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
|
/* $OpenBSD: n_casin.c,v 1.1 2008/10/07 22:25:53 martynas Exp $ */
/*
* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
*
* Permission to use, copy, modify, and distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/
/* casin()
*
* Complex circular arc sine
*
*
*
* SYNOPSIS:
*
* double complex casin();
* double complex z, w;
*
* w = casin (z);
*
*
*
* DESCRIPTION:
*
* Inverse complex sine:
*
* 2
* w = -i clog( iz + csqrt( 1 - z ) ).
*
* casin(z) = -i casinh(iz)
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 10100 2.1e-15 3.4e-16
* IEEE -10,+10 30000 2.2e-14 2.7e-15
* Larger relative error can be observed for z near zero.
* Also tested by csin(casin(z)) = z.
*/
#include <complex.h>
#include <math.h>
double complex
casin(double complex z)
{
double complex w;
static double complex ca, ct, zz, z2;
double x, y;
x = creal (z);
y = cimag (z);
if (y == 0.0) {
if (fabs(x) > 1.0) {
w = M_PI_2 + 0.0 * I;
/*mtherr ("casin", DOMAIN);*/
}
else {
w = asin (x) + 0.0 * I;
}
return (w);
}
/* Power series expansion */
/*
b = cabs(z);
if( b < 0.125 ) {
z2.r = (x - y) * (x + y);
z2.i = 2.0 * x * y;
cn = 1.0;
n = 1.0;
ca.r = x;
ca.i = y;
sum.r = x;
sum.i = y;
do {
ct.r = z2.r * ca.r - z2.i * ca.i;
ct.i = z2.r * ca.i + z2.i * ca.r;
ca.r = ct.r;
ca.i = ct.i;
cn *= n;
n += 1.0;
cn /= n;
n += 1.0;
b = cn/n;
ct.r *= b;
ct.i *= b;
sum.r += ct.r;
sum.i += ct.i;
b = fabs(ct.r) + fabs(ct.i);
}
while( b > MACHEP );
w->r = sum.r;
w->i = sum.i;
return;
}
*/
ca = x + y * I;
ct = ca * I;
/* sqrt( 1 - z*z) */
/* cmul( &ca, &ca, &zz ) */
/*x * x - y * y */
zz = (x - y) * (x + y) + (2.0 * x * y) * I;
zz = 1.0 - creal(zz) - cimag(zz) * I;
z2 = csqrt (zz);
zz = ct + z2;
zz = clog (zz);
/* multiply by 1/i = -i */
w = zz * (-1.0 * I);
return (w);
}
|
