about summary refs log tree commit diff
path: root/math/s_catanh.c
blob: 11ea06246eb0c04b0b66aeb18f97ab342f454acf (plain) (blame)
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
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
/* Return arc hyperbole tangent for double value.
   Copyright (C) 1997-2016 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 <math.h>
#include <math_private.h>
#include <float.h>

__complex__ double
__catanh (__complex__ double x)
{
  __complex__ double res;
  int rcls = fpclassify (__real__ x);
  int icls = fpclassify (__imag__ x);

  if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
    {
      if (icls == FP_INFINITE)
	{
	  __real__ res = __copysign (0.0, __real__ x);
	  __imag__ res = __copysign (M_PI_2, __imag__ x);
	}
      else if (rcls == FP_INFINITE || rcls == FP_ZERO)
	{
	  __real__ res = __copysign (0.0, __real__ x);
	  if (icls >= FP_ZERO)
	    __imag__ res = __copysign (M_PI_2, __imag__ x);
	  else
	    __imag__ res = __nan ("");
	}
      else
	{
	  __real__ res = __nan ("");
	  __imag__ res = __nan ("");
	}
    }
  else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
    {
      res = x;
    }
  else
    {
      if (fabs (__real__ x) >= 16.0 / DBL_EPSILON
	  || fabs (__imag__ x) >= 16.0 / DBL_EPSILON)
	{
	  __imag__ res = __copysign (M_PI_2, __imag__ x);
	  if (fabs (__imag__ x) <= 1.0)
	    __real__ res = 1.0 / __real__ x;
	  else if (fabs (__real__ x) <= 1.0)
	    __real__ res = __real__ x / __imag__ x / __imag__ x;
	  else
	    {
	      double h = __ieee754_hypot (__real__ x / 2.0, __imag__ x / 2.0);
	      __real__ res = __real__ x / h / h / 4.0;
	    }
	}
      else
	{
	  if (fabs (__real__ x) == 1.0
	      && fabs (__imag__ x) < DBL_EPSILON * DBL_EPSILON)
	    __real__ res = (__copysign (0.5, __real__ x)
			    * (M_LN2 - __ieee754_log (fabs (__imag__ x))));
	  else
	    {
	      double i2 = 0.0;
	      if (fabs (__imag__ x) >= DBL_EPSILON * DBL_EPSILON)
		i2 = __imag__ x * __imag__ x;

	      double num = 1.0 + __real__ x;
	      num = i2 + num * num;

	      double den = 1.0 - __real__ x;
	      den = i2 + den * den;

	      double f = num / den;
	      if (f < 0.5)
		__real__ res = 0.25 * __ieee754_log (f);
	      else
		{
		  num = 4.0 * __real__ x;
		  __real__ res = 0.25 * __log1p (num / den);
		}
	    }

	  double absx, absy, den;

	  absx = fabs (__real__ x);
	  absy = fabs (__imag__ x);
	  if (absx < absy)
	    {
	      double t = absx;
	      absx = absy;
	      absy = t;
	    }

	  if (absy < DBL_EPSILON / 2.0)
	    {
	      den = (1.0 - absx) * (1.0 + absx);
	      if (den == -0.0)
		den = 0.0;
	    }
	  else if (absx >= 1.0)
	    den = (1.0 - absx) * (1.0 + absx) - absy * absy;
	  else if (absx >= 0.75 || absy >= 0.5)
	    den = -__x2y2m1 (absx, absy);
	  else
	    den = (1.0 - absx) * (1.0 + absx) - absy * absy;

	  __imag__ res = 0.5 * __ieee754_atan2 (2.0 * __imag__ x, den);
	}

      math_check_force_underflow_complex (res);
    }

  return res;
}
weak_alias (__catanh, catanh)
#ifdef NO_LONG_DOUBLE
strong_alias (__catanh, __catanhl)
weak_alias (__catanh, catanhl)
#endif