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}
132weak_alias (__ctanhl, ctanhl)
133