1a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes/*-
2a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * Copyright (c) 2007-2008 David Schultz <das@FreeBSD.ORG>
3a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * All rights reserved.
4a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes *
5a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * Redistribution and use in source and binary forms, with or without
6a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * modification, are permitted provided that the following conditions
7a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * are met:
8a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * 1. Redistributions of source code must retain the above copyright
9a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes *    notice, this list of conditions and the following disclaimer.
10a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * 2. Redistributions in binary form must reproduce the above copyright
11a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes *    notice, this list of conditions and the following disclaimer in the
12a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes *    documentation and/or other materials provided with the distribution.
13a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes *
14a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
15a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
16a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
17a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
18a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
19a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
20a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
21a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
22a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
23a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
24a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * SUCH DAMAGE.
25a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes */
26a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes
27a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <sys/cdefs.h>
288cff2f95d8673b4b9002292d50ce8caa6efb98b6Elliott Hughes__FBSDID("$FreeBSD: head/lib/msun/src/s_csqrtl.c 275819 2014-12-16 09:21:56Z ed $");
29a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes
30a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <complex.h>
31a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <float.h>
32a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <math.h>
33a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes
34a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include "math_private.h"
35a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes
36a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes/*
37a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * gcc doesn't implement complex multiplication or division correctly,
38a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * so we need to handle infinities specially. We turn on this pragma to
39a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * notify conforming c99 compilers that the fast-but-incorrect code that
40a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * gcc generates is acceptable, since the special cases have already been
41a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * handled.
42a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes */
43a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#pragma	STDC CX_LIMITED_RANGE	ON
44a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes
45a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes/* We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). */
46a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#define	THRESH	(LDBL_MAX / 2.414213562373095048801688724209698L)
47a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes
48a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hugheslong double complex
49a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughescsqrtl(long double complex z)
50a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes{
51a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	long double complex result;
52a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	long double a, b;
53a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	long double t;
54a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	int scale;
55a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes
56a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	a = creall(z);
57a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	b = cimagl(z);
58a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes
59a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	/* Handle special cases. */
60a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	if (z == 0)
618cff2f95d8673b4b9002292d50ce8caa6efb98b6Elliott Hughes		return (CMPLXL(0, b));
62a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	if (isinf(b))
638cff2f95d8673b4b9002292d50ce8caa6efb98b6Elliott Hughes		return (CMPLXL(INFINITY, b));
64a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	if (isnan(a)) {
65a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes		t = (b - b) / (b - b);	/* raise invalid if b is not a NaN */
668cff2f95d8673b4b9002292d50ce8caa6efb98b6Elliott Hughes		return (CMPLXL(a, t));	/* return NaN + NaN i */
67a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	}
68a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	if (isinf(a)) {
69a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes		/*
70a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes		 * csqrt(inf + NaN i)  = inf +  NaN i
71a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes		 * csqrt(inf + y i)    = inf +  0 i
72a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes		 * csqrt(-inf + NaN i) = NaN +- inf i
73a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes		 * csqrt(-inf + y i)   = 0   +  inf i
74a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes		 */
75a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes		if (signbit(a))
768cff2f95d8673b4b9002292d50ce8caa6efb98b6Elliott Hughes			return (CMPLXL(fabsl(b - b), copysignl(a, b)));
77a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes		else
788cff2f95d8673b4b9002292d50ce8caa6efb98b6Elliott Hughes			return (CMPLXL(a, copysignl(b - b, b)));
79a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	}
80a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	/*
81a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	 * The remaining special case (b is NaN) is handled just fine by
82a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	 * the normal code path below.
83a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	 */
84a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes
85a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	/* Scale to avoid overflow. */
86a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) {
87a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes		a *= 0.25;
88a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes		b *= 0.25;
89a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes		scale = 1;
90a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	} else {
91a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes		scale = 0;
92a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	}
93a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes
94a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	/* Algorithm 312, CACM vol 10, Oct 1967. */
95a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	if (a >= 0) {
96a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes		t = sqrtl((a + hypotl(a, b)) * 0.5);
978cff2f95d8673b4b9002292d50ce8caa6efb98b6Elliott Hughes		result = CMPLXL(t, b / (2 * t));
98a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	} else {
99a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes		t = sqrtl((-a + hypotl(a, b)) * 0.5);
1008cff2f95d8673b4b9002292d50ce8caa6efb98b6Elliott Hughes		result = CMPLXL(fabsl(b) / (2 * t), copysignl(t, b));
101a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	}
102a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes
103a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	/* Rescale. */
104a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	if (scale)
105a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes		return (result * 2);
106a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes	else
107a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes		return (result);
108a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes}
109