/*      $OpenBSD: s_csqrt.c,v 1.8 2016/09/12 19:47:02 guenther Exp $    */
/*
 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 */

/*                                                      csqrt()
 *
 *      Complex square root
 *
 *
 *
 * SYNOPSIS:
 *
 * double complex csqrt();
 * double complex z, w;
 *
 * w = csqrt (z);
 *
 *
 *
 * DESCRIPTION:
 *
 *
 * If z = x + iy,  r = |z|, then
 *
 *                       1/2
 * Re w  =  [ (r + x)/2 ]   ,
 *
 *                       1/2
 * Im w  =  [ (r - x)/2 ]   .
 *
 * Cancellation error in r-x or r+x is avoided by using the
 * identity  2 Re w Im w  =  y.
 *
 * Note that -w is also a square root of z.  The root chosen
 * is always in the right half plane and Im w has the same sign as y.
 *
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC       -10,+10     25000       3.2e-17     9.6e-18
 *    IEEE      -10,+10   1,000,000     2.9e-16     6.1e-17
 *
 */

#include <complex.h>
#include <float.h>
#include <math.h>

double complex
csqrt(double complex z)
{
        double complex w;
        double x, y, r, t, scale;

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

        if (y == 0.0) {
                if (x == 0.0) {
                        w = 0.0 + y * I;
                }
                else {
                        r = fabs (x);
                        r = sqrt (r);
                        if (x < 0.0) {
                                w = 0.0 + copysign(r, y) * I;
                        }
                        else {
                                w = r + y * I;
                        }
                }
                return (w);
        }
        if (x == 0.0) {
                r = fabs (y);
                r = sqrt (0.5*r);
                if (y > 0)
                        w = r + r * I;
                else
                        w = r - r * I;
                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 {
                x *= 1.8014398509481984e16;  /* 2^54 */
                y *= 1.8014398509481984e16;
                scale = 7.450580596923828125e-9; /* 2^-27 */
#if 0
                x *= 4.0;
                y *= 4.0;
                scale = 0.5;
#endif
        }
        w = x + y * I;
        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 = t - r * I;
        else
                w = t + r * I;
        return (w);
}
DEF_STD(csqrt);
LDBL_MAYBE_CLONE(csqrt);