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 | } |
125 | weak_alias (__ctanh, ctanh) |
126 | #ifdef NO_LONG_DOUBLE |
127 | strong_alias (__ctanh, __ctanhl) |
128 | weak_alias (__ctanh, ctanhl) |
129 | #endif |
130 | |