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