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d5602ceb | 1 | /* Complex hyperbolic tangent for float types. |
688903eb | 2 | Copyright (C) 1997-2018 Free Software Foundation, Inc. |
f6d3a72e PM |
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> | |
8f5b00d3 | 24 | #include <math-underflow.h> |
f6d3a72e PM |
25 | #include <float.h> |
26 | ||
d5602ceb PM |
27 | CFLOAT |
28 | M_DECL_FUNC (__ctanh) (CFLOAT x) | |
f6d3a72e | 29 | { |
d5602ceb | 30 | CFLOAT res; |
f6d3a72e PM |
31 | |
32 | if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x))) | |
33 | { | |
34 | if (isinf (__real__ x)) | |
35 | { | |
d5602ceb PM |
36 | __real__ res = M_COPYSIGN (1, __real__ x); |
37 | if (isfinite (__imag__ x) && M_FABS (__imag__ x) > 1) | |
f6d3a72e | 38 | { |
d5602ceb PM |
39 | FLOAT sinix, cosix; |
40 | M_SINCOS (__imag__ x, &sinix, &cosix); | |
41 | __imag__ res = M_COPYSIGN (0, sinix * cosix); | |
f6d3a72e PM |
42 | } |
43 | else | |
d5602ceb | 44 | __imag__ res = M_COPYSIGN (0, __imag__ x); |
f6d3a72e | 45 | } |
d5602ceb | 46 | else if (__imag__ x == 0) |
f6d3a72e PM |
47 | { |
48 | res = x; | |
49 | } | |
50 | else | |
51 | { | |
d15e83c5 JM |
52 | if (__real__ x == 0) |
53 | __real__ res = __real__ x; | |
54 | else | |
55 | __real__ res = M_NAN; | |
d5602ceb | 56 | __imag__ res = M_NAN; |
f6d3a72e PM |
57 | |
58 | if (isinf (__imag__ x)) | |
59 | feraiseexcept (FE_INVALID); | |
60 | } | |
61 | } | |
62 | else | |
63 | { | |
d5602ceb PM |
64 | FLOAT sinix, cosix; |
65 | FLOAT den; | |
66 | const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2) / 2); | |
f6d3a72e PM |
67 | |
68 | /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y)) | |
69 | = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */ | |
70 | ||
d5602ceb | 71 | if (__glibc_likely (M_FABS (__imag__ x) > M_MIN)) |
f6d3a72e | 72 | { |
d5602ceb | 73 | M_SINCOS (__imag__ x, &sinix, &cosix); |
f6d3a72e PM |
74 | } |
75 | else | |
76 | { | |
77 | sinix = __imag__ x; | |
d5602ceb | 78 | cosix = 1; |
f6d3a72e PM |
79 | } |
80 | ||
d5602ceb | 81 | if (M_FABS (__real__ x) > t) |
f6d3a72e PM |
82 | { |
83 | /* Avoid intermediate overflow when the imaginary part of | |
84 | the result may be subnormal. Ignoring negligible terms, | |
85 | the real part is +/- 1, the imaginary part is | |
86 | sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */ | |
d5602ceb | 87 | FLOAT exp_2t = M_EXP (2 * t); |
f6d3a72e | 88 | |
d5602ceb | 89 | __real__ res = M_COPYSIGN (1, __real__ x); |
f6d3a72e | 90 | __imag__ res = 4 * sinix * cosix; |
d5602ceb | 91 | __real__ x = M_FABS (__real__ x); |
f6d3a72e PM |
92 | __real__ x -= t; |
93 | __imag__ res /= exp_2t; | |
94 | if (__real__ x > t) | |
95 | { | |
96 | /* Underflow (original real part of x has absolute value | |
97 | > 2t). */ | |
98 | __imag__ res /= exp_2t; | |
99 | } | |
100 | else | |
d5602ceb | 101 | __imag__ res /= M_EXP (2 * __real__ x); |
f6d3a72e PM |
102 | } |
103 | else | |
104 | { | |
d5602ceb PM |
105 | FLOAT sinhrx, coshrx; |
106 | if (M_FABS (__real__ x) > M_MIN) | |
f6d3a72e | 107 | { |
d5602ceb PM |
108 | sinhrx = M_SINH (__real__ x); |
109 | coshrx = M_COSH (__real__ x); | |
f6d3a72e PM |
110 | } |
111 | else | |
112 | { | |
113 | sinhrx = __real__ x; | |
d5602ceb | 114 | coshrx = 1; |
f6d3a72e PM |
115 | } |
116 | ||
d5602ceb | 117 | if (M_FABS (sinhrx) > M_FABS (cosix) * M_EPSILON) |
f6d3a72e PM |
118 | den = sinhrx * sinhrx + cosix * cosix; |
119 | else | |
120 | den = cosix * cosix; | |
121 | __real__ res = sinhrx * coshrx / den; | |
122 | __imag__ res = sinix * cosix / den; | |
123 | } | |
124 | math_check_force_underflow_complex (res); | |
125 | } | |
126 | ||
127 | return res; | |
128 | } | |
d5602ceb PM |
129 | |
130 | declare_mgen_alias (__ctanh, ctanh) |