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d5602ceb | 1 | /* Complex tangent function for a complex float type. |
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> | |
70e2ba33 | 24 | #include <fenv_private.h> |
8f5b00d3 | 25 | #include <math-underflow.h> |
f6d3a72e PM |
26 | #include <float.h> |
27 | ||
d5602ceb PM |
28 | CFLOAT |
29 | M_DECL_FUNC (__ctan) (CFLOAT x) | |
f6d3a72e | 30 | { |
d5602ceb | 31 | CFLOAT res; |
f6d3a72e PM |
32 | |
33 | if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x))) | |
34 | { | |
35 | if (isinf (__imag__ x)) | |
36 | { | |
d5602ceb | 37 | if (isfinite (__real__ x) && M_FABS (__real__ x) > 1) |
f6d3a72e | 38 | { |
d5602ceb PM |
39 | FLOAT sinrx, cosrx; |
40 | M_SINCOS (__real__ x, &sinrx, &cosrx); | |
41 | __real__ res = M_COPYSIGN (0, sinrx * cosrx); | |
f6d3a72e PM |
42 | } |
43 | else | |
d5602ceb PM |
44 | __real__ res = M_COPYSIGN (0, __real__ x); |
45 | __imag__ res = M_COPYSIGN (1, __imag__ x); | |
f6d3a72e | 46 | } |
d5602ceb | 47 | else if (__real__ x == 0) |
f6d3a72e PM |
48 | { |
49 | res = x; | |
50 | } | |
51 | else | |
52 | { | |
d5602ceb | 53 | __real__ res = M_NAN; |
d15e83c5 JM |
54 | if (__imag__ x == 0) |
55 | __imag__ res = __imag__ x; | |
56 | else | |
57 | __imag__ res = M_NAN; | |
f6d3a72e PM |
58 | |
59 | if (isinf (__real__ x)) | |
60 | feraiseexcept (FE_INVALID); | |
61 | } | |
62 | } | |
63 | else | |
64 | { | |
d5602ceb PM |
65 | FLOAT sinrx, cosrx; |
66 | FLOAT den; | |
67 | const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2) / 2); | |
f6d3a72e PM |
68 | |
69 | /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y)) | |
70 | = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */ | |
71 | ||
d5602ceb | 72 | if (__glibc_likely (M_FABS (__real__ x) > M_MIN)) |
f6d3a72e | 73 | { |
d5602ceb | 74 | M_SINCOS (__real__ x, &sinrx, &cosrx); |
f6d3a72e PM |
75 | } |
76 | else | |
77 | { | |
78 | sinrx = __real__ x; | |
d5602ceb | 79 | cosrx = 1; |
f6d3a72e PM |
80 | } |
81 | ||
d5602ceb | 82 | if (M_FABS (__imag__ x) > t) |
f6d3a72e PM |
83 | { |
84 | /* Avoid intermediate overflow when the real part of the | |
85 | result may be subnormal. Ignoring negligible terms, the | |
86 | imaginary part is +/- 1, the real part is | |
87 | sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */ | |
d5602ceb | 88 | FLOAT exp_2t = M_EXP (2 * t); |
f6d3a72e | 89 | |
d5602ceb | 90 | __imag__ res = M_COPYSIGN (1, __imag__ x); |
f6d3a72e | 91 | __real__ res = 4 * sinrx * cosrx; |
d5602ceb | 92 | __imag__ x = M_FABS (__imag__ x); |
f6d3a72e PM |
93 | __imag__ x -= t; |
94 | __real__ res /= exp_2t; | |
95 | if (__imag__ x > t) | |
96 | { | |
97 | /* Underflow (original imaginary part of x has absolute | |
98 | value > 2t). */ | |
99 | __real__ res /= exp_2t; | |
100 | } | |
101 | else | |
d5602ceb | 102 | __real__ res /= M_EXP (2 * __imag__ x); |
f6d3a72e PM |
103 | } |
104 | else | |
105 | { | |
d5602ceb PM |
106 | FLOAT sinhix, coshix; |
107 | if (M_FABS (__imag__ x) > M_MIN) | |
f6d3a72e | 108 | { |
d5602ceb PM |
109 | sinhix = M_SINH (__imag__ x); |
110 | coshix = M_COSH (__imag__ x); | |
f6d3a72e PM |
111 | } |
112 | else | |
113 | { | |
114 | sinhix = __imag__ x; | |
d5602ceb | 115 | coshix = 1; |
f6d3a72e PM |
116 | } |
117 | ||
d5602ceb | 118 | if (M_FABS (sinhix) > M_FABS (cosrx) * M_EPSILON) |
f6d3a72e PM |
119 | den = cosrx * cosrx + sinhix * sinhix; |
120 | else | |
121 | den = cosrx * cosrx; | |
122 | __real__ res = sinrx * cosrx / den; | |
123 | __imag__ res = sinhix * coshix / den; | |
124 | } | |
125 | math_check_force_underflow_complex (res); | |
126 | } | |
127 | ||
128 | return res; | |
129 | } | |
d5602ceb PM |
130 | |
131 | declare_mgen_alias (__ctan, ctan) |