1 | /* Complex hyperbole tangent for long 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 | /* To avoid spurious underflows, use this definition to treat IBM long |
27 | double as approximating an IEEE-style format. */ |
28 | #if LDBL_MANT_DIG == 106 |
29 | # undef LDBL_EPSILON |
30 | # define LDBL_EPSILON 0x1p-106L |
31 | #endif |
32 | |
33 | __complex__ long double |
34 | __ctanhl (__complex__ long double x) |
35 | { |
36 | __complex__ long double res; |
37 | |
38 | if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x))) |
39 | { |
40 | if (isinf (__real__ x)) |
41 | { |
42 | __real__ res = __copysignl (1.0, __real__ x); |
43 | if (isfinite (__imag__ x) && fabsl (__imag__ x) > 1.0L) |
44 | { |
45 | long double sinix, cosix; |
46 | __sincosl (__imag__ x, &sinix, &cosix); |
47 | __imag__ res = __copysignl (0.0L, sinix * cosix); |
48 | } |
49 | else |
50 | __imag__ res = __copysignl (0.0, __imag__ x); |
51 | } |
52 | else if (__imag__ x == 0.0) |
53 | { |
54 | res = x; |
55 | } |
56 | else |
57 | { |
58 | __real__ res = __nanl ("" ); |
59 | __imag__ res = __nanl ("" ); |
60 | |
61 | if (isinf (__imag__ x)) |
62 | feraiseexcept (FE_INVALID); |
63 | } |
64 | } |
65 | else |
66 | { |
67 | long double sinix, cosix; |
68 | long double den; |
69 | const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2); |
70 | |
71 | /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y)) |
72 | = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */ |
73 | |
74 | if (__glibc_likely (fabsl (__imag__ x) > LDBL_MIN)) |
75 | { |
76 | __sincosl (__imag__ x, &sinix, &cosix); |
77 | } |
78 | else |
79 | { |
80 | sinix = __imag__ x; |
81 | cosix = 1.0; |
82 | } |
83 | |
84 | if (fabsl (__real__ x) > t) |
85 | { |
86 | /* Avoid intermediate overflow when the imaginary part of |
87 | the result may be subnormal. Ignoring negligible terms, |
88 | the real part is +/- 1, the imaginary part is |
89 | sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */ |
90 | long double exp_2t = __ieee754_expl (2 * t); |
91 | |
92 | __real__ res = __copysignl (1.0, __real__ x); |
93 | __imag__ res = 4 * sinix * cosix; |
94 | __real__ x = fabsl (__real__ x); |
95 | __real__ x -= t; |
96 | __imag__ res /= exp_2t; |
97 | if (__real__ x > t) |
98 | { |
99 | /* Underflow (original real part of x has absolute value |
100 | > 2t). */ |
101 | __imag__ res /= exp_2t; |
102 | } |
103 | else |
104 | __imag__ res /= __ieee754_expl (2 * __real__ x); |
105 | } |
106 | else |
107 | { |
108 | long double sinhrx, coshrx; |
109 | if (fabsl (__real__ x) > LDBL_MIN) |
110 | { |
111 | sinhrx = __ieee754_sinhl (__real__ x); |
112 | coshrx = __ieee754_coshl (__real__ x); |
113 | } |
114 | else |
115 | { |
116 | sinhrx = __real__ x; |
117 | coshrx = 1.0L; |
118 | } |
119 | |
120 | if (fabsl (sinhrx) > fabsl (cosix) * LDBL_EPSILON) |
121 | den = sinhrx * sinhrx + cosix * cosix; |
122 | else |
123 | den = cosix * cosix; |
124 | __real__ res = sinhrx * coshrx / den; |
125 | __imag__ res = sinix * cosix / den; |
126 | } |
127 | math_check_force_underflow_complex (res); |
128 | } |
129 | |
130 | return res; |
131 | } |
132 | weak_alias (__ctanhl, ctanhl) |
133 | |