145
|
1 /* Complex hyperbolic tangent for float types.
|
|
2 Copyright (C) 1997-2018 Free Software Foundation, Inc.
|
111
|
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
|
|
23 ctanhq (__complex128 x)
|
|
24 {
|
|
25 __complex128 res;
|
|
26
|
145
|
27 if (__glibc_unlikely (!finiteq (__real__ x) || !finiteq (__imag__ x)))
|
111
|
28 {
|
145
|
29 if (isinfq (__real__ x))
|
111
|
30 {
|
145
|
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);
|
111
|
40 }
|
145
|
41 else if (__imag__ x == 0)
|
111
|
42 {
|
|
43 res = x;
|
|
44 }
|
|
45 else
|
|
46 {
|
145
|
47 if (__real__ x == 0)
|
|
48 __real__ res = __real__ x;
|
|
49 else
|
|
50 __real__ res = nanq ("");
|
111
|
51 __imag__ res = nanq ("");
|
|
52
|
145
|
53 if (isinfq (__imag__ x))
|
111
|
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
|
145
|
66 if (__glibc_likely (fabsq (__imag__ x) > FLT128_MIN))
|
111
|
67 {
|
|
68 sincosq (__imag__ x, &sinix, &cosix);
|
|
69 }
|
|
70 else
|
|
71 {
|
|
72 sinix = __imag__ x;
|
145
|
73 cosix = 1;
|
111
|
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
|
145
|
84 __real__ res = copysignq (1, __real__ x);
|
111
|
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;
|
145
|
109 coshrx = 1;
|
111
|
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 }
|
145
|
119 math_check_force_underflow_complex (res);
|
111
|
120 }
|
|
121
|
|
122 return res;
|
|
123 }
|