1/*-
2 * Copyright (c) 2007-2008 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 <float.h>
32#include <math.h>
33
34#include "math_private.h"
35
36/*
37 * gcc doesn't implement complex multiplication or division correctly,
38 * so we need to handle infinities specially. We turn on this pragma to
39 * notify conforming c99 compilers that the fast-but-incorrect code that
40 * gcc generates is acceptable, since the special cases have already been
41 * handled.
42 */
43#pragma	STDC CX_LIMITED_RANGE	ON
44
45/* We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). */
46#define	THRESH	(LDBL_MAX / 2.414213562373095048801688724209698L)
47
48long double complex
49csqrtl(long double complex z)
50{
51	long double complex result;
52	long double a, b;
53	long double t;
54	int scale;
55
56	a = creall(z);
57	b = cimagl(z);
58
59	/* Handle special cases. */
60	if (z == 0)
61		return (cpackl(0, b));
62	if (isinf(b))
63		return (cpackl(INFINITY, b));
64	if (isnan(a)) {
65		t = (b - b) / (b - b);	/* raise invalid if b is not a NaN */
66		return (cpackl(a, t));	/* return NaN + NaN i */
67	}
68	if (isinf(a)) {
69		/*
70		 * csqrt(inf + NaN i)  = inf +  NaN i
71		 * csqrt(inf + y i)    = inf +  0 i
72		 * csqrt(-inf + NaN i) = NaN +- inf i
73		 * csqrt(-inf + y i)   = 0   +  inf i
74		 */
75		if (signbit(a))
76			return (cpackl(fabsl(b - b), copysignl(a, b)));
77		else
78			return (cpackl(a, copysignl(b - b, b)));
79	}
80	/*
81	 * The remaining special case (b is NaN) is handled just fine by
82	 * the normal code path below.
83	 */
84
85	/* Scale to avoid overflow. */
86	if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) {
87		a *= 0.25;
88		b *= 0.25;
89		scale = 1;
90	} else {
91		scale = 0;
92	}
93
94	/* Algorithm 312, CACM vol 10, Oct 1967. */
95	if (a >= 0) {
96		t = sqrtl((a + hypotl(a, b)) * 0.5);
97		result = cpackl(t, b / (2 * t));
98	} else {
99		t = sqrtl((-a + hypotl(a, b)) * 0.5);
100		result = cpackl(fabsl(b) / (2 * t), copysignl(t, b));
101	}
102
103	/* Rescale. */
104	if (scale)
105		return (result * 2);
106	else
107		return (result);
108}
109