1/* Complex tangent function for float.
2 Copyright (C) 1997-2016 Free Software Foundation, Inc.
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>
24#include <float.h>
25
26__complex__ float
27__ctanf (__complex__ float x)
28{
29 __complex__ float res;
30
31 if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
32 {
33 if (isinf (__imag__ x))
34 {
35 if (isfinite (__real__ x) && fabsf (__real__ x) > 1.0f)
36 {
37 float sinrx, cosrx;
38 __sincosf (__real__ x, &sinrx, &cosrx);
39 __real__ res = __copysignf (0.0f, sinrx * cosrx);
40 }
41 else
42 __real__ res = __copysignf (0.0, __real__ x);
43 __imag__ res = __copysignf (1.0, __imag__ x);
44 }
45 else if (__real__ x == 0.0)
46 {
47 res = x;
48 }
49 else
50 {
51 __real__ res = __nanf ("");
52 __imag__ res = __nanf ("");
53
54 if (isinf (__real__ x))
55 feraiseexcept (FE_INVALID);
56 }
57 }
58 else
59 {
60 float sinrx, cosrx;
61 float den;
62 const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2 / 2);
63
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). */
66
67 if (__glibc_likely (fabsf (__real__ x) > FLT_MIN))
68 {
69 __sincosf (__real__ x, &sinrx, &cosrx);
70 }
71 else
72 {
73 sinrx = __real__ x;
74 cosrx = 1.0f;
75 }
76
77 if (fabsf (__imag__ x) > t)
78 {
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 float exp_2t = __ieee754_expf (2 * t);
84
85 __imag__ res = __copysignf (1.0, __imag__ x);
86 __real__ res = 4 * sinrx * cosrx;
87 __imag__ x = fabsf (__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_expf (2 * __imag__ x);
98 }
99 else
100 {
101 float sinhix, coshix;
102 if (fabsf (__imag__ x) > FLT_MIN)
103 {
104 sinhix = __ieee754_sinhf (__imag__ x);
105 coshix = __ieee754_coshf (__imag__ x);
106 }
107 else
108 {
109 sinhix = __imag__ x;
110 coshix = 1.0f;
111 }
112
113 if (fabsf (sinhix) > fabsf (cosrx) * FLT_EPSILON)
114 den = cosrx * cosrx + sinhix * sinhix;
115 else
116 den = cosrx * cosrx;
117 __real__ res = sinrx * cosrx / den;
118 __imag__ res = sinhix * coshix / den;
119 }
120 math_check_force_underflow_complex (res);
121 }
122
123 return res;
124}
125#ifndef __ctanf
126weak_alias (__ctanf, ctanf)
127#endif
128