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: head/lib/msun/src/s_ccosh.c 284423 2015-06-15 20:11:06Z tijl $");
41
42 #include <complex.h>
43 #include <math.h>
44
45 #include "math_private.h"
46
47 static const double huge = 0x1p1023;
48
49 double complex
ccosh(double complex z)50 ccosh(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
150 double complex
ccos(double complex z)151 ccos(double complex z)
152 {
153
154 /* ccos(z) = ccosh(I * z) */
155 return (ccosh(CMPLX(-cimag(z), creal(z))));
156 }
157