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("$FreeBSD$");
31
32#include <complex.h>
33#include <float.h>
34#include <math.h>
35
36#include "math_private.h"
37
38/* For avoiding overflow for components >= DBL_MAX / (1 + sqrt(2)). */
39#define	THRESH	0x1.a827999fcef32p+1022
40
41double complex
42csqrt(double complex z)
43{
44	double complex result;
45	double a, b, rx, ry, scale, t;
46
47	a = creal(z);
48	b = cimag(z);
49
50	/* Handle special cases. */
51	if (z == 0)
52		return (CMPLX(0, b));
53	if (isinf(b))
54		return (CMPLX(INFINITY, b));
55	if (isnan(a)) {
56		t = (b - b) / (b - b);	/* raise invalid if b is not a NaN */
57		return (CMPLX(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */
58	}
59	if (isinf(a)) {
60		/*
61		 * csqrt(inf + NaN i)  = inf +  NaN i
62		 * csqrt(inf + y i)    = inf +  0 i
63		 * csqrt(-inf + NaN i) = NaN +- inf i
64		 * csqrt(-inf + y i)   = 0   +  inf i
65		 */
66		if (signbit(a))
67			return (CMPLX(fabs(b - b), copysign(a, b)));
68		else
69			return (CMPLX(a, copysign(b - b, b)));
70	}
71	if (isnan(b)) {
72		t = (a - a) / (a - a);	/* raise invalid */
73		return (CMPLX(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */
74	}
75
76	/* Scale to avoid overflow. */
77	if (fabs(a) >= THRESH || fabs(b) >= THRESH) {
78		/*
79		 * Don't scale a or b if this might give (spurious)
80		 * underflow.  Then the unscaled value is an equivalent
81		 * infinitesmal (or 0).
82		 */
83		if (fabs(a) >= 0x1p-1020)
84			a *= 0.25;
85		if (fabs(b) >= 0x1p-1020)
86			b *= 0.25;
87		scale = 2;
88	} else {
89		scale = 1;
90	}
91
92	/* Scale to reduce inaccuracies when both components are denormal. */
93	if (fabs(a) < 0x1p-1022 && fabs(b) < 0x1p-1022) {
94		a *= 0x1p54;
95		b *= 0x1p54;
96		scale = 0x1p-27;
97	}
98
99	/* Algorithm 312, CACM vol 10, Oct 1967. */
100	if (a >= 0) {
101		t = sqrt((a + hypot(a, b)) * 0.5);
102		rx = scale * t;
103		ry = scale * b / (2 * t);
104	} else {
105		t = sqrt((-a + hypot(a, b)) * 0.5);
106		rx = scale * fabs(b) / (2 * t);
107		ry = copysign(scale * t, b);
108	}
109
110	return (CMPLX(rx, ry));
111}
112
113#if LDBL_MANT_DIG == 53
114__weak_reference(csqrt, csqrtl);
115#endif
116