      MPFR_ZIV_NEXT (loop, Nt);
      MPFR_GROUP_REPREC_2 (group, Nt, t, ti);
    }
    MPFR_ZIV_FREE (loop);
    MPFR_GROUP_CLEAR (group);
    MPFR_SAVE_EXPO_FREE (expo);
  }

  MPFR_RET (mpfr_check_range (y, inexact, rnd_mode));
}