1 /* origin: FreeBSD /usr/src/lib/msun/src/s_csinh.c */
2 /*-
3 * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
4 * All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 * notice unmodified, this list of conditions, and the following
11 * disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in the
14 * documentation and/or other materials provided with the distribution.
15 *
16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
17 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
18 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
19 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
20 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
21 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
22 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
23 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
24 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
25 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
26 */
27 /*
28 * Hyperbolic sine of a complex argument z = x + i y.
29 *
30 * sinh(z) = sinh(x+iy)
31 * = sinh(x) cos(y) + i cosh(x) sin(y).
32 *
33 * Exceptional values are noted in the comments within the source code.
34 * These values and the return value were taken from n1124.pdf.
35 */
36 37 #include "complex_impl.h"
38 39 static const double huge = 0x1p1023;
40 41 double complex csinh(double complex z)
42 {
43 double x, y, h;
44 int32_t hx, hy, ix, iy, lx, ly;
45 46 x = creal(z);
47 y = cimag(z);
48 49 EXTRACT_WORDS(hx, lx, x);
50 EXTRACT_WORDS(hy, ly, y);
51 52 ix = 0x7fffffff & hx;
53 iy = 0x7fffffff & hy;
54 55 /* Handle the nearly-non-exceptional cases where x and y are finite. */
56 if (ix < 0x7ff00000 && iy < 0x7ff00000) {
57 if ((iy | ly) == 0)
58 return CMPLX(sinh(x), y);
59 if (ix < 0x40360000) /* small x: normal case */
60 return CMPLX(sinh(x) * cos(y), cosh(x) * sin(y));
61 62 /* |x| >= 22, so cosh(x) ~= exp(|x|) */
63 if (ix < 0x40862e42) {
64 /* x < 710: exp(|x|) won't overflow */
65 h = exp(fabs(x)) * 0.5;
66 return CMPLX(copysign(h, x) * cos(y), h * sin(y));
67 } else if (ix < 0x4096bbaa) {
68 /* x < 1455: scale to avoid overflow */
69 z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
70 return CMPLX(creal(z) * copysign(1, x), cimag(z));
71 } else {
72 /* x >= 1455: the result always overflows */
73 h = huge * x;
74 return CMPLX(h * cos(y), h * h * sin(y));
75 }
76 }
77 78 /*
79 * sinh(+-0 +- I Inf) = sign(d(+-0, dNaN))0 + I dNaN.
80 * The sign of 0 in the result is unspecified. Choice = normally
81 * the same as dNaN. Raise the invalid floating-point exception.
82 *
83 * sinh(+-0 +- I NaN) = sign(d(+-0, NaN))0 + I d(NaN).
84 * The sign of 0 in the result is unspecified. Choice = normally
85 * the same as d(NaN).
86 */
87 if ((ix | lx) == 0 && iy >= 0x7ff00000)
88 return CMPLX(copysign(0, x * (y - y)), y - y);
89 90 /*
91 * sinh(+-Inf +- I 0) = +-Inf + I +-0.
92 *
93 * sinh(NaN +- I 0) = d(NaN) + I +-0.
94 */
95 if ((iy | ly) == 0 && ix >= 0x7ff00000) {
96 if (((hx & 0xfffff) | lx) == 0)
97 return CMPLX(x, y);
98 return CMPLX(x, copysign(0, y));
99 }
100 101 /*
102 * sinh(x +- I Inf) = dNaN + I dNaN.
103 * Raise the invalid floating-point exception for finite nonzero x.
104 *
105 * sinh(x + I NaN) = d(NaN) + I d(NaN).
106 * Optionally raises the invalid floating-point exception for finite
107 * nonzero x. Choice = don't raise (except for signaling NaNs).
108 */
109 if (ix < 0x7ff00000 && iy >= 0x7ff00000)
110 return CMPLX(y - y, x * (y - y));
111 112 /*
113 * sinh(+-Inf + I NaN) = +-Inf + I d(NaN).
114 * The sign of Inf in the result is unspecified. Choice = normally
115 * the same as d(NaN).
116 *
117 * sinh(+-Inf +- I Inf) = +Inf + I dNaN.
118 * The sign of Inf in the result is unspecified. Choice = always +.
119 * Raise the invalid floating-point exception.
120 *
121 * sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y)
122 */
123 if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
124 if (iy >= 0x7ff00000)
125 return CMPLX(x * x, x * (y - y));
126 return CMPLX(x * cos(y), INFINITY * sin(y));
127 }
128 129 /*
130 * sinh(NaN + I NaN) = d(NaN) + I d(NaN).
131 *
132 * sinh(NaN +- I Inf) = d(NaN) + I d(NaN).
133 * Optionally raises the invalid floating-point exception.
134 * Choice = raise.
135 *
136 * sinh(NaN + I y) = d(NaN) + I d(NaN).
137 * Optionally raises the invalid floating-point exception for finite
138 * nonzero y. Choice = don't raise (except for signaling NaNs).
139 */
140 return CMPLX((x * x) * (y - y), (x + x) * (y - y));
141 }
142