1*05a0b428SJohn Marino /* $OpenBSD: s_cexp.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 /* cexp()
19*05a0b428SJohn Marino *
20*05a0b428SJohn Marino * Complex exponential function
21*05a0b428SJohn Marino *
22*05a0b428SJohn Marino *
23*05a0b428SJohn Marino *
24*05a0b428SJohn Marino * SYNOPSIS:
25*05a0b428SJohn Marino *
26*05a0b428SJohn Marino * double complex cexp ();
27*05a0b428SJohn Marino * double complex z, w;
28*05a0b428SJohn Marino *
29*05a0b428SJohn Marino * w = cexp (z);
30*05a0b428SJohn Marino *
31*05a0b428SJohn Marino *
32*05a0b428SJohn Marino *
33*05a0b428SJohn Marino * DESCRIPTION:
34*05a0b428SJohn Marino *
35*05a0b428SJohn Marino * Returns the exponential of the complex argument z
36*05a0b428SJohn Marino * into the complex result w.
37*05a0b428SJohn Marino *
38*05a0b428SJohn Marino * If
39*05a0b428SJohn Marino * z = x + iy,
40*05a0b428SJohn Marino * r = exp(x),
41*05a0b428SJohn Marino *
42*05a0b428SJohn Marino * then
43*05a0b428SJohn Marino *
44*05a0b428SJohn Marino * w = r cos y + i r sin y.
45*05a0b428SJohn Marino *
46*05a0b428SJohn Marino *
47*05a0b428SJohn Marino * ACCURACY:
48*05a0b428SJohn Marino *
49*05a0b428SJohn Marino * Relative error:
50*05a0b428SJohn Marino * arithmetic domain # trials peak rms
51*05a0b428SJohn Marino * DEC -10,+10 8700 3.7e-17 1.1e-17
52*05a0b428SJohn Marino * IEEE -10,+10 30000 3.0e-16 8.7e-17
53*05a0b428SJohn Marino *
54*05a0b428SJohn Marino */
55*05a0b428SJohn Marino
56*05a0b428SJohn Marino #include <complex.h>
57*05a0b428SJohn Marino #include <float.h>
58*05a0b428SJohn Marino #include <math.h>
59*05a0b428SJohn Marino
60*05a0b428SJohn Marino double complex
cexp(double complex z)61*05a0b428SJohn Marino cexp(double complex z)
62*05a0b428SJohn Marino {
63*05a0b428SJohn Marino double complex w;
64*05a0b428SJohn Marino double r, x, y;
65*05a0b428SJohn Marino
66*05a0b428SJohn Marino x = creal (z);
67*05a0b428SJohn Marino y = cimag (z);
68*05a0b428SJohn Marino r = exp (x);
69*05a0b428SJohn Marino w = r * cos (y) + r * sin (y) * I;
70*05a0b428SJohn Marino return (w);
71*05a0b428SJohn Marino }
72*05a0b428SJohn Marino
73*05a0b428SJohn Marino #if LDBL_MANT_DIG == DBL_MANT_DIG
74*05a0b428SJohn Marino __strong_alias(cexpl, cexp);
75*05a0b428SJohn Marino #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
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