xref: /minix3/lib/libm/complex/csqrt.c (revision 2fe8fb192fe7e8720e3e7a77f928da545e872a6a)
1*2fe8fb19SBen Gras /* $NetBSD: csqrt.c,v 1.1 2007/08/20 16:01:37 drochner Exp $ */
2*2fe8fb19SBen Gras 
3*2fe8fb19SBen Gras /*-
4*2fe8fb19SBen Gras  * Copyright (c) 2007 The NetBSD Foundation, Inc.
5*2fe8fb19SBen Gras  * All rights reserved.
6*2fe8fb19SBen Gras  *
7*2fe8fb19SBen Gras  * This code is derived from software written by Stephen L. Moshier.
8*2fe8fb19SBen Gras  * It is redistributed by the NetBSD Foundation by permission of the author.
9*2fe8fb19SBen Gras  *
10*2fe8fb19SBen Gras  * Redistribution and use in source and binary forms, with or without
11*2fe8fb19SBen Gras  * modification, are permitted provided that the following conditions
12*2fe8fb19SBen Gras  * are met:
13*2fe8fb19SBen Gras  * 1. Redistributions of source code must retain the above copyright
14*2fe8fb19SBen Gras  *    notice, this list of conditions and the following disclaimer.
15*2fe8fb19SBen Gras  * 2. Redistributions in binary form must reproduce the above copyright
16*2fe8fb19SBen Gras  *    notice, this list of conditions and the following disclaimer in the
17*2fe8fb19SBen Gras  *    documentation and/or other materials provided with the distribution.
18*2fe8fb19SBen Gras  *
19*2fe8fb19SBen Gras  * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
20*2fe8fb19SBen Gras  * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
21*2fe8fb19SBen Gras  * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
22*2fe8fb19SBen Gras  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
23*2fe8fb19SBen Gras  * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
24*2fe8fb19SBen Gras  * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
25*2fe8fb19SBen Gras  * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
26*2fe8fb19SBen Gras  * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
27*2fe8fb19SBen Gras  * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
28*2fe8fb19SBen Gras  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
29*2fe8fb19SBen Gras  * POSSIBILITY OF SUCH DAMAGE.
30*2fe8fb19SBen Gras  */
31*2fe8fb19SBen Gras 
32*2fe8fb19SBen Gras #include <complex.h>
33*2fe8fb19SBen Gras #include <math.h>
34*2fe8fb19SBen Gras 
35*2fe8fb19SBen Gras double complex
csqrt(double complex z)36*2fe8fb19SBen Gras csqrt(double complex z)
37*2fe8fb19SBen Gras {
38*2fe8fb19SBen Gras 	double complex w;
39*2fe8fb19SBen Gras 	double x, y, r, t, scale;
40*2fe8fb19SBen Gras 
41*2fe8fb19SBen Gras 	x = creal (z);
42*2fe8fb19SBen Gras 	y = cimag (z);
43*2fe8fb19SBen Gras 
44*2fe8fb19SBen Gras 	if (y == 0.0) {
45*2fe8fb19SBen Gras 		if (x == 0.0) {
46*2fe8fb19SBen Gras 			w = 0.0 + y * I;
47*2fe8fb19SBen Gras 		} else {
48*2fe8fb19SBen Gras 			r = fabs(x);
49*2fe8fb19SBen Gras 			r = sqrt(r);
50*2fe8fb19SBen Gras 			if (x < 0.0) {
51*2fe8fb19SBen Gras 				w = 0.0 + r * I;
52*2fe8fb19SBen Gras 			} else {
53*2fe8fb19SBen Gras 				w = r + y * I;
54*2fe8fb19SBen Gras 			}
55*2fe8fb19SBen Gras 		}
56*2fe8fb19SBen Gras 		return w;
57*2fe8fb19SBen Gras 	}
58*2fe8fb19SBen Gras 	if (x == 0.0) {
59*2fe8fb19SBen Gras 		r = fabs(y);
60*2fe8fb19SBen Gras 		r = sqrt(0.5 * r);
61*2fe8fb19SBen Gras 		if (y > 0)
62*2fe8fb19SBen Gras 			w = r + r * I;
63*2fe8fb19SBen Gras 		else
64*2fe8fb19SBen Gras 			w = r - r * I;
65*2fe8fb19SBen Gras 		return w;
66*2fe8fb19SBen Gras 	}
67*2fe8fb19SBen Gras 	/* Rescale to avoid internal overflow or underflow.  */
68*2fe8fb19SBen Gras 	if ((fabs(x) > 4.0) || (fabs(y) > 4.0)) {
69*2fe8fb19SBen Gras 		x *= 0.25;
70*2fe8fb19SBen Gras 		y *= 0.25;
71*2fe8fb19SBen Gras 		scale = 2.0;
72*2fe8fb19SBen Gras 	} else {
73*2fe8fb19SBen Gras #if 1
74*2fe8fb19SBen Gras 		x *= 1.8014398509481984e16;  /* 2^54 */
75*2fe8fb19SBen Gras 		y *= 1.8014398509481984e16;
76*2fe8fb19SBen Gras 		scale = 7.450580596923828125e-9; /* 2^-27 */
77*2fe8fb19SBen Gras #else
78*2fe8fb19SBen Gras 		x *= 4.0;
79*2fe8fb19SBen Gras 		y *= 4.0;
80*2fe8fb19SBen Gras 		scale = 0.5;
81*2fe8fb19SBen Gras #endif
82*2fe8fb19SBen Gras 	}
83*2fe8fb19SBen Gras 	w = x + y * I;
84*2fe8fb19SBen Gras 	r = cabs(w);
85*2fe8fb19SBen Gras 	if (x > 0) {
86*2fe8fb19SBen Gras 		t = sqrt(0.5 * r + 0.5 * x);
87*2fe8fb19SBen Gras 		r = scale * fabs((0.5 * y) / t );
88*2fe8fb19SBen Gras 		t *= scale;
89*2fe8fb19SBen Gras 	} else {
90*2fe8fb19SBen Gras 		r = sqrt(0.5 * r - 0.5 * x);
91*2fe8fb19SBen Gras 		t = scale * fabs((0.5 * y) / r);
92*2fe8fb19SBen Gras 		r *= scale;
93*2fe8fb19SBen Gras 	}
94*2fe8fb19SBen Gras 	if (y < 0)
95*2fe8fb19SBen Gras 		w = t - r * I;
96*2fe8fb19SBen Gras 	else
97*2fe8fb19SBen Gras 		w = t + r * I;
98*2fe8fb19SBen Gras 	return w;
99*2fe8fb19SBen Gras }
100