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/* $NetBSD: casin.c,v 1.1 2007/08/20 16:01:31 drochner 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.
*
* imported and modified include for newlib 2010/10/03
* Marco Atzeri <marco_atzeri@yahoo.it>
*/
/*
FUNCTION
<<casin>>, <<casinf>>---complex arc sine
INDEX
casin
INDEX
casinf
SYNOPSIS
#include <complex.h>
double complex casin(double complex <[z]>);
float complex casinf(float complex <[z]>);
DESCRIPTION
These functions compute the complex arc sine of <[z]>,
with branch cuts outside the interval [-1, +1] along the real axis.
<<casinf>> is identical to <<casin>>, except that it performs
its calculations on <<floats complex>>.
RETURNS
@ifnottex
These functions return the complex arc sine value, in the range
of a strip mathematically unbounded along the imaginary axis
and in the interval [-pi/2, +pi/2] along the real axis.
@end ifnottex
@tex
These functions return the complex arc sine value, in the range
of a strip mathematically unbounded along the imaginary axis
and in the interval [$-\pi/2$, $+\pi/2$] along the real axis.
@end tex
PORTABILITY
<<casin>> and <<casinf>> are ISO C99
QUICKREF
<<casin>> and <<casinf>> are ISO C99
*/
#include <complex.h>
#include <math.h>
#ifdef __weak_alias
__weak_alias(casin, _casin)
#endif
double complex
casin(double complex z)
{
double complex w;
double complex ca, ct, zz, z2;
double x, y;
x = creal(z);
y = cimag(z);
#if 0 /* MD: test is incorrect, casin(>1) is defined */
if (y == 0.0) {
if (fabs(x) > 1.0) {
w = M_PI_2 + 0.0 * (double complex) I;
#if 0
mtherr ("casin", DOMAIN);
#endif
} else {
w = asin(x) + 0.0 * (double complex) I;
}
return w;
}
#endif
/* Power series expansion */
/*
b = cabs(z);
if( b < 0.125 )
{
z2.r = (x - y) * (x + y);
z2.i = 2.0 * x * y;
cn = 1.0;
n = 1.0;
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 = fabs(ct.r) + fabs(ct.i);
}
while( b > MACHEP );
w->r = sum.r;
w->i = sum.i;
return;
}
*/
ca = x + y * (double complex) I;
ct = ca * (double complex) I;
/* sqrt( 1 - z*z) */
/* cmul( &ca, &ca, &zz ) */
/*x * x - y * y */
zz = (x - y) * (x + y) + (2.0 * x * y) * (double complex) I;
zz = 1.0 - creal(zz) - cimag(zz) * (double complex) I;
z2 = csqrt(zz);
zz = ct + z2;
zz = clog(zz);
/* multiply by 1/i = -i */
w = zz * (-1.0 * (double complex) I);
return w;
}
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