1 /* Complex hyperbole tangent for __float128.
2 Copyright (C) 1997-2012 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 "quadmath-imp.h"
21
22 #ifdef HAVE_FENV_H
23 # include <fenv.h>
24 #endif
25
26
27 __complex128
ctanhq(__complex128 x)28 ctanhq (__complex128 x)
29 {
30 __complex128 res;
31
32 if (__builtin_expect (!finiteq (__real__ x) || !finiteq (__imag__ x), 0))
33 {
34 if (__quadmath_isinf_nsq (__real__ x))
35 {
36 __real__ res = copysignq (1.0Q, __real__ x);
37 __imag__ res = copysignq (0.0Q, __imag__ x);
38 }
39 else if (__imag__ x == 0.0Q)
40 {
41 res = x;
42 }
43 else
44 {
45 __real__ res = nanq ("");
46 __imag__ res = nanq ("");
47
48 #ifdef HAVE_FENV_H
49 if (__quadmath_isinf_nsq (__imag__ x))
50 feraiseexcept (FE_INVALID);
51 #endif
52 }
53 }
54 else
55 {
56 __float128 sinix, cosix;
57 __float128 den;
58 const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q / 2);
59 int icls = fpclassifyq (__imag__ x);
60
61 /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
62 = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
63
64 if (__builtin_expect (icls != QUADFP_SUBNORMAL, 1))
65 {
66 sincosq (__imag__ x, &sinix, &cosix);
67 }
68 else
69 {
70 sinix = __imag__ x;
71 cosix = 1.0Q;
72 }
73
74 if (fabsq (__real__ x) > t)
75 {
76 /* Avoid intermediate overflow when the imaginary part of
77 the result may be subnormal. Ignoring negligible terms,
78 the real part is +/- 1, the imaginary part is
79 sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */
80 __float128 exp_2t = expq (2 * t);
81
82 __real__ res = copysignq (1.0, __real__ x);
83 __imag__ res = 4 * sinix * cosix;
84 __real__ x = fabsq (__real__ x);
85 __real__ x -= t;
86 __imag__ res /= exp_2t;
87 if (__real__ x > t)
88 {
89 /* Underflow (original real part of x has absolute value
90 > 2t). */
91 __imag__ res /= exp_2t;
92 }
93 else
94 __imag__ res /= expq (2 * __real__ x);
95 }
96 else
97 {
98 __float128 sinhrx, coshrx;
99 if (fabsq (__real__ x) > FLT128_MIN)
100 {
101 sinhrx = sinhq (__real__ x);
102 coshrx = coshq (__real__ x);
103 }
104 else
105 {
106 sinhrx = __real__ x;
107 coshrx = 1.0Q;
108 }
109
110 if (fabsq (sinhrx) > fabsq (cosix) * FLT128_EPSILON)
111 den = sinhrx * sinhrx + cosix * cosix;
112 else
113 den = cosix * cosix;
114 __real__ res = sinhrx * coshrx / den;
115 __imag__ res = sinix * cosix / den;
116 }
117 }
118
119 return res;
120 }
121