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
39static const float huge = 0x1p127;
40
41float complex
42csinhf(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
99float complex
100csinf(float complex z)
101{
102
103	z = csinhf(cpackf(-cimagf(z), crealf(z)));
104	return (cpackf(cimagf(z), -crealf(z)));
105}
106