s_csqrt.c revision 175225 
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: head/lib/msun/src/s_csqrt.c 175225 2008-01-11 04:18:25Z das $");
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
44/* We risk spurious overflow for components >= DBL_MAX / (1 + sqrt(2)). */
45#define	THRESH	0x1.a827999fcef32p+1022
46
47double complex
48csqrt(double complex z)
49{
50	double complex result;
51	double a, b;
52	double t;
53	int scale;
54
55	a = creal(z);
56	b = cimag(z);
57
58	/* Handle special cases. */
59	if (z == 0)
60		return (cpack(0, b));
61	if (isinf(b))
62		return (cpack(INFINITY, b));
63	if (isnan(a)) {
64		t = (b - b) / (b - b);	/* raise invalid if b is not a NaN */
65		return (cpack(a, t));	/* return NaN + NaN i */
66	}
67	if (isinf(a)) {
68		/*
69		 * csqrt(inf + NaN i)  = inf +  NaN i
70		 * csqrt(inf + y i)    = inf +  0 i
71		 * csqrt(-inf + NaN i) = NaN +- inf i
72		 * csqrt(-inf + y i)   = 0   +  inf i
73		 */
74		if (signbit(a))
75			return (cpack(fabs(b - b), copysign(a, b)));
76		else
77			return (cpack(a, copysign(b - b, b)));
78	}
79	/*
80	 * The remaining special case (b is NaN) is handled just fine by
81	 * the normal code path below.
82	 */
83
84	/* Scale to avoid overflow. */
85	if (fabs(a) >= THRESH || fabs(b) >= THRESH) {
86		a *= 0.25;
87		b *= 0.25;
88		scale = 1;
89	} else {
90		scale = 0;
91	}
92
93	/* Algorithm 312, CACM vol 10, Oct 1967. */
94	if (a >= 0) {
95		t = sqrt((a + hypot(a, b)) * 0.5);
96		result = cpack(t, b / (2 * t));
97	} else {
98		t = sqrt((-a + hypot(a, b)) * 0.5);
99		result = cpack(fabs(b) / (2 * t), copysign(t, b));
100	}
101
102	/* Rescale. */
103	if (scale)
104		return (result * 2);
105	else
106		return (result);
107}
108