1 /* Complex hyperbolic tangent for float types.
2 Copyright (C) 1997-2018 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>
24 #include <math-underflow.h>
28 M_DECL_FUNC (__ctanh
) (CFLOAT x
)
32 if (__glibc_unlikely (!isfinite (__real__ x
) || !isfinite (__imag__ x
)))
34 if (isinf (__real__ x
))
36 __real__ res
= M_COPYSIGN (1, __real__ x
);
37 if (isfinite (__imag__ x
) && M_FABS (__imag__ x
) > 1)
40 M_SINCOS (__imag__ x
, &sinix
, &cosix
);
41 __imag__ res
= M_COPYSIGN (0, sinix
* cosix
);
44 __imag__ res
= M_COPYSIGN (0, __imag__ x
);
46 else if (__imag__ x
== 0)
53 __real__ res
= __real__ x
;
58 if (isinf (__imag__ x
))
59 feraiseexcept (FE_INVALID
);
66 const int t
= (int) ((M_MAX_EXP
- 1) * M_MLIT (M_LN2
) / 2);
68 /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
69 = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
71 if (__glibc_likely (M_FABS (__imag__ x
) > M_MIN
))
73 M_SINCOS (__imag__ x
, &sinix
, &cosix
);
81 if (M_FABS (__real__ x
) > t
)
83 /* Avoid intermediate overflow when the imaginary part of
84 the result may be subnormal. Ignoring negligible terms,
85 the real part is +/- 1, the imaginary part is
86 sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */
87 FLOAT exp_2t
= M_EXP (2 * t
);
89 __real__ res
= M_COPYSIGN (1, __real__ x
);
90 __imag__ res
= 4 * sinix
* cosix
;
91 __real__ x
= M_FABS (__real__ x
);
93 __imag__ res
/= exp_2t
;
96 /* Underflow (original real part of x has absolute value
98 __imag__ res
/= exp_2t
;
101 __imag__ res
/= M_EXP (2 * __real__ x
);
105 FLOAT sinhrx
, coshrx
;
106 if (M_FABS (__real__ x
) > M_MIN
)
108 sinhrx
= M_SINH (__real__ x
);
109 coshrx
= M_COSH (__real__ x
);
117 if (M_FABS (sinhrx
) > M_FABS (cosix
) * M_EPSILON
)
118 den
= sinhrx
* sinhrx
+ cosix
* cosix
;
121 __real__ res
= sinhrx
* coshrx
/ den
;
122 __imag__ res
= sinix
* cosix
/ den
;
124 math_check_force_underflow_complex (res
);
130 declare_mgen_alias (__ctanh
, ctanh
)