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63551311 | 1 | /* Complex hyperbole tangent for long double. |
bcc8d661 | 2 | Copyright (C) 1997-2012 Free Software Foundation, Inc. |
63551311 UD |
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 | |
41bdb6e2 AJ |
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. | |
63551311 UD |
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 | |
41bdb6e2 | 14 | Lesser General Public License for more details. |
63551311 | 15 | |
41bdb6e2 | 16 | You should have received a copy of the GNU Lesser General Public |
59ba27a6 PE |
17 | License along with the GNU C Library; if not, see |
18 | <http://www.gnu.org/licenses/>. */ | |
63551311 UD |
19 | |
20 | #include <complex.h> | |
779ae82e | 21 | #include <fenv.h> |
63551311 | 22 | #include <math.h> |
9277c064 | 23 | #include <math_private.h> |
bcc8d661 | 24 | #include <float.h> |
63551311 UD |
25 | |
26 | __complex__ long double | |
27 | __ctanhl (__complex__ long double x) | |
28 | { | |
29 | __complex__ long double res; | |
30 | ||
77425c63 | 31 | if (__builtin_expect (!isfinite (__real__ x) || !isfinite (__imag__ x), 0)) |
63551311 | 32 | { |
7edb55ce | 33 | if (__isinf_nsl (__real__ x)) |
63551311 UD |
34 | { |
35 | __real__ res = __copysignl (1.0, __real__ x); | |
36 | __imag__ res = __copysignl (0.0, __imag__ x); | |
37 | } | |
38 | else if (__imag__ x == 0.0) | |
39 | { | |
40 | res = x; | |
41 | } | |
42 | else | |
43 | { | |
44 | __real__ res = __nanl (""); | |
45 | __imag__ res = __nanl (""); | |
779ae82e | 46 | |
7edb55ce | 47 | if (__isinf_nsl (__imag__ x)) |
779ae82e | 48 | feraiseexcept (FE_INVALID); |
63551311 UD |
49 | } |
50 | } | |
51 | else | |
52 | { | |
bcc8d661 | 53 | long double sinix, cosix; |
7799b7b3 | 54 | long double den; |
bcc8d661 | 55 | const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2); |
7799b7b3 | 56 | |
bcc8d661 JM |
57 | /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y)) |
58 | = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */ | |
7799b7b3 | 59 | |
bcc8d661 | 60 | __sincosl (__imag__ x, &sinix, &cosix); |
63551311 | 61 | |
bcc8d661 | 62 | if (fabsl (__real__ x) > t) |
531680ae | 63 | { |
bcc8d661 JM |
64 | /* Avoid intermediate overflow when the imaginary part of |
65 | the result may be subnormal. Ignoring negligible terms, | |
66 | the real part is +/- 1, the imaginary part is | |
67 | sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */ | |
68 | long double exp_2t = __ieee754_expl (2 * t); | |
531680ae | 69 | |
bcc8d661 JM |
70 | __real__ res = __copysignl (1.0, __real__ x); |
71 | __imag__ res = 4 * sinix * cosix; | |
72 | __real__ x = fabsl (__real__ x); | |
73 | __real__ x -= t; | |
74 | __imag__ res /= exp_2t; | |
75 | if (__real__ x > t) | |
76 | { | |
77 | /* Underflow (original real part of x has absolute value | |
78 | > 2t). */ | |
79 | __imag__ res /= exp_2t; | |
80 | } | |
81 | else | |
82 | __imag__ res /= __ieee754_expl (2 * __real__ x); | |
531680ae UD |
83 | } |
84 | else | |
85 | { | |
ca61cf32 JM |
86 | long double sinhrx, coshrx; |
87 | if (fabsl (__real__ x) > LDBL_MIN) | |
88 | { | |
89 | sinhrx = __ieee754_sinhl (__real__ x); | |
90 | coshrx = __ieee754_coshl (__real__ x); | |
91 | } | |
92 | else | |
93 | { | |
94 | sinhrx = __real__ x; | |
95 | coshrx = 1.0L; | |
96 | } | |
bcc8d661 | 97 | |
ca61cf32 JM |
98 | if (fabsl (sinhrx) > fabsl (cosix) * LDBL_EPSILON) |
99 | den = sinhrx * sinhrx + cosix * cosix; | |
100 | else | |
101 | den = cosix * cosix; | |
bcc8d661 JM |
102 | __real__ res = sinhrx * coshrx / den; |
103 | __imag__ res = sinix * cosix / den; | |
531680ae | 104 | } |
63551311 UD |
105 | } |
106 | ||
107 | return res; | |
108 | } | |
109 | weak_alias (__ctanhl, ctanhl) |