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 = 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 * The sign of the result for some exceptional values is unspecified but
36 * must satisfy both sinh(conj(z)) == conj(sinh(z)) and sinh(-z) == -sinh(z).
37 */
38
39#include <sys/cdefs.h>
40__FBSDID("$FreeBSD$");
41
42#include <complex.h>
43#include <math.h>
44
45#include "math_private.h"
46
47static const double huge = 0x1p1023;
48
49double complex
50csinh(double complex z)
51{
52	double x, y, h;
53	int32_t hx, hy, ix, iy, lx, ly;
54
55	x = creal(z);
56	y = cimag(z);
57
58	EXTRACT_WORDS(hx, lx, x);
59	EXTRACT_WORDS(hy, ly, y);
60
61	ix = 0x7fffffff & hx;
62	iy = 0x7fffffff & hy;
63
64	/* Handle the nearly-non-exceptional cases where x and y are finite. */
65	if (ix < 0x7ff00000 && iy < 0x7ff00000) {
66		if ((iy | ly) == 0)
67			return (CMPLX(sinh(x), y));
68		if (ix < 0x40360000)	/* |x| < 22: normal case */
69			return (CMPLX(sinh(x) * cos(y), cosh(x) * sin(y)));
70
71		/* |x| >= 22, so cosh(x) ~= exp(|x|) */
72		if (ix < 0x40862e42) {
73			/* x < 710: exp(|x|) won't overflow */
74			h = exp(fabs(x)) * 0.5;
75			return (CMPLX(copysign(h, x) * cos(y), h * sin(y)));
76		} else if (ix < 0x4096bbaa) {
77			/* x < 1455: scale to avoid overflow */
78			z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
79			return (CMPLX(creal(z) * copysign(1, x), cimag(z)));
80		} else {
81			/* x >= 1455: the result always overflows */
82			h = huge * x;
83			return (CMPLX(h * cos(y), h * h * sin(y)));
84		}
85	}
86
87	/*
88	 * sinh(+-0 +- I Inf) = +-0 + I dNaN.
89	 * The sign of 0 in the result is unspecified.  Choice = same sign
90	 * as the argument.  Raise the invalid floating-point exception.
91	 *
92	 * sinh(+-0 +- I NaN) = +-0 + I d(NaN).
93	 * The sign of 0 in the result is unspecified.  Choice = same sign
94	 * as the argument.
95	 */
96	if ((ix | lx) == 0)		/* && iy >= 0x7ff00000 */
97		return (CMPLX(x, y - y));
98
99	/*
100	 * sinh(+-Inf +- I 0) = +-Inf + I +-0.
101	 *
102	 * sinh(NaN +- I 0)   = d(NaN) + I +-0.
103	 */
104	if ((iy | ly) == 0)		/* && ix >= 0x7ff00000 */
105		return (CMPLX(x + x, y));
106
107	/*
108	 * sinh(x +- I Inf) = dNaN + I dNaN.
109	 * Raise the invalid floating-point exception for finite nonzero x.
110	 *
111	 * sinh(x + I NaN) = d(NaN) + I d(NaN).
112	 * Optionally raises the invalid floating-point exception for finite
113	 * nonzero x.  Choice = don't raise (except for signaling NaNs).
114	 */
115	if (ix < 0x7ff00000)		/* && iy >= 0x7ff00000 */
116		return (CMPLX(y - y, y - y));
117
118	/*
119	 * sinh(+-Inf + I NaN)  = +-Inf + I d(NaN).
120	 * The sign of Inf in the result is unspecified.  Choice = same sign
121	 * as the argument.
122	 *
123	 * sinh(+-Inf +- I Inf) = +-Inf + I dNaN.
124	 * The sign of Inf in the result is unspecified.  Choice = same sign
125	 * as the argument.  Raise the invalid floating-point exception.
126	 *
127	 * sinh(+-Inf + I y)   = +-Inf cos(y) + I Inf sin(y)
128	 */
129	if (ix == 0x7ff00000 && lx == 0) {
130		if (iy >= 0x7ff00000)
131			return (CMPLX(x, y - y));
132		return (CMPLX(x * cos(y), INFINITY * sin(y)));
133	}
134
135	/*
136	 * sinh(NaN1 + I NaN2) = d(NaN1, NaN2) + I d(NaN1, NaN2).
137	 *
138	 * sinh(NaN +- I Inf)  = d(NaN, dNaN) + I d(NaN, dNaN).
139	 * Optionally raises the invalid floating-point exception.
140	 * Choice = raise.
141	 *
142	 * sinh(NaN + I y)     = d(NaN) + I d(NaN).
143	 * Optionally raises the invalid floating-point exception for finite
144	 * nonzero y.  Choice = don't raise (except for signaling NaNs).
145	 */
146	return (CMPLX((x + x) * (y - y), (x * x) * (y - y)));
147}
148
149double complex
150csin(double complex z)
151{
152
153	/* csin(z) = -I * csinh(I * z) = I * conj(csinh(I * conj(z))). */
154	z = csinh(CMPLX(cimag(z), creal(z)));
155	return (CMPLX(cimag(z), creal(z)));
156}
157