xref: /freebsd/lib/msun/src/s_csqrtf.c (revision 2be1a816b9ff69588e55be0a84cbe2a31efc0f2f)
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
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