summaryrefslogtreecommitdiff
path: root/math/s_ctanh.c
blob: fee19105512eeddfe284a7a5e9dadf0d56475578 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
/* Complex hyperbole tangent for double.
   Copyright (C) 1997-2012 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, see
   <http://www.gnu.org/licenses/>.  */

#include <complex.h>
#include <fenv.h>
#include <math.h>
#include <math_private.h>
#include <float.h>

__complex__ double
__ctanh (__complex__ double x)
{
  __complex__ double res;

  if (__builtin_expect (!isfinite (__real__ x) || !isfinite (__imag__ x), 0))
    {
      if (__isinf_ns (__real__ x))
	{
	  __real__ res = __copysign (1.0, __real__ x);
	  __imag__ res = __copysign (0.0, __imag__ x);
	}
      else if (__imag__ x == 0.0)
	{
	  res = x;
	}
      else
	{
	  __real__ res = __nan ("");
	  __imag__ res = __nan ("");

	  if (__isinf_ns (__imag__ x))
	    feraiseexcept (FE_INVALID);
	}
    }
  else
    {
      double sinix, cosix;
      double den;
      const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2);
      int icls = fpclassify (__imag__ x);

      /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
	 = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2).  */

      if (__builtin_expect (icls != FP_SUBNORMAL, 1))
	{
	  __sincos (__imag__ x, &sinix, &cosix);
	}
      else
	{
	  sinix = __imag__ x;
	  cosix = 1.0;
	}

      if (fabs (__real__ x) > t)
	{
	  /* Avoid intermediate overflow when the imaginary part of
	     the result may be subnormal.  Ignoring negligible terms,
	     the real part is +/- 1, the imaginary part is
	     sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x).  */
	  double exp_2t = __ieee754_exp (2 * t);

	  __real__ res = __copysign (1.0, __real__ x);
	  __imag__ res = 4 * sinix * cosix;
	  __real__ x = fabs (__real__ x);
	  __real__ x -= t;
	  __imag__ res /= exp_2t;
	  if (__real__ x > t)
	    {
	      /* Underflow (original real part of x has absolute value
		 > 2t).  */
	      __imag__ res /= exp_2t;
	    }
	  else
	    __imag__ res /= __ieee754_exp (2 * __real__ x);
	}
      else
	{
	  double sinhrx, coshrx;
	  if (fabs (__real__ x) > DBL_MIN)
	    {
	      sinhrx = __ieee754_sinh (__real__ x);
	      coshrx = __ieee754_cosh (__real__ x);
	    }
	  else
	    {
	      sinhrx = __real__ x;
	      coshrx = 1.0;
	    }

	  if (fabs (sinhrx) > fabs (cosix) * DBL_EPSILON)
	    den = sinhrx * sinhrx + cosix * cosix;
	  else
	    den = cosix * cosix;
	  __real__ res = sinhrx * coshrx / den;
	  __imag__ res = sinix * cosix / den;
	}
    }

  return res;
}
weak_alias (__ctanh, ctanh)
#ifdef NO_LONG_DOUBLE
strong_alias (__ctanh, __ctanhl)
weak_alias (__ctanh, ctanhl)
#endif