2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
4 * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
10 * 1. Redistributions of source code must retain the above copyright
11 * notice unmodified, this list of conditions, and the following
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.
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19 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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26 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
30 * Hyperbolic cosine of a complex argument z = x + i y.
32 * cosh(z) = cosh(x+iy)
33 * = cosh(x) cos(y) + i sinh(x) sin(y).
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).
41 #include <sys/cdefs.h>
42 __FBSDID("$FreeBSD$");
47 #include "math_private.h"
49 static const double huge = 0x1p1023;
52 ccosh(double complex z)
55 int32_t hx, hy, ix, iy, lx, ly;
60 EXTRACT_WORDS(hx, lx, x);
61 EXTRACT_WORDS(hy, ly, y);
66 /* Handle the nearly-non-exceptional cases where x and y are finite. */
67 if (ix < 0x7ff00000 && iy < 0x7ff00000) {
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)));
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)));
83 /* x >= 1455: the result always overflows */
85 return (CMPLX(h * h * cos(y), h * sin(y)));
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
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.
99 if ((ix | lx) == 0) /* && iy >= 0x7ff00000 */
100 return (CMPLX(y - y, x * copysign(0, y)));
103 * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0.
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.
109 if ((iy | ly) == 0) /* && ix >= 0x7ff00000 */
110 return (CMPLX(x * x, copysign(0, x) * y));
113 * cosh(x +- I Inf) = dNaN + I dNaN.
114 * Raise the invalid floating-point exception for finite nonzero x.
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).
120 if (ix < 0x7ff00000) /* && iy >= 0x7ff00000 */
121 return (CMPLX(y - y, x * (y - y)));
124 * cosh(+-Inf + I NaN) = +Inf + I d(NaN).
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.
130 * cosh(+-Inf + I y) = +Inf cos(y) +- I Inf sin(y)
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)));
139 * cosh(NaN + I NaN) = d(NaN) + I d(NaN).
141 * cosh(NaN +- I Inf) = d(NaN) + I d(NaN).
142 * Optionally raises the invalid floating-point exception.
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).
149 return (CMPLX(((long double)x * x) * (y - y),
150 ((long double)x + x) * (y - y)));
154 ccos(double complex z)
157 /* ccos(z) = ccosh(I * z) */
158 return (ccosh(CMPLX(-cimag(z), creal(z))));