s_ccosh.c revision 330897 
1/*-
2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
3 *
4 * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
5 * All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 *    notice unmodified, this list of conditions, and the following
12 *    disclaimer.
13 * 2. Redistributions in binary form must reproduce the above copyright
14 *    notice, this list of conditions and the following disclaimer in the
15 *    documentation and/or other materials provided with the distribution.
16 *
17 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
18 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
19 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
20 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
21 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
22 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
23 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
24 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
25 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
26 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
27 */
28
29/*
30 * Hyperbolic cosine of a complex argument z = x + i y.
31 *
32 * cosh(z) = cosh(x+iy)
33 *         = cosh(x) cos(y) + i sinh(x) sin(y).
34 *
35 * Exceptional values are noted in the comments within the source code.
36 * These values and the return value were taken from n1124.pdf.
37 * The sign of the result for some exceptional values is unspecified but
38 * must satisfy both cosh(conj(z)) == conj(cosh(z)) and cosh(-z) == cosh(z).
39 */
40
41#include <sys/cdefs.h>
42__FBSDID("$FreeBSD: stable/11/lib/msun/src/s_ccosh.c 330897 2018-03-14 03:19:51Z eadler $");
43
44#include <complex.h>
45#include <math.h>
46
47#include "math_private.h"
48
49static const double huge = 0x1p1023;
50
51double complex
52ccosh(double complex z)
53{
54	double x, y, h;
55	int32_t hx, hy, ix, iy, lx, ly;
56
57	x = creal(z);
58	y = cimag(z);
59
60	EXTRACT_WORDS(hx, lx, x);
61	EXTRACT_WORDS(hy, ly, y);
62
63	ix = 0x7fffffff & hx;
64	iy = 0x7fffffff & hy;
65
66	/* Handle the nearly-non-exceptional cases where x and y are finite. */
67	if (ix < 0x7ff00000 && iy < 0x7ff00000) {
68		if ((iy | ly) == 0)
69			return (CMPLX(cosh(x), x * y));
70		if (ix < 0x40360000)	/* |x| < 22: normal case */
71			return (CMPLX(cosh(x) * cos(y), sinh(x) * sin(y)));
72
73		/* |x| >= 22, so cosh(x) ~= exp(|x|) */
74		if (ix < 0x40862e42) {
75			/* x < 710: exp(|x|) won't overflow */
76			h = exp(fabs(x)) * 0.5;
77			return (CMPLX(h * cos(y), copysign(h, x) * sin(y)));
78		} else if (ix < 0x4096bbaa) {
79			/* x < 1455: scale to avoid overflow */
80			z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
81			return (CMPLX(creal(z), cimag(z) * copysign(1, x)));
82		} else {
83			/* x >= 1455: the result always overflows */
84			h = huge * x;
85			return (CMPLX(h * h * cos(y), h * sin(y)));
86		}
87	}
88
89	/*
90	 * cosh(+-0 +- I Inf) = dNaN + I (+-)(+-)0.
91	 * The sign of 0 in the result is unspecified.  Choice = product
92	 * of the signs of the argument.  Raise the invalid floating-point
93	 * exception.
94	 *
95	 * cosh(+-0 +- I NaN) = d(NaN) + I (+-)(+-)0.
96	 * The sign of 0 in the result is unspecified.  Choice = product
97	 * of the signs of the argument.
98	 */
99	if ((ix | lx) == 0)		/* && iy >= 0x7ff00000 */
100		return (CMPLX(y - y, x * copysign(0, y)));
101
102	/*
103	 * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0.
104	 *
105	 * cosh(NaN +- I 0)   = d(NaN) + I (+-)(+-)0.
106	 * The sign of 0 in the result is unspecified.  Choice = product
107	 * of the signs of the argument.
108	 */
109	if ((iy | ly) == 0)		/* && ix >= 0x7ff00000 */
110		return (CMPLX(x * x, copysign(0, x) * y));
111
112	/*
113	 * cosh(x +- I Inf) = dNaN + I dNaN.
114	 * Raise the invalid floating-point exception for finite nonzero x.
115	 *
116	 * cosh(x + I NaN) = d(NaN) + I d(NaN).
117	 * Optionally raises the invalid floating-point exception for finite
118	 * nonzero x.  Choice = don't raise (except for signaling NaNs).
119	 */
120	if (ix < 0x7ff00000)		/* && iy >= 0x7ff00000 */
121		return (CMPLX(y - y, x * (y - y)));
122
123	/*
124	 * cosh(+-Inf + I NaN)  = +Inf + I d(NaN).
125	 *
126	 * cosh(+-Inf +- I Inf) = +Inf + I dNaN.
127	 * The sign of Inf in the result is unspecified.  Choice = always +.
128	 * Raise the invalid floating-point exception.
129	 *
130	 * cosh(+-Inf + I y)   = +Inf cos(y) +- I Inf sin(y)
131	 */
132	if (ix == 0x7ff00000 && lx == 0) {
133		if (iy >= 0x7ff00000)
134			return (CMPLX(INFINITY, x * (y - y)));
135		return (CMPLX(INFINITY * cos(y), x * sin(y)));
136	}
137
138	/*
139	 * cosh(NaN + I NaN)  = d(NaN) + I d(NaN).
140	 *
141	 * cosh(NaN +- I Inf) = d(NaN) + I d(NaN).
142	 * Optionally raises the invalid floating-point exception.
143	 * Choice = raise.
144	 *
145	 * cosh(NaN + I y)    = d(NaN) + I d(NaN).
146	 * Optionally raises the invalid floating-point exception for finite
147	 * nonzero y.  Choice = don't raise (except for signaling NaNs).
148	 */
149	return (CMPLX((x * x) * (y - y), (x + x) * (y - y)));
150}
151
152double complex
153ccos(double complex z)
154{
155
156	/* ccos(z) = ccosh(I * z) */
157	return (ccosh(CMPLX(-cimag(z), creal(z))));
158}
159