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/* $OpenBSD: n_csin.c,v 1.1 2008/10/07 22:25:53 martynas Exp $ */
/*
* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
*
* Permission to use, copy, modify, and distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/
/* csin()
*
* Complex circular sine
*
*
*
* SYNOPSIS:
*
* double complex csin();
* double complex z, w;
*
* w = csin (z);
*
*
*
* DESCRIPTION:
*
* If
* z = x + iy,
*
* then
*
* w = sin x cosh y + i cos x sinh y.
*
* csin(z) = -i csinh(iz).
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 8400 5.3e-17 1.3e-17
* IEEE -10,+10 30000 3.8e-16 1.0e-16
* Also tested by csin(casin(z)) = z.
*
*/
#include <complex.h>
#include <math.h>
/* calculate cosh and sinh */
static void
cchsh(double x, double *c, double *s)
{
double e, ei;
if (fabs(x) <= 0.5) {
*c = cosh(x);
*s = sinh(x);
}
else {
e = exp(x);
ei = 0.5/e;
e = 0.5 * e;
*s = e - ei;
*c = e + ei;
}
}
double complex
csin(double complex z)
{
double complex w;
double ch, sh;
cchsh( cimag (z), &ch, &sh );
w = sin (creal(z)) * ch + (cos (creal(z)) * sh) * I;
return (w);
}
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