/* $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 "local-complex.h"

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 = CMPLX(M_PI_2, 0);
#if 0
            mtherr ("casin", DOMAIN);
#endif
        } else {
            w = CMPLX(asin(x), 0);
        }
        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 = CMPLX(x, y);
    ct = ca * (double complex)I;
    /* sqrt( 1 - z*z) */
    /* cmul( &ca, &ca, &zz ) */
    /*x * x  -  y * y */
    zz = CMPLX((x - y) * (x + y), (2.0 * x * y));

    zz = CMPLX(1.0 - creal(zz), -cimag(zz));
    z2 = csqrt(zz);

    zz = ct + z2;
    zz = clog(zz);

    /* multiply by 1/i = -i */
    w = zz * (-1.0 * (double complex)I);
    return w;
}
