1 /* mpfr_tanh -- hyperbolic tangent
2
3 Copyright 2001-2023 Free Software Foundation, Inc.
4 Contributed by the AriC and Caramba 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 https://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 int
27 mpfr_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[%Pd]=%.*Rg rnd=%d", mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode),
36 ("y[%Pd]=%.*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 /* initialize 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 /* The error analysis in algorithms.tex assumes that x is exactly
102 representable with working precision Nt.
103 FIXME: adapt the error analysis for the case Nt < PREC(x). */
104 if (Nt < MPFR_PREC(x))
105 Nt = MPFR_PREC(x);
106
107 /* initialize of intermediary variable */
108 MPFR_GROUP_INIT_2 (group, Nt, t, te);
109
110 MPFR_ZIV_INIT (loop, Nt);
111 for (;;)
112 {
113 /* tanh = (exp(2x)-1)/(exp(2x)+1) */
114 inexact = mpfr_mul_2ui (te, x, 1, MPFR_RNDN); /* 2x */
115 MPFR_ASSERTD(inexact == 0); /* see FIXME above */
116 /* since x > 0, we can only have an overflow */
117 mpfr_exp (te, te, MPFR_RNDN); /* exp(2x) */
118 if (MPFR_UNLIKELY (MPFR_IS_INF (te)))
119 {
120 set_one:
121 inexact = MPFR_FROM_SIGN_TO_INT (sign);
122 mpfr_set4 (y, __gmpfr_one, MPFR_RNDN, sign);
123 if (MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG_SIGN (sign)))
124 {
125 inexact = -inexact;
126 mpfr_nexttozero (y);
127 }
128 break;
129 }
130 d = MPFR_GET_EXP (te); /* For Error calculation */
131 mpfr_add_ui (t, te, 1, MPFR_RNDD); /* exp(2x) + 1 */
132 mpfr_sub_ui (te, te, 1, MPFR_RNDU); /* exp(2x) - 1 */
133 d = d - MPFR_GET_EXP (te);
134 mpfr_div (t, te, t, MPFR_RNDN); /* (exp(2x)-1)/(exp(2x)+1) */
135
136 /* Calculation of the error, see algorithms.tex; the current value
137 of d is k in algorithms.tex. */
138 d = MAX(3, d + 1); /* d = exponent in 2^(max(3,k+1)) */
139 err = Nt - (d + 1);
140
141 /* The inequality is the condition max(3,k+1) <= floor(p/2). */
142 if (MPFR_LIKELY (d <= Nt / 2 &&
143 MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
144 {
145 inexact = mpfr_set4 (y, t, rnd_mode, sign);
146 break;
147 }
148
149 /* if t=1, we still can round since |sinh(x)| < 1 */
150 if (MPFR_GET_EXP (t) == 1)
151 goto set_one;
152
153 /* Actualisation of the precision */
154 MPFR_ZIV_NEXT (loop, Nt);
155 MPFR_GROUP_REPREC_2 (group, Nt, t, te);
156 }
157 MPFR_ZIV_FREE (loop);
158 MPFR_GROUP_CLEAR (group);
159 }
160 MPFR_SAVE_EXPO_FREE (expo);
161 inexact = mpfr_check_range (y, inexact, rnd_mode);
162
163 return inexact;
164 }
165