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/* $OpenBSD: s_clog.c,v 1.7 2016/09/12 19:47:02 guenther 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.
*/
/* clog.c
*
* Complex natural logarithm
*
*
*
* SYNOPSIS:
*
* double complex clog();
* double complex z, w;
*
* w = clog (z);
*
*
*
* DESCRIPTION:
*
* Returns complex logarithm to the base e (2.718...) of
* the complex argument x.
*
* If z = x + iy, r = sqrt( x**2 + y**2 ),
* then
* w = log(r) + i arctan(y/x).
*
* The arctangent ranges from -PI to +PI.
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 7000 8.5e-17 1.9e-17
* IEEE -10,+10 30000 5.0e-15 1.1e-16
*
* Larger relative error can be observed for z near 1 +i0.
* In IEEE arithmetic the peak absolute error is 5.2e-16, rms
* absolute error 1.0e-16.
*/
#include <complex.h>
#include <float.h>
#include <math.h>
double complex
clog(double complex z)
{
double complex w;
double p, rr;
/*rr = sqrt( z->r * z->r + z->i * z->i );*/
rr = cabs(z);
p = log(rr);
rr = atan2 (cimag (z), creal (z));
w = p + rr * I;
return (w);
}
DEF_STD(clog);
LDBL_MAYBE_CLONE(clog);
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