1/* Complex hyperbolic tangent for float types.
2 Copyright (C) 1997-2020 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
5
6 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
10
11 The GNU C Library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
15
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, see
18 <https://www.gnu.org/licenses/>. */
19
20#include <complex.h>
21#include <fenv.h>
22#include <math.h>
23#include <math_private.h>
24#include <math-underflow.h>
25#include <float.h>
26
27CFLOAT
28M_DECL_FUNC (__ctanh) (CFLOAT x)
29{
30 CFLOAT res;
31
32 if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
33 {
34 if (isinf (__real__ x))
35 {
36 __real__ res = M_COPYSIGN (1, __real__ x);
37 if (isfinite (__imag__ x) && M_FABS (__imag__ x) > 1)
38 {
39 FLOAT sinix, cosix;
40 M_SINCOS (__imag__ x, &sinix, &cosix);
41 __imag__ res = M_COPYSIGN (0, sinix * cosix);
42 }
43 else
44 __imag__ res = M_COPYSIGN (0, __imag__ x);
45 }
46 else if (__imag__ x == 0)
47 {
48 res = x;
49 }
50 else
51 {
52 if (__real__ x == 0)
53 __real__ res = __real__ x;
54 else
55 __real__ res = M_NAN;
56 __imag__ res = M_NAN;
57
58 if (isinf (__imag__ x))
59 feraiseexcept (FE_INVALID);
60 }
61 }
62 else
63 {
64 FLOAT sinix, cosix;
65 FLOAT den;
66 const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2) / 2);
67
68 /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
69 = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
70
71 if (__glibc_likely (M_FABS (__imag__ x) > M_MIN))
72 {
73 M_SINCOS (__imag__ x, &sinix, &cosix);
74 }
75 else
76 {
77 sinix = __imag__ x;
78 cosix = 1;
79 }
80
81 if (M_FABS (__real__ x) > t)
82 {
83 /* Avoid intermediate overflow when the imaginary part of
84 the result may be subnormal. Ignoring negligible terms,
85 the real part is +/- 1, the imaginary part is
86 sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */
87 FLOAT exp_2t = M_EXP (2 * t);
88
89 __real__ res = M_COPYSIGN (1, __real__ x);
90 __imag__ res = 4 * sinix * cosix;
91 __real__ x = M_FABS (__real__ x);
92 __real__ x -= t;
93 __imag__ res /= exp_2t;
94 if (__real__ x > t)
95 {
96 /* Underflow (original real part of x has absolute value
97 > 2t). */
98 __imag__ res /= exp_2t;
99 }
100 else
101 __imag__ res /= M_EXP (2 * __real__ x);
102 }
103 else
104 {
105 FLOAT sinhrx, coshrx;
106 if (M_FABS (__real__ x) > M_MIN)
107 {
108 sinhrx = M_SINH (__real__ x);
109 coshrx = M_COSH (__real__ x);
110 }
111 else
112 {
113 sinhrx = __real__ x;
114 coshrx = 1;
115 }
116
117 if (M_FABS (sinhrx) > M_FABS (cosix) * M_EPSILON)
118 den = sinhrx * sinhrx + cosix * cosix;
119 else
120 den = cosix * cosix;
121 __real__ res = sinhrx * coshrx / den;
122 __imag__ res = sinix * cosix / den;
123 }
124 math_check_force_underflow_complex (res);
125 }
126
127 return res;
128}
129
130declare_mgen_alias (__ctanh, ctanh)
131