summaryrefslogtreecommitdiffstats
path: root/lib/msun/src/s_ccosh.c
blob: 2843198c35710c54fabc42eddb2afd9262596005 (plain)
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
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
/*-
 * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
 * All rights reserved.
 *
 * 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 unmodified, 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 AUTHOR ``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 AUTHOR 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.
 */

/*
 * Hyperbolic cosine of a complex argument z = x + i y.
 *
 * cosh(z) = cosh(x+iy)
 *         = cosh(x) cos(y) + i sinh(x) sin(y).
 *
 * Exceptional values are noted in the comments within the source code.
 * These values and the return value were taken from n1124.pdf.
 * The sign of the result for some exceptional values is unspecified but
 * must satisfy both cosh(conj(z)) == conj(cosh(z)) and cosh(-z) == cosh(z).
 */

#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");

#include <complex.h>
#include <math.h>

#include "math_private.h"

static const double huge = 0x1p1023;

double complex
ccosh(double complex z)
{
	double x, y, h;
	int32_t hx, hy, ix, iy, lx, ly;

	x = creal(z);
	y = cimag(z);

	EXTRACT_WORDS(hx, lx, x);
	EXTRACT_WORDS(hy, ly, y);

	ix = 0x7fffffff & hx;
	iy = 0x7fffffff & hy;

	/* Handle the nearly-non-exceptional cases where x and y are finite. */
	if (ix < 0x7ff00000 && iy < 0x7ff00000) {
		if ((iy | ly) == 0)
			return (CMPLX(cosh(x), x * y));
		if (ix < 0x40360000)	/* |x| < 22: normal case */
			return (CMPLX(cosh(x) * cos(y), sinh(x) * sin(y)));

		/* |x| >= 22, so cosh(x) ~= exp(|x|) */
		if (ix < 0x40862e42) {
			/* x < 710: exp(|x|) won't overflow */
			h = exp(fabs(x)) * 0.5;
			return (CMPLX(h * cos(y), copysign(h, x) * sin(y)));
		} else if (ix < 0x4096bbaa) {
			/* x < 1455: scale to avoid overflow */
			z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
			return (CMPLX(creal(z), cimag(z) * copysign(1, x)));
		} else {
			/* x >= 1455: the result always overflows */
			h = huge * x;
			return (CMPLX(h * h * cos(y), h * sin(y)));
		}
	}

	/*
	 * cosh(+-0 +- I Inf) = dNaN + I (+-)(+-)0.
	 * The sign of 0 in the result is unspecified.  Choice = product
	 * of the signs of the argument.  Raise the invalid floating-point
	 * exception.
	 *
	 * cosh(+-0 +- I NaN) = d(NaN) + I (+-)(+-)0.
	 * The sign of 0 in the result is unspecified.  Choice = product
	 * of the signs of the argument.
	 */
	if ((ix | lx) == 0)		/* && iy >= 0x7ff00000 */
		return (CMPLX(y - y, x * copysign(0, y)));

	/*
	 * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0.
	 *
	 * cosh(NaN +- I 0)   = d(NaN) + I (+-)(+-)0.
	 * The sign of 0 in the result is unspecified.  Choice = product
	 * of the signs of the argument.
	 */
	if ((iy | ly) == 0)		/* && ix >= 0x7ff00000 */
		return (CMPLX(x * x, copysign(0, x) * y));

	/*
	 * cosh(x +- I Inf) = dNaN + I dNaN.
	 * Raise the invalid floating-point exception for finite nonzero x.
	 *
	 * cosh(x + I NaN) = d(NaN) + I d(NaN).
	 * Optionally raises the invalid floating-point exception for finite
	 * nonzero x.  Choice = don't raise (except for signaling NaNs).
	 */
	if (ix < 0x7ff00000)		/* && iy >= 0x7ff00000 */
		return (CMPLX(y - y, x * (y - y)));

	/*
	 * cosh(+-Inf + I NaN)  = +Inf + I d(NaN).
	 *
	 * cosh(+-Inf +- I Inf) = +Inf + I dNaN.
	 * The sign of Inf in the result is unspecified.  Choice = always +.
	 * Raise the invalid floating-point exception.
	 *
	 * cosh(+-Inf + I y)   = +Inf cos(y) +- I Inf sin(y)
	 */
	if (ix == 0x7ff00000 && lx == 0) {
		if (iy >= 0x7ff00000)
			return (CMPLX(INFINITY, x * (y - y)));
		return (CMPLX(INFINITY * cos(y), x * sin(y)));
	}

	/*
	 * cosh(NaN + I NaN)  = d(NaN) + I d(NaN).
	 *
	 * cosh(NaN +- I Inf) = d(NaN) + I d(NaN).
	 * Optionally raises the invalid floating-point exception.
	 * Choice = raise.
	 *
	 * cosh(NaN + I y)    = d(NaN) + I d(NaN).
	 * Optionally raises the invalid floating-point exception for finite
	 * nonzero y.  Choice = don't raise (except for signaling NaNs).
	 */
	return (CMPLX((x * x) * (y - y), (x + x) * (y - y)));
}

double complex
ccos(double complex z)
{

	/* ccos(z) = ccosh(I * z) */
	return (ccosh(CMPLX(-cimag(z), creal(z))));
}
OpenPOWER on IntegriCloud