xref: /netbsd-src/lib/libm/complex/csqrt.c (revision 038de09f8aa47838312935ff9eb6b911e6aa804c)
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
csqrt(double complex z)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