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