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      1 /* $NetBSD: csqrtf.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 float complex
     36 csqrtf(float complex z)
     37 {
     38 	float complex w;
     39 	float x, y, r, t, scale;
     40 
     41 	x = crealf (z);
     42 	y = cimagf (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 == 0.0f) && !signbit(y)) {
     49 		if (x < 0.0f) {
     50 			w = 0.0f + sqrtf(-x) * I;
     51 			return w;
     52 		} else if (x == 0.0f) {
     53 			return (0.0f + y * I);
     54 		} else {
     55 			w = sqrtf(x) + y * I;
     56 			return w;
     57 		}
     58 	}
     59 
     60 	if (x == 0.0f) {
     61 		if (y > 0) {
     62 			r = sqrtf(0.5f * y);
     63 			w = r + r * I;
     64 		} else {
     65 			r = sqrtf(-0.5f * y);
     66 			w = r - r * I;
     67 		}
     68 		return w;
     69 	}
     70 
     71 	/* Rescale to avoid internal overflow or underflow.  */
     72 	if ((fabsf(x) > 4.0f) || (fabsf(y) > 4.0f)) {
     73 		x *= 0.25f;
     74 		y *= 0.25f;
     75 		scale = 2.0f;
     76 	} else {
     77 #if 1
     78 		x *= 6.7108864e7f; /* 2^26 */
     79 		y *= 6.7108864e7f;
     80 		scale = 1.220703125e-4f; /* 2^-13 */
     81 #else
     82 		x *= 4.0f;
     83 		y *= 4.0f;
     84 		scale = 0.5f;
     85 #endif
     86 	}
     87 	w = x + y * I;
     88 	r = cabsf(w);
     89 	if( x > 0 ) {
     90 		t = sqrtf(0.5f * r + 0.5f * x);
     91 		r = scale * fabsf((0.5f * y) / t);
     92 		t *= scale;
     93 	} else {
     94 		r = sqrtf(0.5f * r - 0.5f * x);
     95 		t = scale * fabsf((0.5f * y) / r);
     96 		r *= scale;
     97 	}
     98 
     99 	if (y > 0)
    100 		w = t + r * I;
    101 	else
    102 		w = t - r * I;
    103 	return w;
    104 }
    105