1/* mpfr_tanh -- hyperbolic tangent 2 3Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc. 4Contributed by the AriC and Caramel projects, INRIA. 5 6This file is part of the GNU MPFR Library. 7 8The GNU MPFR Library is free software; you can redistribute it and/or modify 9it under the terms of the GNU Lesser General Public License as published by 10the Free Software Foundation; either version 3 of the License, or (at your 11option) any later version. 12 13The GNU MPFR Library is distributed in the hope that it will be useful, but 14WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 15or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 16License for more details. 17 18You should have received a copy of the GNU Lesser General Public License 19along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see 20http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., 2151 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ 22 23#define MPFR_NEED_LONGLONG_H 24#include "mpfr-impl.h" 25 26int 27mpfr_tanh (mpfr_ptr y, mpfr_srcptr xt , mpfr_rnd_t rnd_mode) 28{ 29 /****** Declaration ******/ 30 mpfr_t x; 31 int inexact; 32 MPFR_SAVE_EXPO_DECL (expo); 33 34 MPFR_LOG_FUNC 35 (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode), 36 ("y[%Pu]=%.*Rg inexact=%d", 37 mpfr_get_prec (y), mpfr_log_prec, y, inexact)); 38 39 /* Special value checking */ 40 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt))) 41 { 42 if (MPFR_IS_NAN (xt)) 43 { 44 MPFR_SET_NAN (y); 45 MPFR_RET_NAN; 46 } 47 else if (MPFR_IS_INF (xt)) 48 { 49 /* tanh(inf) = 1 && tanh(-inf) = -1 */ 50 return mpfr_set_si (y, MPFR_INT_SIGN (xt), rnd_mode); 51 } 52 else /* tanh (0) = 0 and xt is zero */ 53 { 54 MPFR_ASSERTD (MPFR_IS_ZERO(xt)); 55 MPFR_SET_ZERO (y); 56 MPFR_SET_SAME_SIGN (y, xt); 57 MPFR_RET (0); 58 } 59 } 60 61 /* tanh(x) = x - x^3/3 + ... so the error is < 2^(3*EXP(x)-1) */ 62 MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, xt, -2 * MPFR_GET_EXP (xt), 1, 0, 63 rnd_mode, {}); 64 65 MPFR_TMP_INIT_ABS (x, xt); 66 67 MPFR_SAVE_EXPO_MARK (expo); 68 69 /* General case */ 70 { 71 /* Declaration of the intermediary variable */ 72 mpfr_t t, te; 73 mpfr_exp_t d; 74 75 /* Declaration of the size variable */ 76 mpfr_prec_t Ny = MPFR_PREC(y); /* target precision */ 77 mpfr_prec_t Nt; /* working precision */ 78 long int err; /* error */ 79 int sign = MPFR_SIGN (xt); 80 MPFR_ZIV_DECL (loop); 81 MPFR_GROUP_DECL (group); 82 83 /* First check for BIG overflow of exp(2*x): 84 For x > 0, exp(2*x) > 2^(2*x) 85 If 2 ^(2*x) > 2^emax or x>emax/2, there is an overflow */ 86 if (MPFR_UNLIKELY (mpfr_cmp_si (x, __gmpfr_emax/2) >= 0)) { 87 /* initialise of intermediary variables 88 since 'set_one' label assumes the variables have been 89 initialize */ 90 MPFR_GROUP_INIT_2 (group, MPFR_PREC_MIN, t, te); 91 goto set_one; 92 } 93 94 /* Compute the precision of intermediary variable */ 95 /* The optimal number of bits: see algorithms.tex */ 96 Nt = Ny + MPFR_INT_CEIL_LOG2 (Ny) + 4; 97 /* if x is small, there will be a cancellation in exp(2x)-1 */ 98 if (MPFR_GET_EXP (x) < 0) 99 Nt += -MPFR_GET_EXP (x); 100 101 /* initialise of intermediary variable */ 102 MPFR_GROUP_INIT_2 (group, Nt, t, te); 103 104 MPFR_ZIV_INIT (loop, Nt); 105 for (;;) { 106 /* tanh = (exp(2x)-1)/(exp(2x)+1) */ 107 mpfr_mul_2ui (te, x, 1, MPFR_RNDN); /* 2x */ 108 /* since x > 0, we can only have an overflow */ 109 mpfr_exp (te, te, MPFR_RNDN); /* exp(2x) */ 110 if (MPFR_UNLIKELY (MPFR_IS_INF (te))) { 111 set_one: 112 inexact = MPFR_FROM_SIGN_TO_INT (sign); 113 mpfr_set4 (y, __gmpfr_one, MPFR_RNDN, sign); 114 if (MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG_SIGN (sign))) 115 { 116 inexact = -inexact; 117 mpfr_nexttozero (y); 118 } 119 break; 120 } 121 d = MPFR_GET_EXP (te); /* For Error calculation */ 122 mpfr_add_ui (t, te, 1, MPFR_RNDD); /* exp(2x) + 1*/ 123 mpfr_sub_ui (te, te, 1, MPFR_RNDU); /* exp(2x) - 1*/ 124 d = d - MPFR_GET_EXP (te); 125 mpfr_div (t, te, t, MPFR_RNDN); /* (exp(2x)-1)/(exp(2x)+1)*/ 126 127 /* Calculation of the error */ 128 d = MAX(3, d + 1); 129 err = Nt - (d + 1); 130 131 if (MPFR_LIKELY ((d <= Nt / 2) && MPFR_CAN_ROUND (t, err, Ny, rnd_mode))) 132 { 133 inexact = mpfr_set4 (y, t, rnd_mode, sign); 134 break; 135 } 136 137 /* if t=1, we still can round since |sinh(x)| < 1 */ 138 if (MPFR_GET_EXP (t) == 1) 139 goto set_one; 140 141 /* Actualisation of the precision */ 142 MPFR_ZIV_NEXT (loop, Nt); 143 MPFR_GROUP_REPREC_2 (group, Nt, t, te); 144 } 145 MPFR_ZIV_FREE (loop); 146 MPFR_GROUP_CLEAR (group); 147 } 148 MPFR_SAVE_EXPO_FREE (expo); 149 inexact = mpfr_check_range (y, inexact, rnd_mode); 150 151 return inexact; 152} 153 154