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63551311 | 1 | /* Complex tangent function for 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> | |
04be94a8 | 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__ double | |
27 | __ctan (__complex__ double x) | |
28 | { | |
29 | __complex__ double res; | |
30 | ||
bc62c2fb | 31 | if (__builtin_expect (!isfinite (__real__ x) || !isfinite (__imag__ x), 0)) |
63551311 | 32 | { |
7edb55ce | 33 | if (__isinf_ns (__imag__ x)) |
63551311 UD |
34 | { |
35 | __real__ res = __copysign (0.0, __real__ x); | |
36 | __imag__ res = __copysign (1.0, __imag__ x); | |
37 | } | |
38 | else if (__real__ x == 0.0) | |
39 | { | |
40 | res = x; | |
41 | } | |
42 | else | |
43 | { | |
44 | __real__ res = __nan (""); | |
45 | __imag__ res = __nan (""); | |
04be94a8 | 46 | |
7edb55ce | 47 | if (__isinf_ns (__real__ x)) |
04be94a8 | 48 | feraiseexcept (FE_INVALID); |
63551311 UD |
49 | } |
50 | } | |
51 | else | |
52 | { | |
bcc8d661 | 53 | double sinrx, cosrx; |
7799b7b3 | 54 | double den; |
bcc8d661 | 55 | const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2); |
6d3bf199 | 56 | int rcls = fpclassify (__real__ x); |
63551311 | 57 | |
bcc8d661 JM |
58 | /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y)) |
59 | = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */ | |
7799b7b3 | 60 | |
6d3bf199 LD |
61 | if (__builtin_expect (rcls != FP_SUBNORMAL, 1)) |
62 | { | |
63 | __sincos (__real__ x, &sinrx, &cosrx); | |
64 | } | |
65 | else | |
66 | { | |
67 | sinrx = __real__ x; | |
68 | cosrx = 1.0; | |
69 | } | |
7799b7b3 | 70 | |
bcc8d661 | 71 | if (fabs (__imag__ x) > t) |
3b6c37d4 | 72 | { |
bcc8d661 JM |
73 | /* Avoid intermediate overflow when the real part of the |
74 | result may be subnormal. Ignoring negligible terms, the | |
75 | imaginary part is +/- 1, the real part is | |
76 | sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */ | |
77 | double exp_2t = __ieee754_exp (2 * t); | |
3b6c37d4 | 78 | |
bcc8d661 JM |
79 | __imag__ res = __copysign (1.0, __imag__ x); |
80 | __real__ res = 4 * sinrx * cosrx; | |
81 | __imag__ x = fabs (__imag__ x); | |
82 | __imag__ x -= t; | |
83 | __real__ res /= exp_2t; | |
84 | if (__imag__ x > t) | |
85 | { | |
86 | /* Underflow (original imaginary part of x has absolute | |
87 | value > 2t). */ | |
88 | __real__ res /= exp_2t; | |
89 | } | |
90 | else | |
91 | __real__ res /= __ieee754_exp (2 * __imag__ x); | |
3b6c37d4 UD |
92 | } |
93 | else | |
94 | { | |
ca61cf32 JM |
95 | double sinhix, coshix; |
96 | if (fabs (__imag__ x) > DBL_MIN) | |
97 | { | |
98 | sinhix = __ieee754_sinh (__imag__ x); | |
99 | coshix = __ieee754_cosh (__imag__ x); | |
100 | } | |
101 | else | |
102 | { | |
103 | sinhix = __imag__ x; | |
104 | coshix = 1.0; | |
105 | } | |
bcc8d661 | 106 | |
ca61cf32 JM |
107 | if (fabs (sinhix) > fabs (cosrx) * DBL_EPSILON) |
108 | den = cosrx * cosrx + sinhix * sinhix; | |
109 | else | |
110 | den = cosrx * cosrx; | |
bcc8d661 JM |
111 | __real__ res = sinrx * cosrx / den; |
112 | __imag__ res = sinhix * coshix / den; | |
3b6c37d4 | 113 | } |
63551311 UD |
114 | } |
115 | ||
116 | return res; | |
117 | } | |
118 | weak_alias (__ctan, ctan) | |
119 | #ifdef NO_LONG_DOUBLE | |
120 | strong_alias (__ctan, __ctanl) | |
121 | weak_alias (__ctan, ctanl) | |
122 | #endif |