contrib/mpc/src/acosh.c

   1 /* mpc_acosh -- inverse hyperbolic cosine of a complex number.
   2
   3 Copyright (C) 2009, 2011, 2012 INRIA
   4
   5 This file is part of GNU MPC.
   6
   7 GNU MPC is free software; you can redistribute it and/or modify it under
   8 the terms of the GNU Lesser General Public License as published by the
   9 Free Software Foundation; either version 3 of the License, or (at your
  10 option) any later version.
  11
  12 GNU MPC is distributed in the hope that it will be useful, but WITHOUT ANY
  13 WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
  14 FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
  15 more details.
  16
  17 You should have received a copy of the GNU Lesser General Public License
  18 along with this program. If not, see http://www.gnu.org/licenses/ .
  19 */
  20
  21 #include "mpc-impl.h"
  22
  23 int
  24 mpc_acosh (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
  25 {
  26   /* acosh(z) =
  27       NaN + i*NaN, if z=0+i*NaN
  28      -i*acos(z), if sign(Im(z)) = -
  29       i*acos(z), if sign(Im(z)) = +
  30       http://functions.wolfram.com/ElementaryFunctions/ArcCosh/27/02/03/01/01/
  31   */
  32   mpc_t a;
  33   mpfr_t tmp;
  34   int inex;
  35
  36   if (mpfr_zero_p (mpc_realref (op)) && mpfr_nan_p (mpc_imagref (op)))
  37     {
  38       mpfr_set_nan (mpc_realref (rop));
  39       mpfr_set_nan (mpc_imagref (rop));
  40       return 0;
  41     }
  42
  43   /* Note reversal of precisions due to later multiplication by i or -i */
  44   mpc_init3 (a, MPC_PREC_IM(rop), MPC_PREC_RE(rop));
  45
  46   if (mpfr_signbit (mpc_imagref (op)))
  47     {
  48       inex = mpc_acos (a, op,
  49                        MPC_RND (INV_RND (MPC_RND_IM (rnd)), MPC_RND_RE (rnd)));
  50
  51       /* change a to -i*a, i.e., -y+i*x to x+i*y */
  52       tmp[0] = mpc_realref (a)[0];
  53       mpc_realref (a)[0] = mpc_imagref (a)[0];
  54       mpc_imagref (a)[0] = tmp[0];
  55       MPFR_CHANGE_SIGN (mpc_imagref (a));
  56       inex = MPC_INEX (MPC_INEX_IM (inex), -MPC_INEX_RE (inex));
  57     }
  58   else
  59     {
  60       inex = mpc_acos (a, op,
  61                        MPC_RND (MPC_RND_IM (rnd), INV_RND(MPC_RND_RE (rnd))));
  62
  63       /* change a to i*a, i.e., y-i*x to x+i*y */
  64       tmp[0] = mpc_realref (a)[0];
  65       mpc_realref (a)[0] = mpc_imagref (a)[0];
  66       mpc_imagref (a)[0] = tmp[0];
  67       MPFR_CHANGE_SIGN (mpc_realref (a));
  68       inex = MPC_INEX (-MPC_INEX_IM (inex), MPC_INEX_RE (inex));
  69     }
  70
  71   mpc_set (rop, a, rnd);
  72
  73   mpc_clear (a);
  74
  75   return inex;
  76 }