1*05a0b428SJohn Marino /* $OpenBSD: s_csin.c,v 1.6 2013/07/03 04:46:36 espie Exp $ */
2*05a0b428SJohn Marino /*
3*05a0b428SJohn Marino * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
4*05a0b428SJohn Marino *
5*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this software for any
6*05a0b428SJohn Marino * purpose with or without fee is hereby granted, provided that the above
7*05a0b428SJohn Marino * copyright notice and this permission notice appear in all copies.
8*05a0b428SJohn Marino *
9*05a0b428SJohn Marino * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
10*05a0b428SJohn Marino * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
11*05a0b428SJohn Marino * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
12*05a0b428SJohn Marino * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
13*05a0b428SJohn Marino * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
14*05a0b428SJohn Marino * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
15*05a0b428SJohn Marino * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
16*05a0b428SJohn Marino */
17*05a0b428SJohn Marino
18*05a0b428SJohn Marino /* csin()
19*05a0b428SJohn Marino *
20*05a0b428SJohn Marino * Complex circular sine
21*05a0b428SJohn Marino *
22*05a0b428SJohn Marino *
23*05a0b428SJohn Marino *
24*05a0b428SJohn Marino * SYNOPSIS:
25*05a0b428SJohn Marino *
26*05a0b428SJohn Marino * double complex csin();
27*05a0b428SJohn Marino * double complex z, w;
28*05a0b428SJohn Marino *
29*05a0b428SJohn Marino * w = csin (z);
30*05a0b428SJohn Marino *
31*05a0b428SJohn Marino *
32*05a0b428SJohn Marino *
33*05a0b428SJohn Marino * DESCRIPTION:
34*05a0b428SJohn Marino *
35*05a0b428SJohn Marino * If
36*05a0b428SJohn Marino * z = x + iy,
37*05a0b428SJohn Marino *
38*05a0b428SJohn Marino * then
39*05a0b428SJohn Marino *
40*05a0b428SJohn Marino * w = sin x cosh y + i cos x sinh y.
41*05a0b428SJohn Marino *
42*05a0b428SJohn Marino * csin(z) = -i csinh(iz).
43*05a0b428SJohn Marino *
44*05a0b428SJohn Marino * ACCURACY:
45*05a0b428SJohn Marino *
46*05a0b428SJohn Marino * Relative error:
47*05a0b428SJohn Marino * arithmetic domain # trials peak rms
48*05a0b428SJohn Marino * DEC -10,+10 8400 5.3e-17 1.3e-17
49*05a0b428SJohn Marino * IEEE -10,+10 30000 3.8e-16 1.0e-16
50*05a0b428SJohn Marino * Also tested by csin(casin(z)) = z.
51*05a0b428SJohn Marino *
52*05a0b428SJohn Marino */
53*05a0b428SJohn Marino
54*05a0b428SJohn Marino #include <complex.h>
55*05a0b428SJohn Marino #include <float.h>
56*05a0b428SJohn Marino #include <math.h>
57*05a0b428SJohn Marino
58*05a0b428SJohn Marino /* calculate cosh and sinh */
59*05a0b428SJohn Marino
60*05a0b428SJohn Marino static void
cchsh(double x,double * c,double * s)61*05a0b428SJohn Marino cchsh(double x, double *c, double *s)
62*05a0b428SJohn Marino {
63*05a0b428SJohn Marino double e, ei;
64*05a0b428SJohn Marino
65*05a0b428SJohn Marino if (fabs(x) <= 0.5) {
66*05a0b428SJohn Marino *c = cosh(x);
67*05a0b428SJohn Marino *s = sinh(x);
68*05a0b428SJohn Marino }
69*05a0b428SJohn Marino else {
70*05a0b428SJohn Marino e = exp(x);
71*05a0b428SJohn Marino ei = 0.5/e;
72*05a0b428SJohn Marino e = 0.5 * e;
73*05a0b428SJohn Marino *s = e - ei;
74*05a0b428SJohn Marino *c = e + ei;
75*05a0b428SJohn Marino }
76*05a0b428SJohn Marino }
77*05a0b428SJohn Marino
78*05a0b428SJohn Marino double complex
csin(double complex z)79*05a0b428SJohn Marino csin(double complex z)
80*05a0b428SJohn Marino {
81*05a0b428SJohn Marino double complex w;
82*05a0b428SJohn Marino double ch, sh;
83*05a0b428SJohn Marino
84*05a0b428SJohn Marino cchsh( cimag (z), &ch, &sh );
85*05a0b428SJohn Marino w = sin (creal(z)) * ch + (cos (creal(z)) * sh) * I;
86*05a0b428SJohn Marino return (w);
87*05a0b428SJohn Marino }
88*05a0b428SJohn Marino
89*05a0b428SJohn Marino #if LDBL_MANT_DIG == DBL_MANT_DIG
90*05a0b428SJohn Marino __strong_alias(csinl, csin);
91*05a0b428SJohn Marino #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
92