80 lines
2.0 KiB
C
80 lines
2.0 KiB
C
/* $OpenBSD: s_clog.c,v 1.6 2013/07/03 04:46:36 espie 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 <float.h>
|
|
#include <openlibm_complex.h>
|
|
#include <openlibm_math.h>
|
|
|
|
#include "math_private.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);
|
|
}
|
|
|
|
#if LDBL_MANT_DIG == DBL_MANT_DIG
|
|
openlibm_strong_reference(clog, clogl);
|
|
#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
|