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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 
27 /*
28  * Hyperbolic sine of a complex argument z.  See s_csinh.c for details.
29  */
30 
31 #include <sys/cdefs.h>
32 __FBSDID("$FreeBSD$");
33 
34 #include <complex.h>
35 #include <math.h>
36 
37 #include "math_private.h"
38 
39 static const float huge = 0x1p127;
40 
41 float complex
csinhf(float complex z)42 csinhf(float complex z)
43 {
44 	float x, y, h;
45 	int32_t hx, hy, ix, iy;
46 
47 	x = crealf(z);
48 	y = cimagf(z);
49 
50 	GET_FLOAT_WORD(hx, x);
51 	GET_FLOAT_WORD(hy, y);
52 
53 	ix = 0x7fffffff & hx;
54 	iy = 0x7fffffff & hy;
55 
56 	if (ix < 0x7f800000 && iy < 0x7f800000) {
57 		if (iy == 0)
58 			return (cpackf(sinhf(x), y));
59 		if (ix < 0x41100000)	/* small x: normal case */
60 			return (cpackf(sinhf(x) * cosf(y), coshf(x) * sinf(y)));
61 
62 		/* |x| >= 9, so cosh(x) ~= exp(|x|) */
63 		if (ix < 0x42b17218) {
64 			/* x < 88.7: expf(|x|) won't overflow */
65 			h = expf(fabsf(x)) * 0.5f;
66 			return (cpackf(copysignf(h, x) * cosf(y), h * sinf(y)));
67 		} else if (ix < 0x4340b1e7) {
68 			/* x < 192.7: scale to avoid overflow */
69 			z = __ldexp_cexpf(cpackf(fabsf(x), y), -1);
70 			return (cpackf(crealf(z) * copysignf(1, x), cimagf(z)));
71 		} else {
72 			/* x >= 192.7: the result always overflows */
73 			h = huge * x;
74 			return (cpackf(h * cosf(y), h * h * sinf(y)));
75 		}
76 	}
77 
78 	if (ix == 0 && iy >= 0x7f800000)
79 		return (cpackf(copysignf(0, x * (y - y)), y - y));
80 
81 	if (iy == 0 && ix >= 0x7f800000) {
82 		if ((hx & 0x7fffff) == 0)
83 			return (cpackf(x, y));
84 		return (cpackf(x, copysignf(0, y)));
85 	}
86 
87 	if (ix < 0x7f800000 && iy >= 0x7f800000)
88 		return (cpackf(y - y, x * (y - y)));
89 
90 	if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) {
91 		if (iy >= 0x7f800000)
92 			return (cpackf(x * x, x * (y - y)));
93 		return (cpackf(x * cosf(y), INFINITY * sinf(y)));
94 	}
95 
96 	return (cpackf((x * x) * (y - y), (x + x) * (y - y)));
97 }
98 
99 float complex
csinf(float complex z)100 csinf(float complex z)
101 {
102 
103 	z = csinhf(cpackf(-cimagf(z), crealf(z)));
104 	return (cpackf(cimagf(z), -crealf(z)));
105 }
106