/* $NetBSD: csqrt.c,v 1.1 2007/08/20 16:01:37 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.
 *
 * The origin source code can be obtained from:
 * ftp.netbsd.org/pub/NetBSD/NetBSD-release-5/src/lib/libm/complex/csqrt.c
 *
 */

#include "prim.h"
#include "math.h"
#include "complex.h"

/**
 * @brief   Square root of complex number
 * @version 1.1
 * @date    2007/08/20
 * @details
 */
complex csqrt(complex z)
{
    complex w;
    double x, y, r, t, scale;

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

    if (y == 0.0) {
        if (x == 0.0) {
            w = cpack(0.0, y);
        } else {
            r = fabs(x);
            r = sqrt(r);
            if (x < 0.0) {
                w = cpack(0.0, r);
            } else {
                w = cpack(r, y);
            }
        }
        return w;
    }
    if (x == 0.0) {
        r = fabs(y);
        r = sqrt(0.5 * r);
        if (y > 0)
            w =  cpack(r, r);
        else
            w = cpack(r, -r);
        return w;
    }
    /* Rescale to avoid internal overflow or underflow.  */
    if ((fabs(x) > 4.0) || (fabs(y) > 4.0)) {
        x *= 0.25;
        y *= 0.25;
        scale = 2.0;
    } else {
#if 1
        x *= 1.8014398509481984e16;  /* 2^54 */
        y *= 1.8014398509481984e16;
        scale = 7.450580596923828125e-9; /* 2^-27 */
#else
        x *= 4.0;
        y *= 4.0;
        scale = 0.5;
#endif
    }
    w = cpack(x, y);
    r = cabs(w);
    if (x > 0) {
        t = sqrt(0.5 * r + 0.5 * x);
        r = scale * fabs((0.5 * y) / t );
        t *= scale;
    } else {
        r = sqrt(0.5 * r - 0.5 * x);
        t = scale * fabs((0.5 * y) / r);
        r *= scale;
    }
    if (y < 0)
        w = cpack(t, -r);
    else
        w = cpack(t, r);
    return w;
}