2 * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
8 * 1. Redistributions of source code must retain the above copyright
9 * notice unmodified, this list of conditions, and the following
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17 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
18 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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20 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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24 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
26 * $FreeBSD: head/lib/msun/src/s_ccosh.c 226599 2011-10-21 06:29:32Z das $
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.
42 #include "math_private.h"
44 static const double huge = 0x1p1023;
47 ccosh(double complex z)
50 int32_t hx, hy, ix, iy, lx, ly;
55 EXTRACT_WORDS(hx, lx, x);
56 EXTRACT_WORDS(hy, ly, y);
61 /* Handle the nearly-non-exceptional cases where x and y are finite. */
62 if (ix < 0x7ff00000 && iy < 0x7ff00000) {
64 return (cpack(cosh(x), x * y));
65 if (ix < 0x40360000) /* small x: normal case */
66 return (cpack(cosh(x) * cos(y), sinh(x) * sin(y)));
68 /* |x| >= 22, so cosh(x) ~= exp(|x|) */
69 if (ix < 0x40862e42) {
70 /* x < 710: exp(|x|) won't overflow */
71 h = exp(fabs(x)) * 0.5;
72 return (cpack(h * cos(y), copysign(h, x) * sin(y)));
73 } else if (ix < 0x4096bbaa) {
74 /* x < 1455: scale to avoid overflow */
75 z = __ldexp_cexp(cpack(fabs(x), y), -1);
76 return (cpack(creal(z), cimag(z) * copysign(1, x)));
78 /* x >= 1455: the result always overflows */
80 return (cpack(h * h * cos(y), h * sin(y)));
85 * cosh(+-0 +- I Inf) = dNaN + I sign(d(+-0, dNaN))0.
86 * The sign of 0 in the result is unspecified. Choice = normally
87 * the same as dNaN. Raise the invalid floating-point exception.
89 * cosh(+-0 +- I NaN) = d(NaN) + I sign(d(+-0, NaN))0.
90 * The sign of 0 in the result is unspecified. Choice = normally
93 if ((ix | lx) == 0 && iy >= 0x7ff00000)
94 return (cpack(y - y, copysign(0, x * (y - y))));
97 * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0.
99 * cosh(NaN +- I 0) = d(NaN) + I sign(d(NaN, +-0))0.
100 * The sign of 0 in the result is unspecified.
102 if ((iy | ly) == 0 && ix >= 0x7ff00000) {
103 if (((hx & 0xfffff) | lx) == 0)
104 return (cpack(x * x, copysign(0, x) * y));
105 return (cpack(x * x, copysign(0, (x + x) * y)));
109 * cosh(x +- I Inf) = dNaN + I dNaN.
110 * Raise the invalid floating-point exception for finite nonzero x.
112 * cosh(x + I NaN) = d(NaN) + I d(NaN).
113 * Optionally raises the invalid floating-point exception for finite
114 * nonzero x. Choice = don't raise (except for signaling NaNs).
116 if (ix < 0x7ff00000 && iy >= 0x7ff00000)
117 return (cpack(y - y, x * (y - y)));
120 * cosh(+-Inf + I NaN) = +Inf + I d(NaN).
122 * cosh(+-Inf +- I Inf) = +Inf + I dNaN.
123 * The sign of Inf in the result is unspecified. Choice = always +.
124 * Raise the invalid floating-point exception.
126 * cosh(+-Inf + I y) = +Inf cos(y) +- I Inf sin(y)
128 if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
129 if (iy >= 0x7ff00000)
130 return (cpack(x * x, x * (y - y)));
131 return (cpack((x * x) * cos(y), x * sin(y)));
135 * cosh(NaN + I NaN) = d(NaN) + I d(NaN).
137 * cosh(NaN +- I Inf) = d(NaN) + I d(NaN).
138 * Optionally raises the invalid floating-point exception.
141 * cosh(NaN + I y) = d(NaN) + I d(NaN).
142 * Optionally raises the invalid floating-point exception for finite
143 * nonzero y. Choice = don't raise (except for signaling NaNs).
145 return (cpack((x * x) * (y - y), (x + x) * (y - y)));
149 ccos(double complex z)
152 /* ccos(z) = ccosh(I * z) */
153 return (ccosh(cpack(-cimag(z), creal(z))));