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
44float complex
45csqrtf(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