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/* $OpenBSD: s_clogl.c,v 1.3 2016/09/12 19:47:02 guenther 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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/* clogl.c |
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* |
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* Complex natural logarithm |
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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 clogl(); |
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* long double complex z, w; |
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* |
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* w = clogl( 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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* Returns complex logarithm to the base e (2.718...) of |
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* the complex argument x. |
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* |
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* If z = x + iy, r = sqrt( x**2 + y**2 ), |
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* then |
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* w = log(r) + i arctan(y/x). |
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* |
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* The arctangent ranges from -PI to +PI. |
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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 7000 8.5e-17 1.9e-17 |
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* IEEE -10,+10 30000 5.0e-15 1.1e-16 |
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* |
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* Larger relative error can be observed for z near 1 +i0. |
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* In IEEE arithmetic the peak absolute error is 5.2e-16, rms |
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* absolute error 1.0e-16. |
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*/ |
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#include <complex.h> |
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#include <math.h> |
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long double complex |
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clogl(long double complex z) |
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{ |
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long double complex w; |
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long double p, rr; |
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/*rr = sqrt(z->r * z->r + z->i * z->i);*/ |
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p = cabsl(z); |
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p = logl(p); |
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rr = atan2l(cimagl(z), creall(z)); |
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w = p + rr * I; |
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return (w); |
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} |
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DEF_STD(clogl); |