73 lines
1.8 KiB
C
73 lines
1.8 KiB
C
/* $OpenBSD: s_clogf.c,v 1.2 2010/07/18 18:42:26 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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/* clogf.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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* void clogf();
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* cmplxf z, w;
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*
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* clogf( &z, &w );
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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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* IEEE -10,+10 30000 1.9e-6 6.2e-8
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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 3.1e-7.
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*
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*/
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#include <openlibm_complex.h>
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#include <openlibm_math.h>
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float complex
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clogf(float complex z)
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{
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float complex w;
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float p, rr, x, y;
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x = crealf(z);
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y = cimagf(z);
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rr = atan2f(y, x);
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p = cabsf(z);
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p = logf(p);
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w = p + rr * I;
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return (w);
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}
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