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 "libm.h"
38
39static const double huge = 0x1p1023;
40
41double 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