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      1 /* $NetBSD: csqrt.c,v 1.4 2017/01/01 19:32:14 maya Exp $ */
      2 
      3 /*-
      4  * Copyright (c) 2007 The NetBSD Foundation, Inc.
      5  * All rights reserved.
      6  *
      7  * This code is derived from software written by Stephen L. Moshier.
      8  * It is redistributed by the NetBSD Foundation by permission of the author.
      9  *
     10  * Redistribution and use in source and binary forms, with or without
     11  * modification, are permitted provided that the following conditions
     12  * are met:
     13  * 1. Redistributions of source code must retain the above copyright
     14  *    notice, this list of conditions and the following disclaimer.
     15  * 2. Redistributions in binary form must reproduce the above copyright
     16  *    notice, this list of conditions and the following disclaimer in the
     17  *    documentation and/or other materials provided with the distribution.
     18  *
     19  * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
     20  * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
     21  * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
     22  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
     23  * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
     24  * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
     25  * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
     26  * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
     27  * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
     28  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
     29  * POSSIBILITY OF SUCH DAMAGE.
     30  */
     31 
     32 #include <complex.h>
     33 #include <math.h>
     34 
     35 double complex
     36 csqrt(double complex z)
     37 {
     38 	double complex w;
     39 	double x, y, r, t, scale;
     40 
     41 	x = creal (z);
     42 	y = cimag (z);
     43 
     44 	/*
     45 	 * input is a real number and imaginary part isn't -0.0.
     46 	 * negative zero is on the branch cut.
     47 	 */
     48 	if ((y == 0.0) && !signbit(y)) {
     49 		if (x == 0.0) {
     50 			w = 0.0 + y * I;
     51 		} else {
     52 			if (x < 0.0) {
     53 				r = sqrt(-x);
     54 				w = 0.0 + r * I;
     55 			} else {
     56 				r = sqrt(x);
     57 				w = r;
     58 			}
     59 		}
     60 		return w;
     61 	}
     62 	if (x == 0.0) {
     63 		if (y > 0) {
     64 			r = sqrt(0.5 * y);
     65 			w = r + r * I;
     66 		} else {
     67 			r = sqrt(-0.5 * y);
     68 			w = r - r * I;
     69 		}
     70 		return w;
     71 	}
     72 	/* Rescale to avoid internal overflow or underflow.  */
     73 	if ((fabs(x) > 4.0) || (fabs(y) > 4.0)) {
     74 		x *= 0.25;
     75 		y *= 0.25;
     76 		scale = 2.0;
     77 	} else {
     78 #if 1
     79 		x *= 1.8014398509481984e16;  /* 2^54 */
     80 		y *= 1.8014398509481984e16;
     81 		scale = 7.450580596923828125e-9; /* 2^-27 */
     82 #else
     83 		x *= 4.0;
     84 		y *= 4.0;
     85 		scale = 0.5;
     86 #endif
     87 	}
     88 	w = x + y * I;
     89 	r = cabs(w);
     90 	if (x > 0) {
     91 		t = sqrt(0.5 * r + 0.5 * x);
     92 		r = scale * fabs((0.5 * y) / t );
     93 		t *= scale;
     94 	} else {
     95 		r = sqrt(0.5 * r - 0.5 * x);
     96 		t = scale * fabs((0.5 * y) / r);
     97 		r *= scale;
     98 	}
     99 	if (y > 0)
    100 		w = t + r * I;
    101 	else
    102 		w = t - r * I;
    103 	return w;
    104 }
    105