/* $NetBSD: catan.c,v 1.1 2007/08/20 16:01:32 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
        <<catan>>, <<catanf>>---complex arc tangent

INDEX
        catan
INDEX
        catanf

SYNOPSIS
       #include <complex.h>
       double complex catan(double complex <[z]>);
       float complex catanf(float complex <[z]>);


DESCRIPTION
        @ifnottex
        These functions compute the complex arc tangent of <[z]>,
        with branch cuts outside the interval [-i, +i] along the
        imaginary axis.
        @end ifnottex
        @tex
        These functions compute the complex arc tangent of <[z]>,
        with branch cuts outside the interval [$-i$, $+i$] along the
        imaginary axis.
        @end tex

        <<catanf>> is identical to <<catan>>, except that it performs
        its calculations on <<floats complex>>.

RETURNS
        @ifnottex
        These functions return the complex arc tangent 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 tangent, 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
        <<catan>> and <<catanf>> are ISO C99

QUICKREF
        <<catan>> and <<catanf>> are ISO C99

*/

#include "local-complex.h"

double complex
catan(double complex z)
{
    double complex w;
    double         a, t, x, x2, y;

    x = creal(z);
    y = cimag(z);

    if ((x == 0.0) && (y > 1.0))
        goto ovrf;

    x2 = x * x;
    a = 1.0 - x2 - (y * y);

    t = 0.5 * atan2(2.0 * x, a);
    w = _redupi(t);

    t = y - 1.0;
    a = x2 + (t * t);
    if (a == 0.0)
        goto ovrf;

    t = y + 1.0;
    a = (x2 + (t * t)) / a;
    w = CMPLX(w, 0.25 * log(a));
    return w;

ovrf:
#if 0
    mtherr ("catan", OVERFLOW);
#endif
    w = CMPLX(HUGE_VAL, HUGE_VAL);
    return w;
}
