/* $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); }