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16f0eced | 1 | /* Complex tangent function for long double. IBM extended format version. |
568035b7 | 2 | Copyright (C) 1997-2013 Free Software Foundation, Inc. |
16f0eced RM |
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 | |
59ba27a6 PE |
17 | License along with the GNU C Library; if not, see |
18 | <http://www.gnu.org/licenses/>. */ | |
16f0eced RM |
19 | |
20 | #include <complex.h> | |
21 | #include <fenv.h> | |
22 | #include <math.h> | |
23 | #include <math_ldbl_opt.h> | |
0ac229c8 | 24 | #include <float.h> |
16f0eced | 25 | |
1ed0291c | 26 | #include <math_private.h> |
16f0eced | 27 | |
28cfe843 AZ |
28 | /* IBM long double GCC builtin sets LDBL_EPSILON == LDBL_DENORM_MIN */ |
29 | static const long double ldbl_eps = 0x1p-106L; | |
16f0eced RM |
30 | |
31 | __complex__ long double | |
32 | __ctanl (__complex__ long double x) | |
33 | { | |
34 | __complex__ long double res; | |
35 | ||
36 | if (!isfinite (__real__ x) || !isfinite (__imag__ x)) | |
37 | { | |
38 | if (__isinfl (__imag__ x)) | |
39 | { | |
40 | __real__ res = __copysignl (0.0, __real__ x); | |
41 | __imag__ res = __copysignl (1.0, __imag__ x); | |
42 | } | |
43 | else if (__real__ x == 0.0) | |
44 | { | |
45 | res = x; | |
46 | } | |
47 | else | |
48 | { | |
49 | __real__ res = __nanl (""); | |
50 | __imag__ res = __nanl (""); | |
51 | ||
0ac229c8 | 52 | if (__isinf_nsl (__real__ x)) |
16f0eced | 53 | feraiseexcept (FE_INVALID); |
16f0eced RM |
54 | } |
55 | } | |
56 | else | |
57 | { | |
0ac229c8 | 58 | long double sinrx, cosrx; |
16f0eced | 59 | long double den; |
28cfe843 | 60 | const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2.0L); |
16f0eced | 61 | |
0ac229c8 AZ |
62 | /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y)) |
63 | = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */ | |
16f0eced | 64 | |
0ac229c8 | 65 | __sincosl (__real__ x, &sinrx, &cosrx); |
16f0eced | 66 | |
0ac229c8 | 67 | if (fabsl (__imag__ x) > t) |
16f0eced | 68 | { |
0ac229c8 AZ |
69 | /* Avoid intermediate overflow when the real part of the |
70 | result may be subnormal. Ignoring negligible terms, the | |
71 | imaginary part is +/- 1, the real part is | |
72 | sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */ | |
73 | long double exp_2t = __ieee754_expl (2 * t); | |
16f0eced | 74 | |
28cfe843 | 75 | __imag__ res = __copysignl (1.0L, __imag__ x); |
0ac229c8 AZ |
76 | __real__ res = 4 * sinrx * cosrx; |
77 | __imag__ x = fabsl (__imag__ x); | |
78 | __imag__ x -= t; | |
79 | __real__ res /= exp_2t; | |
80 | if (__imag__ x > t) | |
81 | { | |
82 | /* Underflow (original imaginary part of x has absolute | |
83 | value > 2t). */ | |
84 | __real__ res /= exp_2t; | |
85 | } | |
86 | else | |
28cfe843 | 87 | __real__ res /= __ieee754_expl (2.0L * __imag__ x); |
16f0eced RM |
88 | } |
89 | else | |
90 | { | |
28cfe843 AZ |
91 | long double sinhix, coshix; |
92 | if (fabsl (__imag__ x) > LDBL_MIN) | |
93 | { | |
94 | sinhix = __ieee754_sinhl (__imag__ x); | |
95 | coshix = __ieee754_coshl (__imag__ x); | |
96 | } | |
97 | else | |
98 | { | |
99 | sinhix = __imag__ x; | |
100 | coshix = 1.0L; | |
101 | } | |
0ac229c8 | 102 | |
28cfe843 AZ |
103 | if (fabsl (sinhix) > fabsl (cosrx) * ldbl_eps) |
104 | den = cosrx * cosrx + sinhix * sinhix; | |
105 | else | |
106 | den = cosrx * cosrx; | |
107 | __real__ res = sinrx * (cosrx / den); | |
108 | __imag__ res = sinhix * (coshix / den); | |
16f0eced | 109 | } |
0ac229c8 | 110 | |
16f0eced | 111 | /* __gcc_qmul does not respect -0.0 so we need the following fixup. */ |
28cfe843 | 112 | if ((__real__ res == 0.0L) && (__real__ x == 0.0L)) |
16f0eced RM |
113 | __real__ res = __real__ x; |
114 | ||
28cfe843 | 115 | if ((__real__ res == 0.0L) && (__imag__ x == 0.0L)) |
16f0eced RM |
116 | __imag__ res = __imag__ x; |
117 | } | |
118 | ||
119 | return res; | |
120 | } | |
121 | long_double_symbol (libm, __ctanl, ctanl); |