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