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
|
/* $NetBSD: cephes_subrl.c,v 1.2 2014/10/10 14:06:40 christos Exp $ */
/*-
* Copyright (c) 2007 The NetBSD Foundation, Inc.
* All rights reserved.
*
* This code is derived from software written by Stephen L. Moshier.
* It is redistributed by the NetBSD Foundation by permission of the author.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
* ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
* TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
* BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*/
#include <complex.h>
#include <math.h>
#include "cephes_subrl.h"
/* calculate cosh and sinh */
void
_cchshl(long double x, long double *c, long double *s)
{
long double e, ei;
if (fabsl(x) <= 0.5L) {
*c = coshl(x);
*s = sinhl(x);
} else {
e = expl(x);
ei = 0.5L / e;
e = 0.5L * e;
*s = e - ei;
*c = e + ei;
}
}
/* Program to subtract nearest integer multiple of PI */
/* extended precision value of PI: */
static const long double DP1 = 3.14159265358979323829596852490908531763125L;
static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
#ifndef __vax__
static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
#define MACHEPL 1.1e-38L
#else
static const long double DP3 = 0L;
#define MACHEPL 1.1e-19L
#endif
long double
_redupil(long double x)
{
long double t;
long long i;
t = x / M_PIL;
if (t >= 0.0L)
t += 0.5L;
else
t -= 0.5L;
i = t; /* the multiple */
t = i;
t = ((x - t * DP1) - t * DP2) - t * DP3;
return t;
}
/* Taylor series expansion for cosh(2y) - cos(2x) */
long double
_ctansl(long double complex z)
{
long double f, x, x2, y, y2, rn, t;
long double d;
x = fabsl(2.0L * creall(z));
y = fabsl(2.0L * cimagl(z));
x = _redupil(x);
x = x * x;
y = y * y;
x2 = 1.0;
y2 = 1.0;
f = 1.0;
rn = 0.0;
d = 0.0;
do {
rn += 1.0L;
f *= rn;
rn += 1.0L;
f *= rn;
x2 *= x;
y2 *= y;
t = y2 + x2;
t /= f;
d += t;
rn += 1.0L;
f *= rn;
rn += 1.0L;
f *= rn;
x2 *= x;
y2 *= y;
t = y2 - x2;
t /= f;
d += t;
} while (fabsl(t/d) > MACHEPL);
return d;
}
|
