relibc_openlibm/src/s_clogf.c

/*	$OpenBSD: s_clogf.c,v 1.2 2010/07/18 18:42:26 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.
 */

/*							clogf.c
 *
 *	Complex natural logarithm
 *
 *
 *
 * SYNOPSIS:
 *
 * void clogf();
 * cmplxf z, w;
 *
 * clogf( &z, &w );
 *
 *
 *
 * 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
 *    IEEE      -10,+10     30000       1.9e-6       6.2e-8
 *
 * Larger relative error can be observed for z near 1 +i0.
 * In IEEE arithmetic the peak absolute error is 3.1e-7.
 *
 */

#include <openlibm_complex.h>
#include <openlibm_math.h>

float complex
clogf(float complex z)
{
	float complex w;
	float p, rr, x, y;

	x = crealf(z);
	y = cimagf(z);
	rr = atan2f(y, x);
	p = cabsf(z);
	p = logf(p);
	w = p + rr * I;
	return (w);
}