]>
Commit | Line | Data |
---|---|---|
63551311 | 1 | /* Complex tangent function for long 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 | 25 | |
2f318445 JM |
26 | /* To avoid spurious underflows, use this definition to treat IBM long |
27 | double as approximating an IEEE-style format. */ | |
28 | #if LDBL_MANT_DIG == 106 | |
29 | # undef LDBL_EPSILON | |
30 | # define LDBL_EPSILON 0x1p-106L | |
31 | #endif | |
32 | ||
63551311 UD |
33 | __complex__ long double |
34 | __ctanl (__complex__ long double x) | |
35 | { | |
b4012b75 | 36 | __complex__ long double res; |
63551311 | 37 | |
a1ffb40e | 38 | if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x))) |
63551311 | 39 | { |
fe8c2b33 | 40 | if (isinf (__imag__ x)) |
63551311 | 41 | { |
61f89378 JM |
42 | if (isfinite (__real__ x) && fabsl (__real__ x) > 1.0L) |
43 | { | |
44 | long double sinrx, cosrx; | |
45 | __sincosl (__real__ x, &sinrx, &cosrx); | |
46 | __real__ res = __copysignl (0.0L, sinrx * cosrx); | |
47 | } | |
48 | else | |
49 | __real__ res = __copysignl (0.0, __real__ x); | |
63551311 UD |
50 | __imag__ res = __copysignl (1.0, __imag__ x); |
51 | } | |
52 | else if (__real__ x == 0.0) | |
53 | { | |
54 | res = x; | |
55 | } | |
56 | else | |
57 | { | |
58 | __real__ res = __nanl (""); | |
59 | __imag__ res = __nanl (""); | |
04be94a8 | 60 | |
fe8c2b33 | 61 | if (isinf (__real__ x)) |
04be94a8 | 62 | feraiseexcept (FE_INVALID); |
63551311 UD |
63 | } |
64 | } | |
65 | else | |
66 | { | |
bcc8d661 | 67 | long double sinrx, cosrx; |
7799b7b3 | 68 | long double den; |
bcc8d661 | 69 | const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2); |
63551311 | 70 | |
bcc8d661 JM |
71 | /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y)) |
72 | = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */ | |
7799b7b3 | 73 | |
a67894c5 | 74 | if (__glibc_likely (fabsl (__real__ x) > LDBL_MIN)) |
6d3bf199 LD |
75 | { |
76 | __sincosl (__real__ x, &sinrx, &cosrx); | |
77 | } | |
78 | else | |
79 | { | |
80 | sinrx = __real__ x; | |
81 | cosrx = 1.0; | |
82 | } | |
3b6c37d4 | 83 | |
bcc8d661 | 84 | if (fabsl (__imag__ x) > t) |
3b6c37d4 | 85 | { |
bcc8d661 JM |
86 | /* Avoid intermediate overflow when the real part of the |
87 | result may be subnormal. Ignoring negligible terms, the | |
88 | imaginary part is +/- 1, the real part is | |
89 | sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */ | |
90 | long double exp_2t = __ieee754_expl (2 * t); | |
3b6c37d4 | 91 | |
bcc8d661 JM |
92 | __imag__ res = __copysignl (1.0, __imag__ x); |
93 | __real__ res = 4 * sinrx * cosrx; | |
94 | __imag__ x = fabsl (__imag__ x); | |
95 | __imag__ x -= t; | |
96 | __real__ res /= exp_2t; | |
97 | if (__imag__ x > t) | |
98 | { | |
99 | /* Underflow (original imaginary part of x has absolute | |
100 | value > 2t). */ | |
101 | __real__ res /= exp_2t; | |
102 | } | |
103 | else | |
104 | __real__ res /= __ieee754_expl (2 * __imag__ x); | |
3b6c37d4 UD |
105 | } |
106 | else | |
107 | { | |
ca61cf32 JM |
108 | long double sinhix, coshix; |
109 | if (fabsl (__imag__ x) > LDBL_MIN) | |
110 | { | |
111 | sinhix = __ieee754_sinhl (__imag__ x); | |
112 | coshix = __ieee754_coshl (__imag__ x); | |
113 | } | |
114 | else | |
115 | { | |
116 | sinhix = __imag__ x; | |
117 | coshix = 1.0L; | |
118 | } | |
bcc8d661 | 119 | |
ca61cf32 JM |
120 | if (fabsl (sinhix) > fabsl (cosrx) * LDBL_EPSILON) |
121 | den = cosrx * cosrx + sinhix * sinhix; | |
122 | else | |
123 | den = cosrx * cosrx; | |
bcc8d661 JM |
124 | __real__ res = sinrx * cosrx / den; |
125 | __imag__ res = sinhix * coshix / den; | |
3b6c37d4 | 126 | } |
d96164c3 | 127 | math_check_force_underflow_complex (res); |
63551311 UD |
128 | } |
129 | ||
130 | return res; | |
131 | } | |
132 | weak_alias (__ctanl, ctanl) |