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/* $OpenBSD: s_csinl.c,v 1.2 2011/07/20 19:28:33 martynas 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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/* csinl() |
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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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* long double complex csinl(); |
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* long double complex z, w; |
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* |
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* w = csinl( 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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* |
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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 <complex.h> |
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#include <math.h> |
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static void |
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cchshl(long double x, long double *c, long double *s) |
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{ |
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long double e, ei; |
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if(fabsl(x) <= 0.5L) { |
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*c = coshl(x); |
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*s = sinhl(x); |
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} else { |
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e = expl(x); |
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ei = 0.5L/e; |
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e = 0.5L * 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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long double complex |
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csinl(long double complex z) |
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{ |
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long double complex w; |
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long double ch, sh; |
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cchshl(cimagl(z), &ch, &sh); |
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w = sinl(creall(z)) * ch + (cosl(creall(z)) * sh) * I; |
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return (w); |
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} |