1/*-
2 * SPDX-License-Identifier: BSD-2-Clause
3 *
4 * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG>
5 * All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 *    notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 *    notice, this list of conditions and the following disclaimer in the
14 *    documentation and/or other materials provided with the distribution.
15 *
16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
17 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
18 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
19 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
20 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
21 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
22 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
23 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
24 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
25 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
26 * SUCH DAMAGE.
27 */
28
29#include <complex.h>
30#include <math.h>
31
32#include "math_private.h"
33
34float complex
35csqrtf(float complex z)
36{
37	double t;
38	float a, b;
39
40	a = creal(z);
41	b = cimag(z);
42
43	/* Handle special cases. */
44	if (z == 0)
45		return (CMPLXF(0, b));
46	if (isinf(b))
47		return (CMPLXF(INFINITY, b));
48	if (isnan(a)) {
49		t = (b - b) / (b - b);	/* raise invalid if b is not a NaN */
50		return (CMPLXF(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */
51	}
52	if (isinf(a)) {
53		/*
54		 * csqrtf(inf + NaN i)  = inf +  NaN i
55		 * csqrtf(inf + y i)    = inf +  0 i
56		 * csqrtf(-inf + NaN i) = NaN +- inf i
57		 * csqrtf(-inf + y i)   = 0   +  inf i
58		 */
59		if (signbit(a))
60			return (CMPLXF(fabsf(b - b), copysignf(a, b)));
61		else
62			return (CMPLXF(a, copysignf(b - b, b)));
63	}
64	if (isnan(b)) {
65		t = (a - a) / (a - a);	/* raise invalid */
66		return (CMPLXF(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */
67	}
68
69	/*
70	 * We compute t in double precision to avoid overflow and to
71	 * provide correct rounding in nearly all cases.
72	 * This is Algorithm 312, CACM vol 10, Oct 1967.
73	 */
74	if (a >= 0) {
75		t = sqrt((a + hypot(a, b)) * 0.5);
76		return (CMPLXF(t, b / (2 * t)));
77	} else {
78		t = sqrt((-a + hypot(a, b)) * 0.5);
79		return (CMPLXF(fabsf(b) / (2 * t), copysignf(t, b)));
80	}
81}
82