s_ccosh.c revision 284810 
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 * The sign of the result for some exceptional values is unspecified but
36 * must satisfy both cosh(conj(z)) == conj(cosh(z)) and cosh(-z) == cosh(z).
37 */
38
39#include <sys/cdefs.h>
40__FBSDID("$FreeBSD: stable/10/lib/msun/src/s_ccosh.c 284810 2015-06-25 13:01:10Z tijl $");
41
42#include <complex.h>
43#include <math.h>
44
45#include "math_private.h"
46
47static const double huge = 0x1p1023;
48
49double complex
50ccosh(double complex z)
51{
52	double x, y, h;
53	int32_t hx, hy, ix, iy, lx, ly;
54
55	x = creal(z);
56	y = cimag(z);
57
58	EXTRACT_WORDS(hx, lx, x);
59	EXTRACT_WORDS(hy, ly, y);
60
61	ix = 0x7fffffff & hx;
62	iy = 0x7fffffff & hy;
63
64	/* Handle the nearly-non-exceptional cases where x and y are finite. */
65	if (ix < 0x7ff00000 && iy < 0x7ff00000) {
66		if ((iy | ly) == 0)
67			return (CMPLX(cosh(x), x * y));
68		if (ix < 0x40360000)	/* |x| < 22: normal case */
69			return (CMPLX(cosh(x) * cos(y), sinh(x) * sin(y)));
70
71		/* |x| >= 22, so cosh(x) ~= exp(|x|) */
72		if (ix < 0x40862e42) {
73			/* x < 710: exp(|x|) won't overflow */
74			h = exp(fabs(x)) * 0.5;
75			return (CMPLX(h * cos(y), copysign(h, x) * sin(y)));
76		} else if (ix < 0x4096bbaa) {
77			/* x < 1455: scale to avoid overflow */
78			z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
79			return (CMPLX(creal(z), cimag(z) * copysign(1, x)));
80		} else {
81			/* x >= 1455: the result always overflows */
82			h = huge * x;
83			return (CMPLX(h * h * cos(y), h * sin(y)));
84		}
85	}
86
87	/*
88	 * cosh(+-0 +- I Inf) = dNaN + I (+-)(+-)0.
89	 * The sign of 0 in the result is unspecified.  Choice = product
90	 * of the signs of the argument.  Raise the invalid floating-point
91	 * exception.
92	 *
93	 * cosh(+-0 +- I NaN) = d(NaN) + I (+-)(+-)0.
94	 * The sign of 0 in the result is unspecified.  Choice = product
95	 * of the signs of the argument.
96	 */
97	if ((ix | lx) == 0)		/* && iy >= 0x7ff00000 */
98		return (CMPLX(y - y, x * copysign(0, y)));
99
100	/*
101	 * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0.
102	 *
103	 * cosh(NaN +- I 0)   = d(NaN) + I (+-)(+-)0.
104	 * The sign of 0 in the result is unspecified.  Choice = product
105	 * of the signs of the argument.
106	 */
107	if ((iy | ly) == 0)		/* && ix >= 0x7ff00000 */
108		return (CMPLX(x * x, copysign(0, x) * y));
109
110	/*
111	 * cosh(x +- I Inf) = dNaN + I dNaN.
112	 * Raise the invalid floating-point exception for finite nonzero x.
113	 *
114	 * cosh(x + I NaN) = d(NaN) + I d(NaN).
115	 * Optionally raises the invalid floating-point exception for finite
116	 * nonzero x.  Choice = don't raise (except for signaling NaNs).
117	 */
118	if (ix < 0x7ff00000)		/* && iy >= 0x7ff00000 */
119		return (CMPLX(y - y, x * (y - y)));
120
121	/*
122	 * cosh(+-Inf + I NaN)  = +Inf + I d(NaN).
123	 *
124	 * cosh(+-Inf +- I Inf) = +Inf + I dNaN.
125	 * The sign of Inf in the result is unspecified.  Choice = always +.
126	 * Raise the invalid floating-point exception.
127	 *
128	 * cosh(+-Inf + I y)   = +Inf cos(y) +- I Inf sin(y)
129	 */
130	if (ix == 0x7ff00000 && lx == 0) {
131		if (iy >= 0x7ff00000)
132			return (CMPLX(INFINITY, x * (y - y)));
133		return (CMPLX(INFINITY * cos(y), x * sin(y)));
134	}
135
136	/*
137	 * cosh(NaN + I NaN)  = d(NaN) + I d(NaN).
138	 *
139	 * cosh(NaN +- I Inf) = d(NaN) + I d(NaN).
140	 * Optionally raises the invalid floating-point exception.
141	 * Choice = raise.
142	 *
143	 * cosh(NaN + I y)    = d(NaN) + I d(NaN).
144	 * Optionally raises the invalid floating-point exception for finite
145	 * nonzero y.  Choice = don't raise (except for signaling NaNs).
146	 */
147	return (CMPLX((x * x) * (y - y), (x + x) * (y - y)));
148}
149
150double complex
151ccos(double complex z)
152{
153
154	/* ccos(z) = ccosh(I * z) */
155	return (ccosh(CMPLX(-cimag(z), creal(z))));
156}
157