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
|
/* $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 */
/* On platforms where long double is as wide as double. */
#ifdef _LDBL_EQ_DBL
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;
}
}
#endif
/* 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) */
/* On platforms where long double is as wide as double. */
#ifdef _LDBL_EQ_DBL
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;
}
#endif
|
