s_csqrtf.c revision 330897 
1/*-
2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
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: stable/11/lib/msun/src/s_csqrtf.c 330897 2018-03-14 03:19:51Z eadler $");
31
32#include <complex.h>
33#include <math.h>
34
35#include "math_private.h"
36
37/*
38 * gcc doesn't implement complex multiplication or division correctly,
39 * so we need to handle infinities specially. We turn on this pragma to
40 * notify conforming c99 compilers that the fast-but-incorrect code that
41 * gcc generates is acceptable, since the special cases have already been
42 * handled.
43 */
44#pragma	STDC CX_LIMITED_RANGE	ON
45
46float complex
47csqrtf(float complex z)
48{
49	float a = crealf(z), b = cimagf(z);
50	double t;
51
52	/* Handle special cases. */
53	if (z == 0)
54		return (CMPLXF(0, b));
55	if (isinf(b))
56		return (CMPLXF(INFINITY, b));
57	if (isnan(a)) {
58		t = (b - b) / (b - b);	/* raise invalid if b is not a NaN */
59		return (CMPLXF(a, t));	/* return NaN + NaN i */
60	}
61	if (isinf(a)) {
62		/*
63		 * csqrtf(inf + NaN i)  = inf +  NaN i
64		 * csqrtf(inf + y i)    = inf +  0 i
65		 * csqrtf(-inf + NaN i) = NaN +- inf i
66		 * csqrtf(-inf + y i)   = 0   +  inf i
67		 */
68		if (signbit(a))
69			return (CMPLXF(fabsf(b - b), copysignf(a, b)));
70		else
71			return (CMPLXF(a, copysignf(b - b, b)));
72	}
73	/*
74	 * The remaining special case (b is NaN) is handled just fine by
75	 * the normal code path below.
76	 */
77
78	/*
79	 * We compute t in double precision to avoid overflow and to
80	 * provide correct rounding in nearly all cases.
81	 * This is Algorithm 312, CACM vol 10, Oct 1967.
82	 */
83	if (a >= 0) {
84		t = sqrt((a + hypot(a, b)) * 0.5);
85		return (CMPLXF(t, b / (2.0 * t)));
86	} else {
87		t = sqrt((-a + hypot(a, b)) * 0.5);
88		return (CMPLXF(fabsf(b) / (2.0 * t), copysignf(t, b)));
89	}
90}
91