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 <sys/cdefs.h>
30 __FBSDID("$FreeBSD$");
31
32 #include <complex.h>
33 #include <math.h>
34
35 #include "math_private.h"
36
37 float complex
csqrtf(float complex z)38 csqrtf(float complex z)
39 {
40 double t;
41 float a, b;
42
43 a = creal(z);
44 b = cimag(z);
45
46 /* Handle special cases. */
47 if (z == 0)
48 return (CMPLXF(0, b));
49 if (isinf(b))
50 return (CMPLXF(INFINITY, b));
51 if (isnan(a)) {
52 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
53 return (CMPLXF(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */
54 }
55 if (isinf(a)) {
56 /*
57 * csqrtf(inf + NaN i) = inf + NaN i
58 * csqrtf(inf + y i) = inf + 0 i
59 * csqrtf(-inf + NaN i) = NaN +- inf i
60 * csqrtf(-inf + y i) = 0 + inf i
61 */
62 if (signbit(a))
63 return (CMPLXF(fabsf(b - b), copysignf(a, b)));
64 else
65 return (CMPLXF(a, copysignf(b - b, b)));
66 }
67 if (isnan(b)) {
68 t = (a - a) / (a - a); /* raise invalid */
69 return (CMPLXF(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */
70 }
71
72 /*
73 * We compute t in double precision to avoid overflow and to
74 * provide correct rounding in nearly all cases.
75 * This is Algorithm 312, CACM vol 10, Oct 1967.
76 */
77 if (a >= 0) {
78 t = sqrt((a + hypot(a, b)) * 0.5);
79 return (CMPLXF(t, b / (2 * t)));
80 } else {
81 t = sqrt((-a + hypot(a, b)) * 0.5);
82 return (CMPLXF(fabsf(b) / (2 * t), copysignf(t, b)));
83 }
84 }
85