1 /* $NetBSD: cephes_subrl.c,v 1.2 2014/10/10 14:06:40 christos Exp $ */
2
3 /*-
4 * Copyright (c) 2007 The NetBSD Foundation, Inc.
5 * All rights reserved.
6 *
7 * This code is derived from software written by Stephen L. Moshier.
8 * It is redistributed by the NetBSD Foundation by permission of the author.
9 *
10 * Redistribution and use in source and binary forms, with or without
11 * modification, are permitted provided that the following conditions
12 * are met:
13 * 1. Redistributions of source code must retain the above copyright
14 * notice, this list of conditions and the following disclaimer.
15 * 2. Redistributions in binary form must reproduce the above copyright
16 * notice, this list of conditions and the following disclaimer in the
17 * documentation and/or other materials provided with the distribution.
18 *
19 * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
20 * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
21 * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
22 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
23 * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
24 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
25 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
26 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
27 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
28 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
29 * POSSIBILITY OF SUCH DAMAGE.
30 */
31
32 #include <complex.h>
33 #include <math.h>
34 #include "cephes_subrl.h"
35
36 #ifdef _HAVE_LONG_DOUBLE_MATH
37 /* calculate cosh and sinh */
38
39 void
_cchshl(long double x,long double * c,long double * s)40 _cchshl(long double x, long double *c, long double *s)
41 {
42 long double e, ei;
43
44 if (fabsl(x) <= 0.5L) {
45 *c = coshl(x);
46 *s = sinhl(x);
47 } else {
48 e = expl(x);
49 ei = 0.5L / e;
50 e = 0.5L * e;
51 *s = e - ei;
52 *c = e + ei;
53 }
54 }
55
56 /* Program to subtract nearest integer multiple of PI */
57
58 /* extended precision value of PI: */
59 static const long double DP1 = 3.14159265358979323829596852490908531763125L;
60 static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
61 #ifndef __vax__
62 static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
63 #define MACHEPL 1.1e-38L
64 #else
65 static const long double DP3 = 0L;
66 #define MACHEPL 1.1e-19L
67 #endif
68
69 long double
_redupil(long double x)70 _redupil(long double x)
71 {
72 long double t;
73 long long i;
74
75 t = x / M_PIL;
76 if (t >= 0.0L)
77 t += 0.5L;
78 else
79 t -= 0.5L;
80
81 i = t; /* the multiple */
82 t = i;
83 t = ((x - t * DP1) - t * DP2) - t * DP3;
84 return t;
85 }
86
87 /* Taylor series expansion for cosh(2y) - cos(2x) */
88
89 long double
_ctansl(long double complex z)90 _ctansl(long double complex z)
91 {
92 long double f, x, x2, y, y2, rn, t;
93 long double d;
94
95 x = fabsl(2.0L * creall(z));
96 y = fabsl(2.0L * cimagl(z));
97
98 x = _redupil(x);
99
100 x = x * x;
101 y = y * y;
102 x2 = 1.0L;
103 y2 = 1.0L;
104 f = 1.0L;
105 rn = 0.0L;
106 d = 0.0L;
107 do {
108 rn += 1.0L;
109 f *= rn;
110 rn += 1.0L;
111 f *= rn;
112 x2 *= x;
113 y2 *= y;
114 t = y2 + x2;
115 t /= f;
116 d += t;
117
118 rn += 1.0L;
119 f *= rn;
120 rn += 1.0L;
121 f *= rn;
122 x2 *= x;
123 y2 *= y;
124 t = y2 - x2;
125 t /= f;
126 d += t;
127 } while (fabsl(t/d) > MACHEPL);
128 return d;
129 }
130
131 #endif
132
