1/* Complex hyperbole tangent for double.
2 Copyright (C) 1997-2016 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 <http://www.gnu.org/licenses/>. */
19
20#include <complex.h>
21#include <fenv.h>
22#include <math.h>
23#include <math_private.h>
24#include <float.h>
25
26__complex__ double
27__ctanh (__complex__ double x)
28{
29 __complex__ double res;
30
31 if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
32 {
33 if (isinf (__real__ x))
34 {
35 __real__ res = __copysign (1.0, __real__ x);
36 if (isfinite (__imag__ x) && fabs (__imag__ x) > 1.0)
37 {
38 double sinix, cosix;
39 __sincos (__imag__ x, &sinix, &cosix);
40 __imag__ res = __copysign (0.0, sinix * cosix);
41 }
42 else
43 __imag__ res = __copysign (0.0, __imag__ x);
44 }
45 else if (__imag__ x == 0.0)
46 {
47 res = x;
48 }
49 else
50 {
51 __real__ res = __nan ("");
52 __imag__ res = __nan ("");
53
54 if (isinf (__imag__ x))
55 feraiseexcept (FE_INVALID);
56 }
57 }
58 else
59 {
60 double sinix, cosix;
61 double den;
62 const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2);
63
64 /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
65 = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
66
67 if (__glibc_likely (fabs (__imag__ x) > DBL_MIN))
68 {
69 __sincos (__imag__ x, &sinix, &cosix);
70 }
71 else
72 {
73 sinix = __imag__ x;
74 cosix = 1.0;
75 }
76
77 if (fabs (__real__ x) > t)
78 {
79 /* Avoid intermediate overflow when the imaginary part of
80 the result may be subnormal. Ignoring negligible terms,
81 the real part is +/- 1, the imaginary part is
82 sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */
83 double exp_2t = __ieee754_exp (2 * t);
84
85 __real__ res = __copysign (1.0, __real__ x);
86 __imag__ res = 4 * sinix * cosix;
87 __real__ x = fabs (__real__ x);
88 __real__ x -= t;
89 __imag__ res /= exp_2t;
90 if (__real__ x > t)
91 {
92 /* Underflow (original real part of x has absolute value
93 > 2t). */
94 __imag__ res /= exp_2t;
95 }
96 else
97 __imag__ res /= __ieee754_exp (2 * __real__ x);
98 }
99 else
100 {
101 double sinhrx, coshrx;
102 if (fabs (__real__ x) > DBL_MIN)
103 {
104 sinhrx = __ieee754_sinh (__real__ x);
105 coshrx = __ieee754_cosh (__real__ x);
106 }
107 else
108 {
109 sinhrx = __real__ x;
110 coshrx = 1.0;
111 }
112
113 if (fabs (sinhrx) > fabs (cosix) * DBL_EPSILON)
114 den = sinhrx * sinhrx + cosix * cosix;
115 else
116 den = cosix * cosix;
117 __real__ res = sinhrx * coshrx / den;
118 __imag__ res = sinix * cosix / den;
119 }
120 math_check_force_underflow_complex (res);
121 }
122
123 return res;
124}
125weak_alias (__ctanh, ctanh)
126#ifdef NO_LONG_DOUBLE
127strong_alias (__ctanh, __ctanhl)
128weak_alias (__ctanh, ctanhl)
129#endif
130