1 /* mpfr_cosh -- hyperbolic cosine
2
3 Copyright 2001-2002, 2004-2023 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 /* The computation of cosh is done by *
27 * cosh= 1/2[e^(x)+e^(-x)] */
28
29 int
30 mpfr_cosh (mpfr_ptr y, mpfr_srcptr xt, mpfr_rnd_t rnd_mode)
31 {
32 mpfr_t x;
33 int inexact;
34 MPFR_SAVE_EXPO_DECL (expo);
35
36 MPFR_LOG_FUNC (
37 ("x[%Pd]=%.*Rg rnd=%d", mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode),
38 ("y[%Pd]=%.*Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y,
39 inexact));
40
41 if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(xt)))
42 {
43 if (MPFR_IS_NAN(xt))
44 {
45 MPFR_SET_NAN(y);
46 MPFR_RET_NAN;
47 }
48 else if (MPFR_IS_INF(xt))
49 {
50 MPFR_SET_INF(y);
51 MPFR_SET_POS(y);
52 MPFR_RET(0);
53 }
54 else
55 {
56 MPFR_ASSERTD(MPFR_IS_ZERO(xt));
57 return mpfr_set_ui (y, 1, rnd_mode); /* cosh(0) = 1 */
58 }
59 }
60
61 MPFR_SAVE_EXPO_MARK (expo);
62
63 /* cosh(x) = 1+x^2/2 + ... <= 1+x^2 for x <= 2.9828...,
64 thus the error < 2^(2*EXP(x)). If x >= 1, then EXP(x) >= 1,
65 thus the following will always fail. */
66 MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, __gmpfr_one, -2 * MPFR_GET_EXP (xt), 0,
67 1, rnd_mode, inexact = _inexact; goto end);
68
69 MPFR_TMP_INIT_ABS(x, xt);
70 /* General case */
71 {
72 /* Declaration of the intermediary variable */
73 mpfr_t t, te;
74 /* Declaration of the size variable */
75 mpfr_prec_t Ny = MPFR_PREC(y); /* Precision of output variable */
76 mpfr_prec_t Nt; /* Precision of the intermediary variable */
77 long int err; /* Precision of error */
78 MPFR_ZIV_DECL (loop);
79 MPFR_GROUP_DECL (group);
80
81 /* compute the precision of intermediary variable */
82 /* The optimal number of bits : see algorithms.tex */
83 Nt = Ny + 3 + MPFR_INT_CEIL_LOG2 (Ny);
84
85 /* initialize of intermediary variables */
86 MPFR_GROUP_INIT_2 (group, Nt, t, te);
87
88 /* First computation of cosh */
89 MPFR_ZIV_INIT (loop, Nt);
90 for (;;)
91 {
92 MPFR_BLOCK_DECL (flags);
93
94 /* Compute cosh */
95 MPFR_BLOCK (flags, mpfr_exp (te, x, MPFR_RNDD)); /* exp(x) */
96 /* exp can overflow (but not underflow since x>0) */
97 if (MPFR_OVERFLOW (flags))
98 /* cosh(x) > exp(x), cosh(x) underflows too */
99 {
100 inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN_POS);
101 MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
102 break;
103 }
104 mpfr_ui_div (t, 1, te, MPFR_RNDU); /* 1/exp(x) */
105 mpfr_add (t, te, t, MPFR_RNDU); /* exp(x) + 1/exp(x)*/
106 mpfr_div_2ui (t, t, 1, MPFR_RNDN); /* 1/2(exp(x) + 1/exp(x))*/
107
108 /* Estimation of the error */
109 err = Nt - 3;
110 /* Check if we can round */
111 if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
112 {
113 inexact = mpfr_set (y, t, rnd_mode);
114 break;
115 }
116
117 /* Actualisation of the precision */
118 MPFR_ZIV_NEXT (loop, Nt);
119 MPFR_GROUP_REPREC_2 (group, Nt, t, te);
120 }
121 MPFR_ZIV_FREE (loop);
122 MPFR_GROUP_CLEAR (group);
123 }
124
125 end:
126 MPFR_SAVE_EXPO_FREE (expo);
127 return mpfr_check_range (y, inexact, rnd_mode);
128 }