1 /*-
2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
3 *
4 * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
5 * All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 * notice unmodified, this list of conditions, and the following
12 * disclaimer.
13 * 2. Redistributions in binary form must reproduce the above copyright
14 * notice, this list of conditions and the following disclaimer in the
15 * documentation and/or other materials provided with the distribution.
16 *
17 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
18 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
19 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
20 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
21 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
22 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
23 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
24 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
25 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
26 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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 * The sign of the result for some exceptional values is unspecified but
38 * must satisfy both sinh(conj(z)) == conj(sinh(z)) and sinh(-z) == -sinh(z).
39 */
40
41 #include <sys/cdefs.h>
42 __FBSDID("$FreeBSD: head/lib/msun/src/s_csinh.c 336362 2018-07-17 07:42:14Z bde $");
43
44 #include <complex.h>
45 #include <math.h>
46
47 #include "math_private.h"
48
49 static const double huge = 0x1p1023;
50
51 double complex
csinh(double complex z)52 csinh(double complex z)
53 {
54 double x, y, h;
55 int32_t hx, hy, ix, iy, lx, ly;
56
57 x = creal(z);
58 y = cimag(z);
59
60 EXTRACT_WORDS(hx, lx, x);
61 EXTRACT_WORDS(hy, ly, y);
62
63 ix = 0x7fffffff & hx;
64 iy = 0x7fffffff & hy;
65
66 /* Handle the nearly-non-exceptional cases where x and y are finite. */
67 if (ix < 0x7ff00000 && iy < 0x7ff00000) {
68 if ((iy | ly) == 0)
69 return (CMPLX(sinh(x), y));
70 if (ix < 0x40360000) /* |x| < 22: normal case */
71 return (CMPLX(sinh(x) * cos(y), cosh(x) * sin(y)));
72
73 /* |x| >= 22, so cosh(x) ~= exp(|x|) */
74 if (ix < 0x40862e42) {
75 /* x < 710: exp(|x|) won't overflow */
76 h = exp(fabs(x)) * 0.5;
77 return (CMPLX(copysign(h, x) * cos(y), h * sin(y)));
78 } else if (ix < 0x4096bbaa) {
79 /* x < 1455: scale to avoid overflow */
80 z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
81 return (CMPLX(creal(z) * copysign(1, x), cimag(z)));
82 } else {
83 /* x >= 1455: the result always overflows */
84 h = huge * x;
85 return (CMPLX(h * cos(y), h * h * sin(y)));
86 }
87 }
88
89 /*
90 * sinh(+-0 +- I Inf) = +-0 + I dNaN.
91 * The sign of 0 in the result is unspecified. Choice = same sign
92 * as the argument. Raise the invalid floating-point exception.
93 *
94 * sinh(+-0 +- I NaN) = +-0 + I d(NaN).
95 * The sign of 0 in the result is unspecified. Choice = same sign
96 * as the argument.
97 */
98 if ((ix | lx) == 0) /* && iy >= 0x7ff00000 */
99 return (CMPLX(x, y - y));
100
101 /*
102 * sinh(+-Inf +- I 0) = +-Inf + I +-0.
103 *
104 * sinh(NaN +- I 0) = d(NaN) + I +-0.
105 */
106 if ((iy | ly) == 0) /* && ix >= 0x7ff00000 */
107 return (CMPLX(x + x, y));
108
109 /*
110 * sinh(x +- I Inf) = dNaN + I dNaN.
111 * Raise the invalid floating-point exception for finite nonzero x.
112 *
113 * sinh(x + I NaN) = d(NaN) + I d(NaN).
114 * Optionally raises the invalid floating-point exception for finite
115 * nonzero x. Choice = don't raise (except for signaling NaNs).
116 */
117 if (ix < 0x7ff00000) /* && iy >= 0x7ff00000 */
118 return (CMPLX(y - y, y - y));
119
120 /*
121 * sinh(+-Inf + I NaN) = +-Inf + I d(NaN).
122 * The sign of Inf in the result is unspecified. Choice = same sign
123 * as the argument.
124 *
125 * sinh(+-Inf +- I Inf) = +-Inf + I dNaN.
126 * The sign of Inf in the result is unspecified. Choice = same sign
127 * as the argument. Raise the invalid floating-point exception.
128 *
129 * sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y)
130 */
131 if (ix == 0x7ff00000 && lx == 0) {
132 if (iy >= 0x7ff00000)
133 return (CMPLX(x, y - y));
134 return (CMPLX(x * cos(y), INFINITY * sin(y)));
135 }
136
137 /*
138 * sinh(NaN1 + I NaN2) = d(NaN1, NaN2) + I d(NaN1, NaN2).
139 *
140 * sinh(NaN +- I Inf) = d(NaN, dNaN) + I d(NaN, dNaN).
141 * Optionally raises the invalid floating-point exception.
142 * Choice = raise.
143 *
144 * sinh(NaN + I y) = d(NaN) + I d(NaN).
145 * Optionally raises the invalid floating-point exception for finite
146 * nonzero y. Choice = don't raise (except for signaling NaNs).
147 */
148 return (CMPLX(((long double)x + x) * (y - y),
149 ((long double)x * x) * (y - y)));
150 }
151
152 double complex
csin(double complex z)153 csin(double complex z)
154 {
155
156 /* csin(z) = -I * csinh(I * z) = I * conj(csinh(I * conj(z))). */
157 z = csinh(CMPLX(cimag(z), creal(z)));
158 return (CMPLX(cimag(z), creal(z)));
159 }
160