1 /* mpfr_asinh -- inverse hyperbolic sine 2 3 Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc. 4 Contributed by the AriC and Caramel projects, INRIA. 5 6 This file is part of the GNU MPFR Library. 7 8 The GNU MPFR Library is free software; you can redistribute it and/or modify 9 it under the terms of the GNU Lesser General Public License as published by 10 the Free Software Foundation; either version 3 of the License, or (at your 11 option) any later version. 12 13 The GNU MPFR Library is distributed in the hope that it will be useful, but 14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 15 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 16 License for more details. 17 18 You should have received a copy of the GNU Lesser General Public License 19 along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see 20 http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., 21 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ 22 23 #define MPFR_NEED_LONGLONG_H 24 #include "mpfr-impl.h" 25 26 /* The computation of asinh is done by * 27 * asinh = ln(x + sqrt(x^2 + 1)) */ 28 29 int 30 mpfr_asinh (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode) 31 { 32 int inexact; 33 int signx, neg; 34 mpfr_prec_t Ny, Nt; 35 mpfr_t t; /* auxiliary variables */ 36 mpfr_exp_t err; 37 MPFR_SAVE_EXPO_DECL (expo); 38 MPFR_ZIV_DECL (loop); 39 40 MPFR_LOG_FUNC ( 41 ("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode), 42 ("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y, 43 inexact)); 44 45 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) 46 { 47 if (MPFR_IS_NAN (x)) 48 { 49 MPFR_SET_NAN (y); 50 MPFR_RET_NAN; 51 } 52 else if (MPFR_IS_INF (x)) 53 { 54 MPFR_SET_INF (y); 55 MPFR_SET_SAME_SIGN (y, x); 56 MPFR_RET (0); 57 } 58 else /* x is necessarily 0 */ 59 { 60 MPFR_ASSERTD (MPFR_IS_ZERO (x)); 61 MPFR_SET_ZERO (y); /* asinh(0) = 0 */ 62 MPFR_SET_SAME_SIGN (y, x); 63 MPFR_RET (0); 64 } 65 } 66 67 /* asinh(x) = x - x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */ 68 MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -2 * MPFR_GET_EXP (x), 2, 0, 69 rnd_mode, {}); 70 71 Ny = MPFR_PREC (y); /* Precision of output variable */ 72 73 signx = MPFR_SIGN (x); 74 neg = MPFR_IS_NEG (x); 75 76 /* General case */ 77 78 /* compute the precision of intermediary variable */ 79 /* the optimal number of bits : see algorithms.tex */ 80 Nt = Ny + 4 + MPFR_INT_CEIL_LOG2 (Ny); 81 82 MPFR_SAVE_EXPO_MARK (expo); 83 84 /* initialize intermediary variables */ 85 mpfr_init2 (t, Nt); 86 87 /* First computation of asinh */ 88 MPFR_ZIV_INIT (loop, Nt); 89 for (;;) 90 { 91 /* compute asinh */ 92 mpfr_mul (t, x, x, MPFR_RNDD); /* x^2 */ 93 mpfr_add_ui (t, t, 1, MPFR_RNDD); /* x^2+1 */ 94 mpfr_sqrt (t, t, MPFR_RNDN); /* sqrt(x^2+1) */ 95 (neg ? mpfr_sub : mpfr_add) (t, t, x, MPFR_RNDN); /* sqrt(x^2+1)+x */ 96 mpfr_log (t, t, MPFR_RNDN); /* ln(sqrt(x^2+1)+x)*/ 97 98 if (MPFR_LIKELY (MPFR_IS_PURE_FP (t))) 99 { 100 /* error estimate -- see algorithms.tex */ 101 err = Nt - (MAX (4 - MPFR_GET_EXP (t), 0) + 1); 102 if (MPFR_LIKELY (MPFR_IS_ZERO (t) 103 || MPFR_CAN_ROUND (t, err, Ny, rnd_mode))) 104 break; 105 } 106 107 /* actualisation of the precision */ 108 MPFR_ZIV_NEXT (loop, Nt); 109 mpfr_set_prec (t, Nt); 110 } 111 MPFR_ZIV_FREE (loop); 112 113 inexact = mpfr_set4 (y, t, rnd_mode, signx); 114 115 mpfr_clear (t); 116 117 MPFR_SAVE_EXPO_FREE (expo); 118 return mpfr_check_range (y, inexact, rnd_mode); 119 } 120