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63551311 | 1 | /* Complex tangent function for double. |
f7a9f785 | 2 | Copyright (C) 1997-2016 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 | ||
a1ffb40e | 31 | if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x))) |
63551311 | 32 | { |
fe8c2b33 | 33 | if (isinf (__imag__ x)) |
63551311 | 34 | { |
61f89378 JM |
35 | if (isfinite (__real__ x) && fabs (__real__ x) > 1.0) |
36 | { | |
37 | double sinrx, cosrx; | |
38 | __sincos (__real__ x, &sinrx, &cosrx); | |
39 | __real__ res = __copysign (0.0, sinrx * cosrx); | |
40 | } | |
41 | else | |
42 | __real__ res = __copysign (0.0, __real__ x); | |
63551311 UD |
43 | __imag__ res = __copysign (1.0, __imag__ x); |
44 | } | |
45 | else if (__real__ x == 0.0) | |
46 | { | |
47 | res = x; | |
48 | } | |
49 | else | |
50 | { | |
51 | __real__ res = __nan (""); | |
52 | __imag__ res = __nan (""); | |
04be94a8 | 53 | |
fe8c2b33 | 54 | if (isinf (__real__ x)) |
04be94a8 | 55 | feraiseexcept (FE_INVALID); |
63551311 UD |
56 | } |
57 | } | |
58 | else | |
59 | { | |
bcc8d661 | 60 | double sinrx, cosrx; |
7799b7b3 | 61 | double den; |
bcc8d661 | 62 | const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2); |
63551311 | 63 | |
bcc8d661 JM |
64 | /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y)) |
65 | = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */ | |
7799b7b3 | 66 | |
a67894c5 | 67 | if (__glibc_likely (fabs (__real__ x) > DBL_MIN)) |
6d3bf199 LD |
68 | { |
69 | __sincos (__real__ x, &sinrx, &cosrx); | |
70 | } | |
71 | else | |
72 | { | |
73 | sinrx = __real__ x; | |
74 | cosrx = 1.0; | |
75 | } | |
7799b7b3 | 76 | |
bcc8d661 | 77 | if (fabs (__imag__ x) > t) |
3b6c37d4 | 78 | { |
bcc8d661 JM |
79 | /* Avoid intermediate overflow when the real part of the |
80 | result may be subnormal. Ignoring negligible terms, the | |
81 | imaginary part is +/- 1, the real part is | |
82 | sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */ | |
83 | double exp_2t = __ieee754_exp (2 * t); | |
3b6c37d4 | 84 | |
bcc8d661 JM |
85 | __imag__ res = __copysign (1.0, __imag__ x); |
86 | __real__ res = 4 * sinrx * cosrx; | |
87 | __imag__ x = fabs (__imag__ x); | |
88 | __imag__ x -= t; | |
89 | __real__ res /= exp_2t; | |
90 | if (__imag__ x > t) | |
91 | { | |
92 | /* Underflow (original imaginary part of x has absolute | |
93 | value > 2t). */ | |
94 | __real__ res /= exp_2t; | |
95 | } | |
96 | else | |
97 | __real__ res /= __ieee754_exp (2 * __imag__ x); | |
3b6c37d4 UD |
98 | } |
99 | else | |
100 | { | |
ca61cf32 JM |
101 | double sinhix, coshix; |
102 | if (fabs (__imag__ x) > DBL_MIN) | |
103 | { | |
104 | sinhix = __ieee754_sinh (__imag__ x); | |
105 | coshix = __ieee754_cosh (__imag__ x); | |
106 | } | |
107 | else | |
108 | { | |
109 | sinhix = __imag__ x; | |
110 | coshix = 1.0; | |
111 | } | |
bcc8d661 | 112 | |
ca61cf32 JM |
113 | if (fabs (sinhix) > fabs (cosrx) * DBL_EPSILON) |
114 | den = cosrx * cosrx + sinhix * sinhix; | |
115 | else | |
116 | den = cosrx * cosrx; | |
bcc8d661 JM |
117 | __real__ res = sinrx * cosrx / den; |
118 | __imag__ res = sinhix * coshix / den; | |
3b6c37d4 | 119 | } |
d96164c3 | 120 | math_check_force_underflow_complex (res); |
63551311 UD |
121 | } |
122 | ||
123 | return res; | |
124 | } | |
125 | weak_alias (__ctan, ctan) | |
126 | #ifdef NO_LONG_DOUBLE | |
127 | strong_alias (__ctan, __ctanl) | |
128 | weak_alias (__ctan, ctanl) | |
129 | #endif |