1 /* Complex hyperbole tangent for double.
2 Copyright (C) 1997-2012 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
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.
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.
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/>. */
23 #include <math_private.h>
27 __ctanh (__complex__ double x)
29 __complex__ double res;
31 if (__builtin_expect (!isfinite (__real__ x) || !isfinite (__imag__ x), 0))
33 if (__isinf_ns (__real__ x))
35 __real__ res = __copysign (1.0, __real__ x);
36 __imag__ res = __copysign (0.0, __imag__ x);
38 else if (__imag__ x == 0.0)
44 __real__ res = __nan ("");
45 __imag__ res = __nan ("");
47 if (__isinf_ns (__imag__ x))
48 feraiseexcept (FE_INVALID);
55 const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2);
56 int icls = fpclassify (__imag__ x);
58 /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
59 = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
61 if (__builtin_expect (icls != FP_SUBNORMAL, 1))
63 __sincos (__imag__ x, &sinix, &cosix);
71 if (fabs (__real__ x) > t)
73 /* Avoid intermediate overflow when the imaginary part of
74 the result may be subnormal. Ignoring negligible terms,
75 the real part is +/- 1, the imaginary part is
76 sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */
77 double exp_2t = __ieee754_exp (2 * t);
79 __real__ res = __copysign (1.0, __real__ x);
80 __imag__ res = 4 * sinix * cosix;
81 __real__ x = fabs (__real__ x);
83 __imag__ res /= exp_2t;
86 /* Underflow (original real part of x has absolute value
88 __imag__ res /= exp_2t;
91 __imag__ res /= __ieee754_exp (2 * __real__ x);
95 double sinhrx, coshrx;
96 if (fabs (__real__ x) > DBL_MIN)
98 sinhrx = __ieee754_sinh (__real__ x);
99 coshrx = __ieee754_cosh (__real__ x);
107 if (fabs (sinhrx) > fabs (cosix) * DBL_EPSILON)
108 den = sinhrx * sinhrx + cosix * cosix;
111 __real__ res = sinhrx * coshrx / den;
112 __imag__ res = sinix * cosix / den;
118 weak_alias (__ctanh, ctanh)
119 #ifdef NO_LONG_DOUBLE
120 strong_alias (__ctanh, __ctanhl)
121 weak_alias (__ctanh, ctanhl)