1*2fe8fb19SBen Gras /* $NetBSD: csqrtf.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 float complex
csqrtf(float complex z)36*2fe8fb19SBen Gras csqrtf(float complex z)
37*2fe8fb19SBen Gras {
38*2fe8fb19SBen Gras float complex w;
39*2fe8fb19SBen Gras float x, y, r, t, scale;
40*2fe8fb19SBen Gras
41*2fe8fb19SBen Gras x = crealf (z);
42*2fe8fb19SBen Gras y = cimagf (z);
43*2fe8fb19SBen Gras
44*2fe8fb19SBen Gras if (y == 0.0f) {
45*2fe8fb19SBen Gras if (x < 0.0f) {
46*2fe8fb19SBen Gras w = 0.0f + sqrtf(-x) * I;
47*2fe8fb19SBen Gras return w;
48*2fe8fb19SBen Gras } else if (x == 0.0f) {
49*2fe8fb19SBen Gras return (0.0f + y * I);
50*2fe8fb19SBen Gras } else {
51*2fe8fb19SBen Gras w = sqrtf(x) + y * I;
52*2fe8fb19SBen Gras return w;
53*2fe8fb19SBen Gras }
54*2fe8fb19SBen Gras }
55*2fe8fb19SBen Gras
56*2fe8fb19SBen Gras if (x == 0.0f) {
57*2fe8fb19SBen Gras r = fabsf(y);
58*2fe8fb19SBen Gras r = sqrtf(0.5f * r);
59*2fe8fb19SBen Gras if (y > 0)
60*2fe8fb19SBen Gras w = r + r * I;
61*2fe8fb19SBen Gras else
62*2fe8fb19SBen Gras w = r - r * I;
63*2fe8fb19SBen Gras return w;
64*2fe8fb19SBen Gras }
65*2fe8fb19SBen Gras
66*2fe8fb19SBen Gras /* Rescale to avoid internal overflow or underflow. */
67*2fe8fb19SBen Gras if ((fabsf(x) > 4.0f) || (fabsf(y) > 4.0f)) {
68*2fe8fb19SBen Gras x *= 0.25f;
69*2fe8fb19SBen Gras y *= 0.25f;
70*2fe8fb19SBen Gras scale = 2.0f;
71*2fe8fb19SBen Gras } else {
72*2fe8fb19SBen Gras #if 1
73*2fe8fb19SBen Gras x *= 6.7108864e7f; /* 2^26 */
74*2fe8fb19SBen Gras y *= 6.7108864e7f;
75*2fe8fb19SBen Gras scale = 1.220703125e-4f; /* 2^-13 */
76*2fe8fb19SBen Gras #else
77*2fe8fb19SBen Gras x *= 4.0f;
78*2fe8fb19SBen Gras y *= 4.0f;
79*2fe8fb19SBen Gras scale = 0.5f;
80*2fe8fb19SBen Gras #endif
81*2fe8fb19SBen Gras }
82*2fe8fb19SBen Gras w = x + y * I;
83*2fe8fb19SBen Gras r = cabsf(w);
84*2fe8fb19SBen Gras if( x > 0 ) {
85*2fe8fb19SBen Gras t = sqrtf(0.5f * r + 0.5f * x);
86*2fe8fb19SBen Gras r = scale * fabsf((0.5f * y) / t);
87*2fe8fb19SBen Gras t *= scale;
88*2fe8fb19SBen Gras } else {
89*2fe8fb19SBen Gras r = sqrtf(0.5f * r - 0.5f * x);
90*2fe8fb19SBen Gras t = scale * fabsf((0.5f * y) / r);
91*2fe8fb19SBen Gras r *= scale;
92*2fe8fb19SBen Gras }
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