92 lines
2.0 KiB
C
92 lines
2.0 KiB
C
/* $OpenBSD: s_csin.c,v 1.6 2013/07/03 04:46:36 espie Exp $ */
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/*
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* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose with or without fee is hereby granted, provided that the above
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* copyright notice and this permission notice appear in all copies.
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*
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
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* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
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* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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*/
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/* csin()
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*
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* Complex circular sine
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*
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*
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*
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* SYNOPSIS:
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*
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* double complex csin();
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* double complex z, w;
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*
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* w = csin (z);
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*
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*
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*
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* DESCRIPTION:
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*
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* If
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* z = x + iy,
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*
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* then
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*
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* w = sin x cosh y + i cos x sinh y.
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*
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* csin(z) = -i csinh(iz).
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* DEC -10,+10 8400 5.3e-17 1.3e-17
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* IEEE -10,+10 30000 3.8e-16 1.0e-16
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* Also tested by csin(casin(z)) = z.
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*
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*/
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#include <float.h>
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#include <openlibm_complex.h>
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#include <openlibm_math.h>
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/* calculate cosh and sinh */
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static void
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cchsh(double x, double *c, double *s)
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{
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double e, ei;
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if (fabs(x) <= 0.5) {
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*c = cosh(x);
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*s = sinh(x);
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}
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else {
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e = exp(x);
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ei = 0.5/e;
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e = 0.5 * e;
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*s = e - ei;
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*c = e + ei;
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}
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}
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double complex
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csin(double complex z)
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{
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double complex w;
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double ch, sh;
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cchsh( cimag (z), &ch, &sh );
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w = sin (creal(z)) * ch + (cos (creal(z)) * sh) * I;
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return (w);
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}
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#if LDBL_MANT_DIG == DBL_MANT_DIG
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__strong_alias(csinl, csin);
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#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
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