xref: /src/lib/libm/complex/casinl.c

/* $NetBSD: casinl.c,v 1.1 2014/10/10 00:48:18 christos Exp $ */

/*-
 * Copyright (c) 2007 The NetBSD Foundation, Inc.
 * All rights reserved.
 *
 * This code is derived from software written by Stephen L. Moshier.
 * It is redistributed by the NetBSD Foundation by permission of the author.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
 * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
 * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
 * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 */

#include "../src/namespace.h"
#include <complex.h>
#include <math.h>

#ifdef __weak_alias
__weak_alias(casinl, _casinl)
#endif

long double complex
casinl(long double complex z)
{
	long double complex w;
	long double complex ca, ct, zz, z2;
	long double x, y;

	x = creall(z);
	y = cimagl(z);

#if 0 /* MD: test is incorrect, casin(>1) is defined */
	if (y == 0.0L) {
		if (fabsl(x) > 1.0L) {
			w = M_PI_2L + 0.0L * I;
#if 0
			mtherr ("casinl", DOMAIN);
#endif
		} else {
			w = asinl(x) + 0.0L * I;
		}
		return w;
	}
#endif

/* Power series expansion */
/*
b = cabsl(z);
if( b < 0.125L )
{
z2.r = (x - y) * (x + y);
z2.i = 2.0L * x * y;

cn = 1.0L;
n = 1.0L;
ca.r = x;
ca.i = y;
sum.r = x;
sum.i = y;
do
	{
	ct.r = z2.r * ca.r  -  z2.i * ca.i;
	ct.i = z2.r * ca.i  +  z2.i * ca.r;
	ca.r = ct.r;
	ca.i = ct.i;

	cn *= n;
	n += 1.0;
	cn /= n;
	n += 1.0;
	b = cn/n;

	ct.r *= b;
	ct.i *= b;
	sum.r += ct.r;
	sum.i += ct.i;
	b = fabsl(ct.r) + fabsl(ct.i);
	}
while( b > MACHEPL );
w->r = sum.r;
w->i = sum.i;
return;
}
*/


	ca = x + y * I;
	ct = ca * I;
	/* sqrtl( 1 - z*z) */
	/* cmull( &ca, &ca, &zz ) */
	/*x * x  -  y * y */
	zz = (x - y) * (x + y) + (2.0L * x * y) * I;

	zz = 1.0L - creall(zz) - cimagl(zz) * I;
	z2 = csqrtl(zz);

	zz = ct + z2;
	zz = clogl(zz);
	/* multiply by 1/i = -i */
	w = zz * (-1.0L * I);
	return w;
}