src/acosh.c - master - niceSOFT/mpc

src/acosh.c
83 строки3 KB
Paul Zimmermann
added comment
18 окт 2024, 10:54
18 окт 2024, 10:54b363792
/* 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"

/* We compute acosh(z) using i*acos(z) if Im(z) > 0,
                            -i*acos(z) if Im(z) < 0.
   An alternate formula is Kahan's formula:
   acosh(z) = 2*log(sqrt(0.5*(z+1))+sqrt(0.5*(z-1)))
   (see Table 1 of https://people.freebsd.org/~das/kahan86branch.pdf)
*/

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;
}