ipiq: Add simple IPI latency measure sysctls (2)
[dragonfly.git] / lib / libm / src / s_csinh.c
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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 * $FreeBSD: head/lib/msun/src/s_csinh.c 226599 2011-10-21 06:29:32Z das $
27 */
28
29/*
30 * Hyperbolic sine of a complex argument z = x + i y.
31 *
32 * sinh(z) = sinh(x+iy)
33 * = sinh(x) cos(y) + i cosh(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 */
38
39#include <complex.h>
40#include <math.h>
41
42#include "math_private.h"
43
44static const double huge = 0x1p1023;
45
46double complex
47csinh(double complex z)
48{
49 double x, y, h;
50 int32_t hx, hy, ix, iy, lx, ly;
51
52 x = creal(z);
53 y = cimag(z);
54
55 EXTRACT_WORDS(hx, lx, x);
56 EXTRACT_WORDS(hy, ly, y);
57
58 ix = 0x7fffffff & hx;
59 iy = 0x7fffffff & hy;
60
61 /* Handle the nearly-non-exceptional cases where x and y are finite. */
62 if (ix < 0x7ff00000 && iy < 0x7ff00000) {
63 if ((iy | ly) == 0)
64 return (cpack(sinh(x), y));
65 if (ix < 0x40360000) /* small x: normal case */
66 return (cpack(sinh(x) * cos(y), cosh(x) * sin(y)));
67
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(copysign(h, x) * cos(y), h * 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) * copysign(1, x), cimag(z)));
77 } else {
78 /* x >= 1455: the result always overflows */
79 h = huge * x;
80 return (cpack(h * cos(y), h * h * sin(y)));
81 }
82 }
83
84 /*
85 * sinh(+-0 +- I Inf) = sign(d(+-0, dNaN))0 + I dNaN.
86 * The sign of 0 in the result is unspecified. Choice = normally
87 * the same as dNaN. Raise the invalid floating-point exception.
88 *
89 * sinh(+-0 +- I NaN) = sign(d(+-0, NaN))0 + I d(NaN).
90 * The sign of 0 in the result is unspecified. Choice = normally
91 * the same as d(NaN).
92 */
93 if ((ix | lx) == 0 && iy >= 0x7ff00000)
94 return (cpack(copysign(0, x * (y - y)), y - y));
95
96 /*
97 * sinh(+-Inf +- I 0) = +-Inf + I +-0.
98 *
99 * sinh(NaN +- I 0) = d(NaN) + I +-0.
100 */
101 if ((iy | ly) == 0 && ix >= 0x7ff00000) {
102 if (((hx & 0xfffff) | lx) == 0)
103 return (cpack(x, y));
104 return (cpack(x, copysign(0, y)));
105 }
106
107 /*
108 * sinh(x +- I Inf) = dNaN + I dNaN.
109 * Raise the invalid floating-point exception for finite nonzero x.
110 *
111 * sinh(x + I NaN) = d(NaN) + I d(NaN).
112 * Optionally raises the invalid floating-point exception for finite
113 * nonzero x. Choice = don't raise (except for signaling NaNs).
114 */
115 if (ix < 0x7ff00000 && iy >= 0x7ff00000)
116 return (cpack(y - y, x * (y - y)));
117
118 /*
119 * sinh(+-Inf + I NaN) = +-Inf + I d(NaN).
120 * The sign of Inf in the result is unspecified. Choice = normally
121 * the same as d(NaN).
122 *
123 * sinh(+-Inf +- I Inf) = +Inf + I dNaN.
124 * The sign of Inf in the result is unspecified. Choice = always +.
125 * Raise the invalid floating-point exception.
126 *
127 * sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y)
128 */
129 if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
130 if (iy >= 0x7ff00000)
131 return (cpack(x * x, x * (y - y)));
132 return (cpack(x * cos(y), INFINITY * sin(y)));
133 }
134
135 /*
136 * sinh(NaN + I NaN) = d(NaN) + I d(NaN).
137 *
138 * sinh(NaN +- I Inf) = d(NaN) + I d(NaN).
139 * Optionally raises the invalid floating-point exception.
140 * Choice = raise.
141 *
142 * sinh(NaN + I y) = d(NaN) + I d(NaN).
143 * Optionally raises the invalid floating-point exception for finite
144 * nonzero y. Choice = don't raise (except for signaling NaNs).
145 */
146 return (cpack((x * x) * (y - y), (x + x) * (y - y)));
147}
148
149double complex
150csin(double complex z)
151{
152
153 /* csin(z) = -I * csinh(I * z) */
154 z = csinh(cpack(-cimag(z), creal(z)));
155 return (cpack(cimag(z), -creal(z)));
156}