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 } 77