1 /*-
2 * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG>
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
13 *
14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
24 * SUCH DAMAGE.
25 */
26
27 #include <sys/cdefs.h>
28 __FBSDID("$FreeBSD$");
29
30 #include <complex.h>
31 #include <math.h>
32
33 #include "math_private.h"
34
35 /*
36 * gcc doesn't implement complex multiplication or division correctly,
37 * so we need to handle infinities specially. We turn on this pragma to
38 * notify conforming c99 compilers that the fast-but-incorrect code that
39 * gcc generates is acceptable, since the special cases have already been
40 * handled.
41 */
42 #pragma STDC CX_LIMITED_RANGE ON
43
44 float complex
csqrtf(float complex z)45 csqrtf(float complex z)
46 {
47 float a = crealf(z), b = cimagf(z);
48 double t;
49
50 /* Handle special cases. */
51 if (z == 0)
52 return (cpackf(0, b));
53 if (isinf(b))
54 return (cpackf(INFINITY, b));
55 if (isnan(a)) {
56 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
57 return (cpackf(a, t)); /* return NaN + NaN i */
58 }
59 if (isinf(a)) {
60 /*
61 * csqrtf(inf + NaN i) = inf + NaN i
62 * csqrtf(inf + y i) = inf + 0 i
63 * csqrtf(-inf + NaN i) = NaN +- inf i
64 * csqrtf(-inf + y i) = 0 + inf i
65 */
66 if (signbit(a))
67 return (cpackf(fabsf(b - b), copysignf(a, b)));
68 else
69 return (cpackf(a, copysignf(b - b, b)));
70 }
71 /*
72 * The remaining special case (b is NaN) is handled just fine by
73 * the normal code path below.
74 */
75
76 /*
77 * We compute t in double precision to avoid overflow and to
78 * provide correct rounding in nearly all cases.
79 * This is Algorithm 312, CACM vol 10, Oct 1967.
80 */
81 if (a >= 0) {
82 t = sqrt((a + hypot(a, b)) * 0.5);
83 return (cpackf(t, b / (2.0 * t)));
84 } else {
85 t = sqrt((-a + hypot(a, b)) * 0.5);
86 return (cpackf(fabsf(b) / (2.0 * t), copysignf(t, b)));
87 }
88 }
89