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
35float complex
36csqrtf(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