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
|
/* Complex square root of a float type.
Copyright (C) 1997-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Based on an algorithm by Stephen L. Moshier <moshier@world.std.com>.
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 <math-underflow.h>
#include <float.h>
CFLOAT
M_DECL_FUNC (__csqrt) (CFLOAT x)
{
CFLOAT 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 = M_HUGE_VAL;
__imag__ res = __imag__ x;
}
else if (rcls == FP_INFINITE)
{
if (__real__ x < 0)
{
__real__ res = icls == FP_NAN ? M_NAN : 0;
__imag__ res = M_COPYSIGN (M_HUGE_VAL, __imag__ x);
}
else
{
__real__ res = __real__ x;
__imag__ res = (icls == FP_NAN
? M_NAN : M_COPYSIGN (0, __imag__ x));
}
}
else
{
__real__ res = M_NAN;
__imag__ res = M_NAN;
}
}
else
{
if (__glibc_unlikely (icls == FP_ZERO))
{
if (__real__ x < 0)
{
__real__ res = 0;
__imag__ res = M_COPYSIGN (M_SQRT (-__real__ x), __imag__ x);
}
else
{
__real__ res = M_FABS (M_SQRT (__real__ x));
__imag__ res = M_COPYSIGN (0, __imag__ x);
}
}
else if (__glibc_unlikely (rcls == FP_ZERO))
{
FLOAT r;
if (M_FABS (__imag__ x) >= 2 * M_MIN)
r = M_SQRT (M_LIT (0.5) * M_FABS (__imag__ x));
else
r = M_LIT (0.5) * M_SQRT (2 * M_FABS (__imag__ x));
__real__ res = r;
__imag__ res = M_COPYSIGN (r, __imag__ x);
}
else
{
FLOAT d, r, s;
int scale = 0;
if (M_FABS (__real__ x) > M_MAX / 4)
{
scale = 1;
__real__ x = M_SCALBN (__real__ x, -2 * scale);
__imag__ x = M_SCALBN (__imag__ x, -2 * scale);
}
else if (M_FABS (__imag__ x) > M_MAX / 4)
{
scale = 1;
if (M_FABS (__real__ x) >= 4 * M_MIN)
__real__ x = M_SCALBN (__real__ x, -2 * scale);
else
__real__ x = 0;
__imag__ x = M_SCALBN (__imag__ x, -2 * scale);
}
else if (M_FABS (__real__ x) < 2 * M_MIN
&& M_FABS (__imag__ x) < 2 * M_MIN)
{
scale = -((M_MANT_DIG + 1) / 2);
__real__ x = M_SCALBN (__real__ x, -2 * scale);
__imag__ x = M_SCALBN (__imag__ x, -2 * scale);
}
d = M_HYPOT (__real__ x, __imag__ x);
/* Use the identity 2 Re res Im res = Im x
to avoid cancellation error in d +/- Re x. */
if (__real__ x > 0)
{
r = M_SQRT (M_LIT (0.5) * (d + __real__ x));
if (scale == 1 && M_FABS (__imag__ x) < 1)
{
/* Avoid possible intermediate underflow. */
s = __imag__ x / r;
r = M_SCALBN (r, scale);
scale = 0;
}
else
s = M_LIT (0.5) * (__imag__ x / r);
}
else
{
s = M_SQRT (M_LIT (0.5) * (d - __real__ x));
if (scale == 1 && M_FABS (__imag__ x) < 1)
{
/* Avoid possible intermediate underflow. */
r = M_FABS (__imag__ x / s);
s = M_SCALBN (s, scale);
scale = 0;
}
else
r = M_FABS (M_LIT (0.5) * (__imag__ x / s));
}
if (scale)
{
r = M_SCALBN (r, scale);
s = M_SCALBN (s, scale);
}
math_check_force_underflow (r);
math_check_force_underflow (s);
__real__ res = r;
__imag__ res = M_COPYSIGN (s, __imag__ x);
}
}
return res;
}
declare_mgen_alias (__csqrt, csqrt)
|
