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#if 0
29__FBSDID("$FreeBSD: head/lib/msun/src/s_csqrtl.c 181402 2008-08-08 00:15:16Z das $");
30#else
31__RCSID("$NetBSD: csqrtl.c,v 1.1 2014/10/10 00:48:18 christos Exp $");
32#endif
33
34#include "../src/namespace.h"
35#include <complex.h>
36#include <float.h>
37#include <math.h>
38#include <stdbool.h>
39
40/*
41 * gcc doesn't implement complex multiplication or division correctly,
42 * so we need to handle infinities specially. We turn on this pragma to
43 * notify conforming c99 compilers that the fast-but-incorrect code that
44 * gcc generates is acceptable, since the special cases have already been
45 * handled.
46 */
47// #pragma	STDC CX_LIMITED_RANGE	ON
48
49/* We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). */
50#define	THRESH	(LDBL_MAX / 2.414213562373095048801688724209698L)
51
52#define cpackl(r, i) ((r) + (i) * I)
53
54long double complex
55csqrtl(long double complex z)
56{
57	long double complex result;
58	long double a, b;
59	long double t;
60	bool scale;
61
62	a = creall(z);
63	b = cimagl(z);
64
65	/* Handle special cases. */
66	if (z == 0.0L)
67		return (cpackl(0.0L, b));
68	if (isinf(b))
69		return (cpackl(INFINITY, b));
70	if (isnan(a)) {
71		t = (b - b) / (b - b);	/* raise invalid if b is not a NaN */
72		return (cpackl(a, t));	/* return NaN + NaN i */
73	}
74	if (isinf(a)) {
75		/*
76		 * csqrt(inf + NaN i)  = inf +  NaN i
77		 * csqrt(inf + y i)    = inf +  0 i
78		 * csqrt(-inf + NaN i) = NaN +- inf i
79		 * csqrt(-inf + y i)   = 0   +  inf i
80		 */
81		if (signbit(a))
82			return (cpackl(fabsl(b - b), copysignl(a, b)));
83		else
84			return (cpackl(a, copysignl(b - b, b)));
85	}
86	/*
87	 * The remaining special case (b is NaN) is handled just fine by
88	 * the normal code path below.
89	 */
90
91	/* Scale to avoid overflow. */
92	if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) {
93		a *= 0.25L;
94		b *= 0.25L;
95		scale = true;
96	} else {
97		scale = false;
98	}
99
100	/* Algorithm 312, CACM vol 10, Oct 1967. */
101	if (a >= 0L) {
102		t = sqrtl((a + hypotl(a, b)) * 0.5L);
103		result = cpackl(t, b / (2.0L * t));
104	} else {
105		t = sqrtl((-a + hypotl(a, b)) * 0.5L);
106		result = cpackl(fabsl(b) / (2.0L * t), copysignl(t, b));
107	}
108
109	/* Rescale. */
110	if (scale)
111		return (result * 2.0L);
112	else
113		return (result);
114}
115