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
|
/* Complex square root of float value.
Copyright (C) 1997 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 Library General Public License as
published by the Free Software Foundation; either version 2 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
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with the GNU C Library; see the file COPYING.LIB. If not,
write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA. */
#include <complex.h>
#include <math.h>
#include "math_private.h"
__complex__ float
__csqrtf (__complex__ float x)
{
__complex__ float res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (rcls <= FP_INFINITE || icls <= FP_INFINITE)
{
if (icls == FP_INFINITE)
{
__real__ res = HUGE_VALF;
__imag__ res = __imag__ x;
}
else if (rcls == FP_INFINITE)
{
if (__real__ x < 0.0)
{
__real__ res = icls == FP_NAN ? __nanf ("") : 0;
__imag__ res = __copysignf (HUGE_VALF, __imag__ x);
}
else
{
__real__ res = __real__ x;
__imag__ res = (icls == FP_NAN
? __nanf ("") : __copysignf (0.0, __imag__ x));
}
}
else
{
__real__ res = __nanf ("");
__imag__ res = __nanf ("");
}
}
else
{
if (icls == FP_ZERO)
{
if (__real__ x < 0.0)
{
__real__ res = 0.0;
__imag__ res = __copysignf (__ieee754_sqrtf (-__real__ x),
__imag__ x);
}
else
{
__real__ res = fabsf (__ieee754_sqrtf (__real__ x));
__imag__ res = __copysignf (0.0, __imag__ x);
}
}
else if (rcls == FP_ZERO)
{
float r = __ieee754_sqrtf (0.5 * fabsf (__imag__ x));
__real__ res = __copysignf (r, __imag__ x);
__imag__ res = r;
}
else
{
#if 0 /* FIXME: this is broken. */
__complex__ float q;
float t, r;
if (fabsf (__imag__ x) < 2.0e-4 * fabsf (__real__ x))
t = 0.25 * __imag__ x * (__imag__ x / __real__ x);
else
t = 0.5 * (__ieee754_hypotf (__real__ x, __imag__ x) - __real__ x);
r = __ieee754_sqrtf (t);
__real__ q = __imag__ x / (2.0 * r);
__imag__ q = r;
/* Heron iteration in complex arithmetic. */
res = 0.5 * (q + q / x);
#else
float d, imag;
d = __ieee754_hypotf (__real__ x, __imag__ x);
imag = __ieee754_sqrtf (0.5 * (d - __real__ x));
__real__ res = __ieee754_sqrtf (0.5 * (d + __real__ x));
__imag__ res = __copysignf (imag, __imag__ x);
#endif
}
}
return res;
}
weak_alias (__csqrtf, csqrtf)
|
