/* mpc_acosh -- inverse hyperbolic cosine of a complex number.

Copyright (C) 2009, 2011, 2012 INRIA

This file is part of GNU MPC.

GNU MPC 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 3 of the License, or (at your

option) any later version.

GNU MPC 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 program. If not, see http://www.gnu.org/licenses/ .

*/

#include "mpc-impl.h"

int

mpc_acosh (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)

{

  /* acosh(z) =

      NaN + i*NaN, if z=0+i*NaN

     -i*acos(z), if sign(Im(z)) = -

      i*acos(z), if sign(Im(z)) = +

      http://functions.wolfram.com/ElementaryFunctions/ArcCosh/27/02/03/01/01/

  */

  mpc_t a;

  mpfr_t tmp;

  int inex;

  if (mpfr_zero_p (mpc_realref (op)) && mpfr_nan_p (mpc_imagref (op)))

    {

      mpfr_set_nan (mpc_realref (rop));

      mpfr_set_nan (mpc_imagref (rop));

      return 0;

    }

  /* Note reversal of precisions due to later multiplication by i or -i */

  mpc_init3 (a, MPC_PREC_IM(rop), MPC_PREC_RE(rop));

  if (mpfr_signbit (mpc_imagref (op)))

    {

      inex = mpc_acos (a, op,

                       MPC_RND (INV_RND (MPC_RND_IM (rnd)), MPC_RND_RE (rnd)));

      /* change a to -i*a, i.e., -y+i*x to x+i*y */

      tmp[0] = mpc_realref (a)[0];

      mpc_realref (a)[0] = mpc_imagref (a)[0];

      mpc_imagref (a)[0] = tmp[0];

      MPFR_CHANGE_SIGN (mpc_imagref (a));

      inex = MPC_INEX (MPC_INEX_IM (inex), -MPC_INEX_RE (inex));

    }

  else

    {

      inex = mpc_acos (a, op,

                       MPC_RND (MPC_RND_IM (rnd), INV_RND(MPC_RND_RE (rnd))));

      /* change a to i*a, i.e., y-i*x to x+i*y */

      tmp[0] = mpc_realref (a)[0];

      mpc_realref (a)[0] = mpc_imagref (a)[0];

      mpc_imagref (a)[0] = tmp[0];

      MPFR_CHANGE_SIGN (mpc_realref (a));

      inex = MPC_INEX (-MPC_INEX_IM (inex), MPC_INEX_RE (inex));

    }

  mpc_set (rop, a, rnd);

  mpc_clear (a);

  return inex;

}