1 /* Complex hyperbolic tangent for float types.
2 Copyright (C) 1997-2018 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 __complex128
ctanhq(__complex128 x)23 ctanhq (__complex128 x)
24 {
25 __complex128 res;
26
27 if (__glibc_unlikely (!finiteq (__real__ x) || !finiteq (__imag__ x)))
28 {
29 if (isinfq (__real__ x))
30 {
31 __real__ res = copysignq (1, __real__ x);
32 if (finiteq (__imag__ x) && fabsq (__imag__ x) > 1)
33 {
34 __float128 sinix, cosix;
35 sincosq (__imag__ x, &sinix, &cosix);
36 __imag__ res = copysignq (0, sinix * cosix);
37 }
38 else
39 __imag__ res = copysignq (0, __imag__ x);
40 }
41 else if (__imag__ x == 0)
42 {
43 res = x;
44 }
45 else
46 {
47 if (__real__ x == 0)
48 __real__ res = __real__ x;
49 else
50 __real__ res = nanq ("");
51 __imag__ res = nanq ("");
52
53 if (isinfq (__imag__ x))
54 feraiseexcept (FE_INVALID);
55 }
56 }
57 else
58 {
59 __float128 sinix, cosix;
60 __float128 den;
61 const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q / 2);
62
63 /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
64 = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
65
66 if (__glibc_likely (fabsq (__imag__ x) > FLT128_MIN))
67 {
68 sincosq (__imag__ x, &sinix, &cosix);
69 }
70 else
71 {
72 sinix = __imag__ x;
73 cosix = 1;
74 }
75
76 if (fabsq (__real__ x) > t)
77 {
78 /* Avoid intermediate overflow when the imaginary part of
79 the result may be subnormal. Ignoring negligible terms,
80 the real part is +/- 1, the imaginary part is
81 sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */
82 __float128 exp_2t = expq (2 * t);
83
84 __real__ res = copysignq (1, __real__ x);
85 __imag__ res = 4 * sinix * cosix;
86 __real__ x = fabsq (__real__ x);
87 __real__ x -= t;
88 __imag__ res /= exp_2t;
89 if (__real__ x > t)
90 {
91 /* Underflow (original real part of x has absolute value
92 > 2t). */
93 __imag__ res /= exp_2t;
94 }
95 else
96 __imag__ res /= expq (2 * __real__ x);
97 }
98 else
99 {
100 __float128 sinhrx, coshrx;
101 if (fabsq (__real__ x) > FLT128_MIN)
102 {
103 sinhrx = sinhq (__real__ x);
104 coshrx = coshq (__real__ x);
105 }
106 else
107 {
108 sinhrx = __real__ x;
109 coshrx = 1;
110 }
111
112 if (fabsq (sinhrx) > fabsq (cosix) * FLT128_EPSILON)
113 den = sinhrx * sinhrx + cosix * cosix;
114 else
115 den = cosix * cosix;
116 __real__ res = sinhrx * coshrx / den;
117 __imag__ res = sinix * cosix / den;
118 }
119 math_check_force_underflow_complex (res);
120 }
121
122 return res;
123 }
124