1*05a0b428SJohn Marino /* $OpenBSD: s_csinl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */
2*05a0b428SJohn Marino
3*05a0b428SJohn Marino /*
4*05a0b428SJohn Marino * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
5*05a0b428SJohn Marino *
6*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this software for any
7*05a0b428SJohn Marino * purpose with or without fee is hereby granted, provided that the above
8*05a0b428SJohn Marino * copyright notice and this permission notice appear in all copies.
9*05a0b428SJohn Marino *
10*05a0b428SJohn Marino * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
11*05a0b428SJohn Marino * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
12*05a0b428SJohn Marino * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
13*05a0b428SJohn Marino * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
14*05a0b428SJohn Marino * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
15*05a0b428SJohn Marino * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
16*05a0b428SJohn Marino * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
17*05a0b428SJohn Marino */
18*05a0b428SJohn Marino
19*05a0b428SJohn Marino /* csinl()
20*05a0b428SJohn Marino *
21*05a0b428SJohn Marino * Complex circular sine
22*05a0b428SJohn Marino *
23*05a0b428SJohn Marino *
24*05a0b428SJohn Marino *
25*05a0b428SJohn Marino * SYNOPSIS:
26*05a0b428SJohn Marino *
27*05a0b428SJohn Marino * long double complex csinl();
28*05a0b428SJohn Marino * long double complex z, w;
29*05a0b428SJohn Marino *
30*05a0b428SJohn Marino * w = csinl( z );
31*05a0b428SJohn Marino *
32*05a0b428SJohn Marino *
33*05a0b428SJohn Marino *
34*05a0b428SJohn Marino * DESCRIPTION:
35*05a0b428SJohn Marino *
36*05a0b428SJohn Marino * If
37*05a0b428SJohn Marino * z = x + iy,
38*05a0b428SJohn Marino *
39*05a0b428SJohn Marino * then
40*05a0b428SJohn Marino *
41*05a0b428SJohn Marino * w = sin x cosh y + i cos x sinh y.
42*05a0b428SJohn Marino *
43*05a0b428SJohn Marino *
44*05a0b428SJohn Marino *
45*05a0b428SJohn Marino * ACCURACY:
46*05a0b428SJohn Marino *
47*05a0b428SJohn Marino * Relative error:
48*05a0b428SJohn Marino * arithmetic domain # trials peak rms
49*05a0b428SJohn Marino * DEC -10,+10 8400 5.3e-17 1.3e-17
50*05a0b428SJohn Marino * IEEE -10,+10 30000 3.8e-16 1.0e-16
51*05a0b428SJohn Marino * Also tested by csin(casin(z)) = z.
52*05a0b428SJohn Marino *
53*05a0b428SJohn Marino */
54*05a0b428SJohn Marino
55*05a0b428SJohn Marino #include <complex.h>
56*05a0b428SJohn Marino #include <math.h>
57*05a0b428SJohn Marino
58*05a0b428SJohn Marino static void
cchshl(long double x,long double * c,long double * s)59*05a0b428SJohn Marino cchshl(long double x, long double *c, long double *s)
60*05a0b428SJohn Marino {
61*05a0b428SJohn Marino long double e, ei;
62*05a0b428SJohn Marino
63*05a0b428SJohn Marino if(fabsl(x) <= 0.5L) {
64*05a0b428SJohn Marino *c = coshl(x);
65*05a0b428SJohn Marino *s = sinhl(x);
66*05a0b428SJohn Marino } else {
67*05a0b428SJohn Marino e = expl(x);
68*05a0b428SJohn Marino ei = 0.5L/e;
69*05a0b428SJohn Marino e = 0.5L * e;
70*05a0b428SJohn Marino *s = e - ei;
71*05a0b428SJohn Marino *c = e + ei;
72*05a0b428SJohn Marino }
73*05a0b428SJohn Marino }
74*05a0b428SJohn Marino
75*05a0b428SJohn Marino long double complex
csinl(long double complex z)76*05a0b428SJohn Marino csinl(long double complex z)
77*05a0b428SJohn Marino {
78*05a0b428SJohn Marino long double complex w;
79*05a0b428SJohn Marino long double ch, sh;
80*05a0b428SJohn Marino
81*05a0b428SJohn Marino cchshl(cimagl(z), &ch, &sh);
82*05a0b428SJohn Marino w = sinl(creall(z)) * ch + (cosl(creall(z)) * sh) * I;
83*05a0b428SJohn Marino return (w);
84*05a0b428SJohn Marino }
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