s_ccosh.c revision a0ee07829a9ba7e99ef68e8c12551301cc797f0f 
1/*-
2 * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 *    notice unmodified, this list of conditions, and the following
10 *    disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 *    notice, this list of conditions and the following disclaimer in the
13 *    documentation and/or other materials provided with the distribution.
14 *
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
16 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
17 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
18 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
19 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
20 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
21 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
22 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
23 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
24 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
25 */
26
27/*
28 * Hyperbolic cosine of a complex argument z = x + i y.
29 *
30 * cosh(z) = cosh(x+iy)
31 *         = cosh(x) cos(y) + i sinh(x) sin(y).
32 *
33 * Exceptional values are noted in the comments within the source code.
34 * These values and the return value were taken from n1124.pdf.
35 */
36
37#include <sys/cdefs.h>
38__FBSDID("$FreeBSD$");
39
40#include <complex.h>
41#include <math.h>
42
43#include "math_private.h"
44
45static const double huge = 0x1p1023;
46
47double complex
48ccosh(double complex z)
49{
50	double x, y, h;
51	int32_t hx, hy, ix, iy, lx, ly;
52
53	x = creal(z);
54	y = cimag(z);
55
56	EXTRACT_WORDS(hx, lx, x);
57	EXTRACT_WORDS(hy, ly, y);
58
59	ix = 0x7fffffff & hx;
60	iy = 0x7fffffff & hy;
61
62	/* Handle the nearly-non-exceptional cases where x and y are finite. */
63	if (ix < 0x7ff00000 && iy < 0x7ff00000) {
64		if ((iy | ly) == 0)
65			return (cpack(cosh(x), x * y));
66		if (ix < 0x40360000)	/* small x: normal case */
67			return (cpack(cosh(x) * cos(y), sinh(x) * sin(y)));
68
69		/* |x| >= 22, so cosh(x) ~= exp(|x|) */
70		if (ix < 0x40862e42) {
71			/* x < 710: exp(|x|) won't overflow */
72			h = exp(fabs(x)) * 0.5;
73			return (cpack(h * cos(y), copysign(h, x) * sin(y)));
74		} else if (ix < 0x4096bbaa) {
75			/* x < 1455: scale to avoid overflow */
76			z = __ldexp_cexp(cpack(fabs(x), y), -1);
77			return (cpack(creal(z), cimag(z) * copysign(1, x)));
78		} else {
79			/* x >= 1455: the result always overflows */
80			h = huge * x;
81			return (cpack(h * h * cos(y), h * sin(y)));
82		}
83	}
84
85	/*
86	 * cosh(+-0 +- I Inf) = dNaN + I sign(d(+-0, dNaN))0.
87	 * The sign of 0 in the result is unspecified.  Choice = normally
88	 * the same as dNaN.  Raise the invalid floating-point exception.
89	 *
90	 * cosh(+-0 +- I NaN) = d(NaN) + I sign(d(+-0, NaN))0.
91	 * The sign of 0 in the result is unspecified.  Choice = normally
92	 * the same as d(NaN).
93	 */
94	if ((ix | lx) == 0 && iy >= 0x7ff00000)
95		return (cpack(y - y, copysign(0, x * (y - y))));
96
97	/*
98	 * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0.
99	 *
100	 * cosh(NaN +- I 0)   = d(NaN) + I sign(d(NaN, +-0))0.
101	 * The sign of 0 in the result is unspecified.
102	 */
103	if ((iy | ly) == 0 && ix >= 0x7ff00000) {
104		if (((hx & 0xfffff) | lx) == 0)
105			return (cpack(x * x, copysign(0, x) * y));
106		return (cpack(x * x, copysign(0, (x + x) * y)));
107	}
108
109	/*
110	 * cosh(x +- I Inf) = dNaN + I dNaN.
111	 * Raise the invalid floating-point exception for finite nonzero x.
112	 *
113	 * cosh(x + I NaN) = d(NaN) + I d(NaN).
114	 * Optionally raises the invalid floating-point exception for finite
115	 * nonzero x.  Choice = don't raise (except for signaling NaNs).
116	 */
117	if (ix < 0x7ff00000 && iy >= 0x7ff00000)
118		return (cpack(y - y, x * (y - y)));
119
120	/*
121	 * cosh(+-Inf + I NaN)  = +Inf + I d(NaN).
122	 *
123	 * cosh(+-Inf +- I Inf) = +Inf + I dNaN.
124	 * The sign of Inf in the result is unspecified.  Choice = always +.
125	 * Raise the invalid floating-point exception.
126	 *
127	 * cosh(+-Inf + I y)   = +Inf cos(y) +- I Inf sin(y)
128	 */
129	if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
130		if (iy >= 0x7ff00000)
131			return (cpack(x * x, x * (y - y)));
132		return (cpack((x * x) * cos(y), x * sin(y)));
133	}
134
135	/*
136	 * cosh(NaN + I NaN)  = d(NaN) + I d(NaN).
137	 *
138	 * cosh(NaN +- I Inf) = d(NaN) + I d(NaN).
139	 * Optionally raises the invalid floating-point exception.
140	 * Choice = raise.
141	 *
142	 * cosh(NaN + I y)    = d(NaN) + I d(NaN).
143	 * Optionally raises the invalid floating-point exception for finite
144	 * nonzero y.  Choice = don't raise (except for signaling NaNs).
145	 */
146	return (cpack((x * x) * (y - y), (x + x) * (y - y)));
147}
148
149double complex
150ccos(double complex z)
151{
152
153	/* ccos(z) = ccosh(I * z) */
154	return (ccosh(cpack(-cimag(z), creal(z))));
155}
156