1*05a0b428SJohn Marino /* $OpenBSD: s_ccos.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 /* ccos()
19*05a0b428SJohn Marino *
20*05a0b428SJohn Marino * Complex circular cosine
21*05a0b428SJohn Marino *
22*05a0b428SJohn Marino *
23*05a0b428SJohn Marino *
24*05a0b428SJohn Marino * SYNOPSIS:
25*05a0b428SJohn Marino *
26*05a0b428SJohn Marino * double complex ccos();
27*05a0b428SJohn Marino * double complex z, w;
28*05a0b428SJohn Marino *
29*05a0b428SJohn Marino * w = ccos (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 = cos x cosh y - i sin x sinh y.
41*05a0b428SJohn Marino *
42*05a0b428SJohn Marino *
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 4.5e-17 1.3e-17
49*05a0b428SJohn Marino * IEEE -10,+10 30000 3.8e-16 1.0e-16
50*05a0b428SJohn Marino */
51*05a0b428SJohn Marino
52*05a0b428SJohn Marino #include <complex.h>
53*05a0b428SJohn Marino #include <float.h>
54*05a0b428SJohn Marino #include <math.h>
55*05a0b428SJohn Marino
56*05a0b428SJohn Marino /* calculate cosh and sinh */
57*05a0b428SJohn Marino
58*05a0b428SJohn Marino static void
_cchsh(double x,double * c,double * s)59*05a0b428SJohn Marino _cchsh(double x, double *c, double *s)
60*05a0b428SJohn Marino {
61*05a0b428SJohn Marino double e, ei;
62*05a0b428SJohn Marino
63*05a0b428SJohn Marino if (fabs(x) <= 0.5) {
64*05a0b428SJohn Marino *c = cosh(x);
65*05a0b428SJohn Marino *s = sinh(x);
66*05a0b428SJohn Marino }
67*05a0b428SJohn Marino else {
68*05a0b428SJohn Marino e = exp(x);
69*05a0b428SJohn Marino ei = 0.5/e;
70*05a0b428SJohn Marino e = 0.5 * e;
71*05a0b428SJohn Marino *s = e - ei;
72*05a0b428SJohn Marino *c = e + ei;
73*05a0b428SJohn Marino }
74*05a0b428SJohn Marino }
75*05a0b428SJohn Marino
76*05a0b428SJohn Marino double complex
ccos(double complex z)77*05a0b428SJohn Marino ccos(double complex z)
78*05a0b428SJohn Marino {
79*05a0b428SJohn Marino double complex w;
80*05a0b428SJohn Marino double ch, sh;
81*05a0b428SJohn Marino
82*05a0b428SJohn Marino _cchsh( cimag(z), &ch, &sh );
83*05a0b428SJohn Marino w = cos(creal (z)) * ch - (sin (creal (z)) * sh) * I;
84*05a0b428SJohn Marino return (w);
85*05a0b428SJohn Marino }
86*05a0b428SJohn Marino
87*05a0b428SJohn Marino #if LDBL_MANT_DIG == DBL_MANT_DIG
88*05a0b428SJohn Marino __strong_alias(ccosl, ccos);
89*05a0b428SJohn Marino #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
90