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csqrtf.c revision 1.2 
      1 /* $NetBSD: csqrtf.c,v 1.2 2016/12/31 20:01:15 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 	/* Input is a real number that isn't on the branch cut */
     45 	if ((y == 0.0f) && !signbit(y)) {
     46 		if (x < 0.0f) {
     47 			w = 0.0f + sqrtf(-x) * I;
     48 			return w;
     49 		} else if (x == 0.0f) {
     50 			return (0.0f + y * I);
     51 		} else {
     52 			w = sqrtf(x) + y * I;
     53 			return w;
     54 		}
     55 	}
     56 
     57 	if (x == 0.0f) {
     58 		r = fabsf(y);
     59 		r = sqrtf(0.5f * r);
     60 		if (y > 0)
     61 			w = r + r * I;
     62 		else
     63 			w = r - r * I;
     64 		return w;
     65 	}
     66 
     67 	/* Rescale to avoid internal overflow or underflow.  */
     68 	if ((fabsf(x) > 4.0f) || (fabsf(y) > 4.0f)) {
     69 		x *= 0.25f;
     70 		y *= 0.25f;
     71 		scale = 2.0f;
     72 	} else {
     73 #if 1
     74 		x *= 6.7108864e7f; /* 2^26 */
     75 		y *= 6.7108864e7f;
     76 		scale = 1.220703125e-4f; /* 2^-13 */
     77 #else
     78 		x *= 4.0f;
     79 		y *= 4.0f;
     80 		scale = 0.5f;
     81 #endif
     82 	}
     83 	w = x + y * I;
     84 	r = cabsf(w);
     85 	if( x > 0 ) {
     86 		t = sqrtf(0.5f * r + 0.5f * x);
     87 		r = scale * fabsf((0.5f * y) / t);
     88 		t *= scale;
     89 	} else {
     90 		r = sqrtf(0.5f * r - 0.5f * x);
     91 		t = scale * fabsf((0.5f * y) / r);
     92 		r *= scale;
     93 	}
     94 
     95 	if (signbit(y))
     96 		w = t - r * I;
     97 	else
     98 		w = t + r * I;
     99 	return w;
    100 }
    101