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
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
|
/* Return arc hyperbolic sine for a complex float type, with the
imaginary part of the result possibly adjusted for use in
computing other functions.
Copyright (C) 1997-2024 Free Software Foundation, Inc.
This file is part of the GNU C Library.
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 <math.h>
#include <math_private.h>
#include <math-underflow.h>
#include <float.h>
/* Return the complex inverse hyperbolic sine of finite nonzero Z,
with the imaginary part of the result subtracted from pi/2 if ADJ
is nonzero. */
CFLOAT
M_DECL_FUNC (__kernel_casinh) (CFLOAT x, int adj)
{
CFLOAT res;
FLOAT rx, ix;
CFLOAT y;
/* Avoid cancellation by reducing to the first quadrant. */
rx = M_FABS (__real__ x);
ix = M_FABS (__imag__ x);
if (rx >= 1 / M_EPSILON || ix >= 1 / M_EPSILON)
{
/* For large x in the first quadrant, x + csqrt (1 + x * x)
is sufficiently close to 2 * x to make no significant
difference to the result; avoid possible overflow from
the squaring and addition. */
__real__ y = rx;
__imag__ y = ix;
if (adj)
{
FLOAT t = __real__ y;
__real__ y = M_COPYSIGN (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = M_SUF (__clog) (y);
__real__ res += M_MLIT (M_LN2);
}
else if (rx >= M_LIT (0.5) && ix < M_EPSILON / 8)
{
FLOAT s = M_HYPOT (1, rx);
__real__ res = M_LOG (rx + s);
if (adj)
__imag__ res = M_ATAN2 (s, __imag__ x);
else
__imag__ res = M_ATAN2 (ix, s);
}
else if (rx < M_EPSILON / 8 && ix >= M_LIT (1.5))
{
FLOAT s = M_SQRT ((ix + 1) * (ix - 1));
__real__ res = M_LOG (ix + s);
if (adj)
__imag__ res = M_ATAN2 (rx, M_COPYSIGN (s, __imag__ x));
else
__imag__ res = M_ATAN2 (s, rx);
}
else if (ix > 1 && ix < M_LIT (1.5) && rx < M_LIT (0.5))
{
if (rx < M_EPSILON * M_EPSILON)
{
FLOAT ix2m1 = (ix + 1) * (ix - 1);
FLOAT s = M_SQRT (ix2m1);
__real__ res = M_LOG1P (2 * (ix2m1 + ix * s)) / 2;
if (adj)
__imag__ res = M_ATAN2 (rx, M_COPYSIGN (s, __imag__ x));
else
__imag__ res = M_ATAN2 (s, rx);
}
else
{
FLOAT ix2m1 = (ix + 1) * (ix - 1);
FLOAT rx2 = rx * rx;
FLOAT f = rx2 * (2 + rx2 + 2 * ix * ix);
FLOAT d = M_SQRT (ix2m1 * ix2m1 + f);
FLOAT dp = d + ix2m1;
FLOAT dm = f / dp;
FLOAT r1 = M_SQRT ((dm + rx2) / 2);
FLOAT r2 = rx * ix / r1;
__real__ res = M_LOG1P (rx2 + dp + 2 * (rx * r1 + ix * r2)) / 2;
if (adj)
__imag__ res = M_ATAN2 (rx + r1, M_COPYSIGN (ix + r2, __imag__ x));
else
__imag__ res = M_ATAN2 (ix + r2, rx + r1);
}
}
else if (ix == 1 && rx < M_LIT (0.5))
{
if (rx < M_EPSILON / 8)
{
__real__ res = M_LOG1P (2 * (rx + M_SQRT (rx))) / 2;
if (adj)
__imag__ res = M_ATAN2 (M_SQRT (rx), M_COPYSIGN (1, __imag__ x));
else
__imag__ res = M_ATAN2 (1, M_SQRT (rx));
}
else
{
FLOAT d = rx * M_SQRT (4 + rx * rx);
FLOAT s1 = M_SQRT ((d + rx * rx) / 2);
FLOAT s2 = M_SQRT ((d - rx * rx) / 2);
__real__ res = M_LOG1P (rx * rx + d + 2 * (rx * s1 + s2)) / 2;
if (adj)
__imag__ res = M_ATAN2 (rx + s1, M_COPYSIGN (1 + s2, __imag__ x));
else
__imag__ res = M_ATAN2 (1 + s2, rx + s1);
}
}
else if (ix < 1 && rx < M_LIT (0.5))
{
if (ix >= M_EPSILON)
{
if (rx < M_EPSILON * M_EPSILON)
{
FLOAT onemix2 = (1 + ix) * (1 - ix);
FLOAT s = M_SQRT (onemix2);
__real__ res = M_LOG1P (2 * rx / s) / 2;
if (adj)
__imag__ res = M_ATAN2 (s, __imag__ x);
else
__imag__ res = M_ATAN2 (ix, s);
}
else
{
FLOAT onemix2 = (1 + ix) * (1 - ix);
FLOAT rx2 = rx * rx;
FLOAT f = rx2 * (2 + rx2 + 2 * ix * ix);
FLOAT d = M_SQRT (onemix2 * onemix2 + f);
FLOAT dp = d + onemix2;
FLOAT dm = f / dp;
FLOAT r1 = M_SQRT ((dp + rx2) / 2);
FLOAT r2 = rx * ix / r1;
__real__ res = M_LOG1P (rx2 + dm + 2 * (rx * r1 + ix * r2)) / 2;
if (adj)
__imag__ res = M_ATAN2 (rx + r1, M_COPYSIGN (ix + r2,
__imag__ x));
else
__imag__ res = M_ATAN2 (ix + r2, rx + r1);
}
}
else
{
FLOAT s = M_HYPOT (1, rx);
__real__ res = M_LOG1P (2 * rx * (rx + s)) / 2;
if (adj)
__imag__ res = M_ATAN2 (s, __imag__ x);
else
__imag__ res = M_ATAN2 (ix, s);
}
math_check_force_underflow_nonneg (__real__ res);
}
else
{
__real__ y = (rx - ix) * (rx + ix) + 1;
__imag__ y = 2 * rx * ix;
y = M_SUF (__csqrt) (y);
__real__ y += rx;
__imag__ y += ix;
if (adj)
{
FLOAT t = __real__ y;
__real__ y = M_COPYSIGN (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = M_SUF (__clog) (y);
}
/* Give results the correct sign for the original argument. */
__real__ res = M_COPYSIGN (__real__ res, __real__ x);
__imag__ res = M_COPYSIGN (__imag__ res, (adj ? 1 : __imag__ x));
return res;
}
|
