1*d30dc8cbSJohn Marino /* mpc_acosh -- inverse hyperbolic cosine of a complex number.
2*d30dc8cbSJohn Marino
3*d30dc8cbSJohn Marino Copyright (C) 2009, 2011, 2012 INRIA
4*d30dc8cbSJohn Marino
5*d30dc8cbSJohn Marino This file is part of GNU MPC.
6*d30dc8cbSJohn Marino
7*d30dc8cbSJohn Marino GNU MPC is free software; you can redistribute it and/or modify it under
8*d30dc8cbSJohn Marino the terms of the GNU Lesser General Public License as published by the
9*d30dc8cbSJohn Marino Free Software Foundation; either version 3 of the License, or (at your
10*d30dc8cbSJohn Marino option) any later version.
11*d30dc8cbSJohn Marino
12*d30dc8cbSJohn Marino GNU MPC is distributed in the hope that it will be useful, but WITHOUT ANY
13*d30dc8cbSJohn Marino WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
14*d30dc8cbSJohn Marino FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
15*d30dc8cbSJohn Marino more details.
16*d30dc8cbSJohn Marino
17*d30dc8cbSJohn Marino You should have received a copy of the GNU Lesser General Public License
18*d30dc8cbSJohn Marino along with this program. If not, see http://www.gnu.org/licenses/ .
19*d30dc8cbSJohn Marino */
20*d30dc8cbSJohn Marino
21*d30dc8cbSJohn Marino #include "mpc-impl.h"
22*d30dc8cbSJohn Marino
23*d30dc8cbSJohn Marino int
mpc_acosh(mpc_ptr rop,mpc_srcptr op,mpc_rnd_t rnd)24*d30dc8cbSJohn Marino mpc_acosh (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
25*d30dc8cbSJohn Marino {
26*d30dc8cbSJohn Marino /* acosh(z) =
27*d30dc8cbSJohn Marino NaN + i*NaN, if z=0+i*NaN
28*d30dc8cbSJohn Marino -i*acos(z), if sign(Im(z)) = -
29*d30dc8cbSJohn Marino i*acos(z), if sign(Im(z)) = +
30*d30dc8cbSJohn Marino http://functions.wolfram.com/ElementaryFunctions/ArcCosh/27/02/03/01/01/
31*d30dc8cbSJohn Marino */
32*d30dc8cbSJohn Marino mpc_t a;
33*d30dc8cbSJohn Marino mpfr_t tmp;
34*d30dc8cbSJohn Marino int inex;
35*d30dc8cbSJohn Marino
36*d30dc8cbSJohn Marino if (mpfr_zero_p (mpc_realref (op)) && mpfr_nan_p (mpc_imagref (op)))
37*d30dc8cbSJohn Marino {
38*d30dc8cbSJohn Marino mpfr_set_nan (mpc_realref (rop));
39*d30dc8cbSJohn Marino mpfr_set_nan (mpc_imagref (rop));
40*d30dc8cbSJohn Marino return 0;
41*d30dc8cbSJohn Marino }
42*d30dc8cbSJohn Marino
43*d30dc8cbSJohn Marino /* Note reversal of precisions due to later multiplication by i or -i */
44*d30dc8cbSJohn Marino mpc_init3 (a, MPC_PREC_IM(rop), MPC_PREC_RE(rop));
45*d30dc8cbSJohn Marino
46*d30dc8cbSJohn Marino if (mpfr_signbit (mpc_imagref (op)))
47*d30dc8cbSJohn Marino {
48*d30dc8cbSJohn Marino inex = mpc_acos (a, op,
49*d30dc8cbSJohn Marino MPC_RND (INV_RND (MPC_RND_IM (rnd)), MPC_RND_RE (rnd)));
50*d30dc8cbSJohn Marino
51*d30dc8cbSJohn Marino /* change a to -i*a, i.e., -y+i*x to x+i*y */
52*d30dc8cbSJohn Marino tmp[0] = mpc_realref (a)[0];
53*d30dc8cbSJohn Marino mpc_realref (a)[0] = mpc_imagref (a)[0];
54*d30dc8cbSJohn Marino mpc_imagref (a)[0] = tmp[0];
55*d30dc8cbSJohn Marino MPFR_CHANGE_SIGN (mpc_imagref (a));
56*d30dc8cbSJohn Marino inex = MPC_INEX (MPC_INEX_IM (inex), -MPC_INEX_RE (inex));
57*d30dc8cbSJohn Marino }
58*d30dc8cbSJohn Marino else
59*d30dc8cbSJohn Marino {
60*d30dc8cbSJohn Marino inex = mpc_acos (a, op,
61*d30dc8cbSJohn Marino MPC_RND (MPC_RND_IM (rnd), INV_RND(MPC_RND_RE (rnd))));
62*d30dc8cbSJohn Marino
63*d30dc8cbSJohn Marino /* change a to i*a, i.e., y-i*x to x+i*y */
64*d30dc8cbSJohn Marino tmp[0] = mpc_realref (a)[0];
65*d30dc8cbSJohn Marino mpc_realref (a)[0] = mpc_imagref (a)[0];
66*d30dc8cbSJohn Marino mpc_imagref (a)[0] = tmp[0];
67*d30dc8cbSJohn Marino MPFR_CHANGE_SIGN (mpc_realref (a));
68*d30dc8cbSJohn Marino inex = MPC_INEX (-MPC_INEX_IM (inex), MPC_INEX_RE (inex));
69*d30dc8cbSJohn Marino }
70*d30dc8cbSJohn Marino
71*d30dc8cbSJohn Marino mpc_set (rop, a, rnd);
72*d30dc8cbSJohn Marino
73*d30dc8cbSJohn Marino mpc_clear (a);
74*d30dc8cbSJohn Marino
75*d30dc8cbSJohn Marino return inex;
76*d30dc8cbSJohn Marino }
77