summary refs log tree commit diff
path: root/math/s_ctanh_template.c
blob: 7fcaddbcbc6a0745d9fc985011a139b2df09c028 (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
/* Complex hyperbolic tangent for float types.
   Copyright (C) 1997-2021 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
   <https://www.gnu.org/licenses/>.  */

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

CFLOAT
M_DECL_FUNC (__ctanh) (CFLOAT x)
{
  CFLOAT res;

  if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
    {
      if (isinf (__real__ x))
	{
	  __real__ res = M_COPYSIGN (1, __real__ x);
	  if (isfinite (__imag__ x) && M_FABS (__imag__ x) > 1)
	    {
	      FLOAT sinix, cosix;
	      M_SINCOS (__imag__ x, &sinix, &cosix);
	      __imag__ res = M_COPYSIGN (0, sinix * cosix);
	    }
	  else
	    __imag__ res = M_COPYSIGN (0, __imag__ x);
	}
      else if (__imag__ x == 0)
	{
	  res = x;
	}
      else
	{
	  if (__real__ x == 0)
	    __real__ res = __real__ x;
	  else
	    __real__ res = M_NAN;
	  __imag__ res = M_NAN;

	  if (isinf (__imag__ x))
	    feraiseexcept (FE_INVALID);
	}
    }
  else
    {
      FLOAT sinix, cosix;
      FLOAT den;
      const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2) / 2);

      /* 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 (__glibc_likely (M_FABS (__imag__ x) > M_MIN))
	{
	  M_SINCOS (__imag__ x, &sinix, &cosix);
	}
      else
	{
	  sinix = __imag__ x;
	  cosix = 1;
	}

      if (M_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).  */
	  FLOAT exp_2t = M_EXP (2 * t);

	  __real__ res = M_COPYSIGN (1, __real__ x);
	  __imag__ res = 4 * sinix * cosix;
	  __real__ x = M_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 /= M_EXP (2 * __real__ x);
	}
      else
	{
	  FLOAT sinhrx, coshrx;
	  if (M_FABS (__real__ x) > M_MIN)
	    {
	      sinhrx = M_SINH (__real__ x);
	      coshrx = M_COSH (__real__ x);
	    }
	  else
	    {
	      sinhrx = __real__ x;
	      coshrx = 1;
	    }

	  if (M_FABS (sinhrx) > M_FABS (cosix) * M_EPSILON)
	    den = sinhrx * sinhrx + cosix * cosix;
	  else
	    den = cosix * cosix;
	  __real__ res = sinhrx * coshrx / den;
	  __imag__ res = sinix * cosix / den;
	}
      math_check_force_underflow_complex (res);
    }

  return res;
}

declare_mgen_alias (__ctanh, ctanh)