/*-
 * Copyright (c) 2014-2021 Carsten Sonne Larsen <cs@innolan.net>
 * 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 AUTHOR ``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 AUTHOR 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 original source code can be obtained from:
 * http://cvsweb.netbsd.org/bsdweb.cgi/src/lib/libm/complex/csqrt.c?rev=1.1
 *
 * Project homepage:
 * https://amath.innolan.net
 *
 */

#include "prim.h"

/**
 * @brief Square root of complex number
 */
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;
}